ncert solutions for class 11 maths

NCERT Solutions for Class 11 Maths consist of solved answers for all the chapters, exercise-wise. This is a great material for students who are preparing for Class 11 exams. The solutions provided here are with respect to the NCERT syllabus and curriculum. These materials are prepared by our experts keeping in mind students understanding level.
Class 11 Maths NCERT Solutions

NCERT solutions for 11th standard Maths subject covers the chapters which are present in the textbook, exercise-wise. The chapters covered here are Sets, Trigonometric functions, sequences and series, Three-dimensional geometry, Relations and Functions, statistics, binomial theorem, probability, etc. The solutions for these chapters are available in PDF format, which students can download easily and learn them at per their convenience.

NCERT Solutions for Class 11 Maths Chapter 16 Probability

Probability Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. NCERT Solutions for Class 11 Maths Chapter 16 Probability All Exercises were prepared by Experienced LearnCBSE.in Teachers.

Free download NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1, Ex 16.2, Ex 16.3, and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, https://www.learncbse.in/ncert-solutions-for-class-11th-maths-chapter-16-probability/Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

  • Probability Class 11 Ex 16.1
  • Probability Class 11 Ex 16.2
  • Probability Class 11 Ex 16.3
  • Probability Class 11 Miscellaneous Exercise
  • प्रायिकता प्रश्नावली 16.1 का हल हिंदी में
  • प्रायिकता प्रश्नावली 16.2 का हल हिंदी में
  • प्रायिकता प्रश्नावली 16.3 का हल हिंदी में
  • प्रायिकता विविध प्रश्नावली का हल हिंदी में

Topics and Sub Topics in Class 11 Maths Chapter 16 Probability:

Section NameTopic Name
16Probability
16.1Introduction
16.2Random Experiments
16.3Event
16.4Axiomatic Approach to Probability

NCERT Solutions for Class 11 Maths Chapter 16 Exercise.16.1

Ex 16.1 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q1.1

Ex 16.1 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q2.1

NCERT Solutions For Class 11 Maths(Download PDF)

More Resources for CBSE Class 11

Ex 16.1 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q3.1

Ex 16.1 Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q4.1

Ex 16.1 Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q5.1

Ex 16.1 Class 11 Maths Question-6
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q6.1

Ex 16.1 Class 11 Maths Question-7
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q7.1

Ex 16.1 Class 11 Maths Question-8
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q8
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q8.1

Ex 16.1 Class 11 Maths Question-9
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q9
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q9.1

Ex 16.1 Class 11 Maths Question-10
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q10
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q10.1

Ex 16.1 Class 11 Maths Question-11
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q11
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q11.1

Ex 16.1 Class 11 Maths Question-12
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q12
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q12.1

Ex 16.1 Class 11 Maths Question-13
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q13
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q13.1

Ex 16.1 Class 11 Maths Question-14
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q14
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q14.1

Ex 16.1 Class 11 Maths Question-15
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q15
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q15.1

Ex 16.1 Class 11 Maths Question-16
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q16
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1 Q16.1

NCERT Solutions for Class 11 Maths Chapter 16 Probability (प्रायिकता) Hindi Medium Ex 16.1

NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1 all question answers
NCERT Solutions for Class 11 Maths Chapter 16 Probability (प्रायिकता)
NCERT Solutions for Class 11 Maths Chapter 16 Probability Exercise 16.1 in Hindi Medium
NCERT Solutions for Class 11 Maths Chapter 16 Probability Exercise 16.1
NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1
NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1 in pdf form
NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1 free download

NCERT Solutions for Class 11 Maths Chapter 16 Exercise.16.2

Ex 16.2 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q1.1

Ex 16.2 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q2.1

Ex 16.2 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q3.1

Ex 16.2 Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q4.1

Ex 16.2 Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q5.1

NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q5.2
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q5.3

Ex 16.2 Class 11 Maths Question-6
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q6.1

NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q6.2

Ex 16.2 Class 11 Maths Question-7
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q7.1

NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.2 Q7.2

NCERT Solutions for Class 11 Maths Chapter 16 Exercise.16.3

Ex 16.3 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q1.1

NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q1.2

Ex 16.3 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q2.1

Ex 16.3 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q3.1

Ex 16.3 Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q4.1

Ex 16.3 Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q5.1

Ex 16.3 Class 11 Maths Question-6
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q6.1

Ex 16.3 Class 11 Maths Question-7
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q7.1

NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q7.2

Ex 16.3 Class 11 Maths Question-8
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q8
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q8.1

NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q8.2
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q8.3

Ex 16.3 Class 11 Maths Question-9
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q9
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q9.1

Ex 16.3 Class 11 Maths Question-10
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q10
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q10.1

Ex 16.3 Class 11 Maths Question-11
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q11
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q11.1

Ex 16.3 Class 11 Maths Question-12
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q12
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q12.1

Ex 16.3 Class 11 Maths Question-13
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q13
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q13.1

Ex 16.3 Class 11 Maths Question-14
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q14
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q14.1

Ex 16.3 Class 11 Maths Question-15
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q15
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q15.1

Ex 16.3 Class 11 Maths Question-16
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q16
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q16.1

Ex 16.3 Class 11 Maths Question-17
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q17
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q17.1

Ex 16.3 Class 11 Maths Question-18
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q18
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q18.1

Ex 16.3 Class 11 Maths Question-19
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q19
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q19.1

Ex 16.3 Class 11 Maths Question-20
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q20
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q20.1

Ex 16.3 Class 11 Maths Question-21
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q21
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q21.1

NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.3 Q21.2

Class 11 Maths NCERT Solutions – Miscellaneous Questions

Miscellaneous Exercise Class 11 Maths Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q1.1

Miscellaneous Exercise Class 11 MathsQuestion-2
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q2.1

Miscellaneous Exercise Class 11 MathsQuestion-3
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q3.1

Miscellaneous Exercise Class 11 MathsQuestion-4
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q4.1

Miscellaneous Exercise Class 11 MathsQuestion-5
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q5.1

Miscellaneous Exercise Class 11 MathsQuestion-6
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q6.1

Miscellaneous Exercise Class 11 MathsQuestion-7
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q7.1

Miscellaneous Exercise Class 11 MathsQuestion-8
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q8
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q8.1

Miscellaneous Exercise Class 11 Maths Question-9
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q9
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q9.1

NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q9.2

Miscellaneous Exercise Class 11 MathsQuestion-10
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q10
Ans.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Miscellaneous Ex Q10.1

Exercise 16.1

Question 1

Write the sample space when a coin is tossed thrice.

Question 2

Write the sample space when a dice is rolled twice.

Question 3

Write the sample space when a coin is tossed four times.

Question 4

Find the sample space of a coin and a die are tossed together.

Question 5

Find the sample space when a die is rolled and a coin is tossed only if in case there is head in the coin.

Question 6

Room x is having 2 girls and 2 boys while Room y is having 3 girls and 1 boy. Determine the sample space where a person gets a room.

Question 7

A bag contains dies of several colors such as red, white and blue. Dies are selected as random and rolled and the colour and the number in it’s uppermost face is noted down.  Determine the sample space.

Question 8

An experimental setup consists of a family consisting a boy and a girl with 2 children.

(i) Determine the sample space if the person conducting the experiment is interested in knowing whether it is a boy or a girl according to the order of their birth.

(ii) Determine the sample space  if the person conducting the experiment is interested in knowing the number of girls in the family?

Question 9

A experimental setup consists of a box containing 1 red ball and 3 identical white balls. At a time 2 balls are drawn at random in succession without replacement. Find the sample space of the experimental setup.

Question 10

An experimental setup consists of tossing up of a coin in the air and if head comes up it is tossed again. If a tail occurs in the first event then a die is rolled only once. Find the sample space of the  experiment.

Question 11

3 bulbs are selected at a random from a bag of bulbs. Depending upon several tests each bulb is termed as defective  or non-defective . Determine the sample space of this series of events.

Question 12

An experiment consists of tossing a coin. During the conduction of the experiment if head comes up then a die is thrown instantly , if there is any even number on the die then it is thrown again . determine the sample space of the experiment.

Question 13

A box containing 4 slips of paper written 1,2,3 and 4 separately. They are then mixed thoroughly and drawn one at a time twice without replacement. Determine the sample space of the experiment

Question 14

An experiment consists of rolling a die then tossing a coin if any even number comes up while rolling the die. Also it was noted that if any odd number comes up the coin is tossed twice. Determine the sample space of the experiment.

Question 15

A coin is tossed if tail comes up a ball is drawn from a box containing 3 black balls and 2 red balls . A die is thrown is head comes up. Determine the sample space of the experiment.

Question 16

A die is rolled continuously unless and until a six shows up. Determine the sample space for this experiment.

Exercise 16.2

Question 1

An experiment consists of rolling of a die .Event E denotes that the die shows 4 and event F denotes that the die shows even number.

Are these both events that is A and B mutually exclusive?

Question 2

An experiment consists of a die thrown in which the following events occurred:

(a) P : numbers less than 7

(b) Q : numbers larger than 7

(c) R : numbers which are product of 3

(d) S : numbers which are smaller than 4

(e) T : even numbers which are larger than 4

(f) U : numbers not less than 3

Also, P∪Q ,  P∩Q , Q∪R , T∩U ,

S∩T , P – R , S – T ,

Question 3

An experiment consists throwing of a pair of dice and noting down the numbers that came up. Determine the following events:

(i) The sum of numbers is larger than 8

(ii) 2 occur on both of the die.

(iii) The sum of numbers is at least 7 and a multiple of 3.

Determine the events which are mutually exclusive?

Question 4

In an experiment 3 coins at a time .Let P be the event in which there 3 heads. Q be the event  in which there is 2 heads and 1 tail  and R be the  event in  which there is 3 tails and S denotes the event in which head shows in the first coin. Find the events:

(a) Mutually exclusive?

(b) Simple?

(c) Compound?

Question 5

In an experiment 3 coins are tossed.

(a) 2 events which are mutually exclusive.

(b) 3 events which are mutually exhaustive and exclusive.

(c) 2 events, which are not mutually exclusive.

(d) 2 events which are mutually exclusive but not exhaustive.

(e) 3 events which are mutually exclusive but not exhaustive.

Question 6

An experiment consists of throwing up of a dice and includes events A,B and C:

A = an even number on throwing of the first die

B = an odd number on throwing of the first die

C = sum of numbers on the dice will less than equals to 5.

(a) A     (b) not B       (c) A or B     (d) A and B

(e) A but not C     (f) B or C     (g) B or C    (h) A∩B′∩C′

Question 7

An experiment consists of throwing up of a dice and includes A, B and C.

A = an even number on throwing of the first die

B = an odd number on throwing of the first die

C = sum of numbers on the dice will less than equals to 5.

Give answer in true or false.

(a) B and A are mutually exclusive events.

(b) B and A are mutually exclusive and exhaustive events.

(c) A = B’

(d) A and C are mutually exclusive and exhaustive events.

(e) B’ and A are mutually exclusive events.

 (f) A’ , B’ & C are mutually exhaustive and exclusive.

Exercise 16.3

Question 2

An experiment consists of tossing up of a coin, determine the probability of getting at least one tail?

Question 3

An experiment consists of throwing of a dice in which the following events occurs:

(a) A prime number

(b) Number larger than 3

(c) Number less than or equal to 1

(d) Number more than 6

(e) Number less than 6

Question 4

An experiment consists of a pack of 52 cards.

(a) Find the number of elements present in the sample space.

(b) Find the probability of ace of spades

(c) Find the probability of (i) an ace (ii) black card

Question 5

An unbiased coin is marked 1 on one face while 6 on the other face , while the die is having markings such as 1,2,3,4,5,6 on its 6 faces .

Determine the probability that the sum of the numbers turning up is

(i) 3

(ii) 12

Question 6

A city council consists of 4 men and 6 women .Find the probability of selecting a woman among the council members if the selection is on random basis.

Question 7

An experiment consists of tossing up of an unbiased coin 4 times. Each time head appears a person is awarded with Re.1 and each time a tail a turns up that person looses Rs.1.50. Determine sample space of different money of 4 tosses and the propability of each of the head and tail.

Question 8

An experiment consists of tossing up of 3 coins .Find out the probability of the following events:

(a) Three heads

(b) Two heads

(c) At least two heads

(d) At most two heads

(e) No heads

(f) Three tails

(g) Exactly two tails

(h) No tails

(i) At most two tails

Question 10

From the word ‘ASSASSINATION’ a letter is chosen at a random basis. Then, determine the probability of getting (a) a vowel (b) an consonant

Question 11

A person chooses 6 different natural numbers at random basis from numbers ranging from 1 to 20. If and only if this 6-digit number  matches with the number decided by the lottery committee , the person wins the prize. Determine the probability of wining the prize ?

Question 12

Check whether the following probabilities are defined or not :

(i) P(Q) = 0.5 , P(R) = 0.7 , P(Q∩R) = 0.6

(ii) P(Q) = 0.5 , P(R) = 0.4 , P(Q∪R) = 0.8

Question 16

Events Q and R are such that P(not Q or not R ) = 0.25 . Find out whether Q and R are mutually exclusive or not ?

Question 17

Events Q and R are such that P(Q) = 0.42 , P® = 0.48 & P(Q and R) = 0.16. Find:

(a) P( not Q)

(b) P(not R)

(c) P( Q or R)

Question 18

In class XII of a school , 40% of the students studies mathematics & 30% of the students studies biology. 10% of the students of the class studies both maths and biology. If a student is selected as a random from the class , determine the probability of the student studying mathematics or biology.

Question 19

In an entrance test that is based on the basis of two examinations, the probability of a random student passing the examination is 0.8 and the probability of the candidate passing the second examination is 0.7. The probability of passing at least one of the examination is 0.95. find out the probability of passing both  the examinations?

Question 20

The probability that a student will pass the final examination in oth English and Hindi is 0.5. The probability of passing the neither of the subjects is 0.1. If the probability of passing the subject English alone is 0.75 then, find out the probability of passing in the Hindi subject?

Question 21

A class of strength 60 students , 30 students opted for NCC, 32 opted for NSS and 24 students opted for both NCC and NSS. Find the probability if one student is selected at a random that:

(a) Candidate opted out for NCC or NSS

(b) Candidates opted neither NCC nor NSS

(c) Candidates opted for NSS but not NCC

NCERT Solutions for Class 11 Maths Chapter 15 Statistics

Statistics Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. NCERT Solutions for Class 11 Maths Chapter 15 Statistics All Exercises were prepared by Experienced LearnCBSE.in Teachers.

Free download NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1, Ex 15.2, Ex 15.3, and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics
NCERT Solutions for Class 11 Maths Chapter 15 Statistics

Topics and Sub Topics in Class 11 Maths Chapter 15 Statistics:

Section NameTopic Name
15Statistics
15.1Introduction
15.2Measures of Dispersion
15.3Range
15.4Mean Deviation
15.5Variance and Standard Deviation
15 .6Analysis of Frequency Distributions

NCERT Solutions for Class 11 Maths Statistics Ex 15.1

Find the mean deviation about the mean for the data in Exercises 1 and 2.

Ex 15.1 Class 11 Maths Question 1.
4, 7, 8, 9, 10, 12, 13, 17
Solution:
Mean of the given data is
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q1

Ex 15.1 Class 11 Maths Question 2.
38, 70, 48, 40, 42, 55, 63, 46, 54, 44
Solution:
Mean of the given data is
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q2

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q2.1

Ex 15.1 Class 11 Maths Question 3.
13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17
Solution:
Arranging the data in ascending order, we have
10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18
Here n = 12 (which is even)
So median is the average of 6th and 7th observations
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q3

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q3.1

Ex 15.1 Class 11 Maths Question 4.
36, 72, 46, 42, 60, 45, 53, 46, 51, 49
Solution:
Arranging the data in ascending order, we have 36, 42, 45, 46, 46, 49, 51, 53, 60, 72
Here n = 10 (which is even)
So median is the average of 5th and 6th observations
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q4

Find the mean deviation about the mean for the data in Exercises 5 and 6.

Ex 15.1 Class 11 Maths Question 5.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q5
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q5.1

Ex 15.1 Class 11 Maths Question 6.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q6
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q6.1

Find the mean deviation about the median for the data in Exercises 7 and 8.

Ex 15.1 Class 11 Maths Question 7.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q7
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q7.1

Ex 15.1 Class 11 Maths Question 8.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q8
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q8.1

Find the mean deviation about the mean for the data in Exercises 9 and 10.

Ex 15.1 Class 11 Maths Question 9.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q9
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q9.1

Ex 15.1 Class 11 Maths Question 10.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q10
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q10.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q10.2

Ex 15.1 Class 11 Maths Question 11.
Find the mean deviation about median for the following data:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q11
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q11.1

Ex 15.1 Class 11 Maths Question 12.
Calculate the mean deviation about median age for the age distribution of 100 persons given below:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q12
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q12.1
[Hint: Convert the given data into continuous frequency distribution by subtracting 0.5 from lower limit and adding 0.5 to the upper limit of each class interval]
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q12.2

NCERT Solutions for Class 11 Maths Chapter 15 Statistics (सांख्यिकी) Hindi Medium Ex 15.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics (सांख्यिकी)
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Exercise 15.1 in Hindi Medium
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Exercise 15.1
NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.1
NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.1 in pdf form
NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.1 free download
NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.1 all question answers
11 Maths Exercise 15.1 solutions in hindi
11 Maths Exercise 15.1 solutions in pdf
11 Maths Exercise 15.1 solutions free download
11 Maths Exercise 15.1 solutions all question guide

NCERT Solutions for Class 11 Maths Statistics Ex 15.2

Find the mean and variance for each of the data in Exercises 1 to 5.

Ex 15.2 Class 11 Maths Question 1.
6, 7, 10, 12, 13, 4, 8, 12
Solution:
Here xi = 6, 7, 10, 12, 13, 4, 8, 12
∴ Σxi = 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72
n = 8
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q1.1

Ex 15.2 Class 11 Maths Question 2.
First n natural numbers
Solution:
Here xi = 1, 2, 3, 4, ……….n
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q2

Ex 15.2 Class 11 Maths Question 3.
First 10 multiples of 3
Solution:
Here xi = 3, 6, 9, 12, 15, 18, 21, 27, 30,
Σxi = 3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 = 165
n = 10
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q3

Ex 15.2 Class 11 Maths Question 4.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q4
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q4.1

Ex 15.2 Class 11 Maths Question 5.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q5
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q5.1

Ex 15.2 Class 11 Maths Question 6.
Find the mean and standard deviation using short-cut method
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q6
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q6.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q6.2

Find the mean and variance for the following frequency distributions in Exercises 7 and 8.

Ex 15.2 Class 11 Maths Question 7.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q7
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q7.1

Ex 15.2 Class 11 Maths Question 8.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q8
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q8.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q8.2

Ex 15.2 Class 11 Maths Question 9.
Find the mean, variance and standard deviation using short-cut method.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q9
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q9.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q9.2

Ex 15.2 Class 11 Maths Question 10.
The diameters of circles (in mm) drawn in a design are given below:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q10
Calculate the standard deviation and mean diameter of the circles.
[Hint: First make the data continuous by making the classes as 32.5 – 36.5, 36.5 – 40.5, 40.5 – 44.5, 44.5 – 48.5, 48.5 – 52.5 and then proceed.]
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q10.1

NCERT Solutions for Class 11 Maths Statistics Ex 15.3

Ex 15.3 Class 11 Maths Question 1.
From the data given below state which group is more variable, A or B?
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q1
Solution:
For Group A :
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q1.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q1.2
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q1.3

Ex 15.3 Class 11 Maths Question 2.
From the prices of shares X and Y below, find out which is more stable in value:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q2
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q2.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q2.2

Ex 15.3 Class 11 Maths Question 3.
An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q3
(i) Which firm A or B pays larger amount as monthly wages?
(ii) Which firm, AorB, shows greater variability in individual wages?
Solution:
(i) Firm A :
Number of wage earners (n1) = 586
Mean of monthly wages (x1¯¯¯¯¯) = Rs.5253
∴ Total monthly wages = 5253 x 586
= Rs. 3078258
Firm B :
Number of wage earners (n2) = 648
Mean of monthly wages (x2¯¯¯¯¯) = Rs.5253
∴ Total monthly wages = 5253 x 648
= Rs. 3403944
Hence, Firm B pays larger amount as monthly wages.

(ii) Since both the firms have same mean of monthly wages, so the firm with greater variance will have more variability in individual wages. Thus firm B will have more variability in individual wages.

Ex 15.3 Class 11 Maths Question 4.
The following is the record of goals scored by team A in a football session:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q4
For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?
Solution:
For team A:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q4.1

Ex 15.3 Class 11 Maths Question 5.
The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q5
Which is more varying, the length or weight?
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q5.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q5.2

Class 11 Maths NCERT Solutions  – Miscellaneous Questions

Miscellaneous Exercise Class 11 Maths Question 1:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q1

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q1.1
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q1.2

Ex 15.3 Class 11 Maths Question 2:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q2

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q2.1
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q2.2

Ex 15.3 Class 11 Maths Question 3:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q3

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q3.1
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q3.2

Ex 15.3 Class 11 Maths Question 4:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q4

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q4.1

Ex 15.3 Class 11 Maths Question 5:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q5

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q5.1
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q5.2

Ex 15.3 Class 11 Maths Question 6:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q6

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q6.1

Ex 15.3 Class 11 Maths Question 7:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q7.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q7.2

Exercise 15.1

Q1. Calculate the mean deviation about the mean for the given data

5, 8, 9, 10, 11, 13, 14, 18

Q2Calculate the mean deviation about the mean for the given data

39, 71, 49, 41, 43, 56, 64, 47, 55, 45

Q3. Calculate the mean deviation about the median for the given data:

13, 16, 11, 10, 11, 12, 17, 14, 13, 16, 18, 17

Q4. Calculate the mean deviation about the median for the given data:

36, 46, 60, 53, 51, 72, 42, 45, 46, 49

Q5. Calculate the mean deviation about the mean for the given data

xi510152025
fi74635

Q6. Calculate the mean deviation about the mean for the given data

xi1010152025
fi74635

Q7. Calculate the mean deviation about the median for the given data

xi1010152025
fi74635
xi579101215
fi862226

Q8. Calculate the mean deviation about the median for the given data

xi1521273035
fi35678

Q9. Calculate the mean deviation about the mean for the given data:

Income per dayNumber of persons
0 – 1004
100 – 2008
200 – 3009
300 – 40010
400 – 5007
500 – 6005
600 – 7004
700 – 8003

Q10. Calculate the mean deviation about the mean for the given data:

Height in cmNumber of boys
95 – 1059
105 – 11513
115 – 12526
125 – 13530
135 – 14512
145 – 15510

Q11. Calculate the mean deviation about the median for the given data:

MarksNumber of girls
0 – 106
10 – 208
20 – 3014
30 – 4016
40 – 504
50 – 602

Q12.  Calculate the mean deviation about the median for the given data:

AgeNumber
16 – 205
21 – 256
26 – 3012
31 – 3514
36 – 4026
41 – 4512
46 – 5016
51 – 559

Exercise 15.2

Q1. Calculate mean and variance for the given data 6, 7, 10, 12, 13, 4, 8, 12

Q2. Calculate the mean and variance for the first n natural numbers.

Q3. Calculate the mean and variance for the first 10 multiples of 3.

Q4. Calculate the mean and variance for the data

xi6101418242830
fi24712843

Q5. Calculate the mean and variance for the data

xi92939798102104109
fi3232633

Q6. Calculate the mean and standard deviation using short-cut method.

xi606162636465666768
fi21122925121045

Q7. Calculate the mean and variance for the given frequency distribution.

Classes0 – 3030 – 6060 – 9090 – 120120 – 150150 – 180180 – 210
Frequencies23510352

Q8. Calculate the mean and variance for the following frequency distribution.

Classes0 – 1010 – 2020 – 3030 – 4040 – 50
Frequencies5815166

Q9. Calculate the mean, variance and standard deviation using short – cut method:

Height in cmNumber of children
70 – 753
75 – 804
80 – 857
85 – 907
90 – 9515
95 – 1009
100 – 1056
105 – 1106
110 – 1153

Q10. The diameters of circles (in mm) drawn in a design are given below:

DiametersNumber of Children
33 – 3615
37 – 4017
41 – 4421
45 – 4822
49 – 5225

Exercise 15.3

Q1. From the data given below state which group is more variable, A or B

Marks10 – 2020 – 3030 – 4040 – 5050 – 6060 – 7070 – 80
Group A917323340109
Group B1020302543157

Q2. From the prices of shares X and Y below, find out which is more stable in value.

X35545253565852505149
Y108107105105106107104103104101

Q3. An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:

Firm AFirm B
No. of wage earners586648
Mean of monthly wagesRs. 5253Rs. 5253
Variance of the distribution of wages100121

(i) Which firm A or B pays larger amount as monthly wages?

(ii) Which firm, A or B, shows greater variability in individual wages?

Q4. The following is the record of goals scored by team A in a football session:

Number of goals scored01234
Number of matches19753

For team B, the mean number of goals scored per match was 2 with a standard deviation of 1.25 goals. Find which team may be considered more consistent?

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning

Mathematical Reasoning Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning All Exercises were prepared by Experienced LearnCBSE.in Teachers.

Free download NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.1, Ex 14.2, Ex 14.3, Ex 14.4, Ex 14.5 and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning

Topics and Sub Topics in Class 11 Maths Chapter 14 Mathematical Reasoning:

Section NameTopic Name
14Mathematical Reasoning
14.1Introduction
14.2Statements
14.3New Statements from Old
14.4Special Words/Phrases
14.5Implications
14 .6Validating Statements

NCERT Solutions for Class 11 Maths Chapter 14 Exercise.14.1

Ex 14.1 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.1 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.1 Q1.1

Ex 14.1 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.1 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.1 Q2.1

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning (गणितीय विवेचन) Hindi Medium Ex 14.1

NCERT Solutions for Class 9 Maths Chapter 14 Mathematical Reasoning (गणितीय विवेचन)
NCERT Solutions for Class 9 Maths Chapter 14 Mathematical Reasoning Exercise 14.1 in Hindi

More Resources for CBSE Class 11

NCERT Solutions for Class 11 Maths Chapter 14 Exercise.14.2

Ex 14.2 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2 Q1.1

Ex 14.2 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2 Q2.1

Ex 14.2 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2 Q3.1

NCERT Solutions for Class 11 Maths Chapter 14 Exercise.14.3

Ex 14.3 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3 Q1.1

Ex 14.3 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3 Q2.1

Ex 14.3 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3 Q3.1

Ex 14.3 Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3 Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3 Q4.1

NCERT Solutions for Class 11 Maths Chapter 14 Exercise.14.4

Ex 14.4 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4 Q1.1

Ex 14.4 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4 Q2.1

Ex 14.4 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4 Q3.1

Ex 14.4 Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4 Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4 Q4.1

NCERT Solutions for Class 11 Maths Chapter 14 Exercise.14.5

Ex 14.5 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.5 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.5 Q1.1

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.5 Q1.2

Ex 14.5 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.5 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.5 Q2.1

Ex 14.5 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.5 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.5 Q3.1

Ex 14.5 Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.5 Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.5 Q4.1

Ex 14.5 Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.5 Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.5 Q5.1

Class 11 Maths NCERT Solutions – Mathematical Reasoning Miscellaneous Questions

Miscellaneous Exercise Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q1.1

Miscellaneous Exercise Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q2.1

Miscellaneous Exercise Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q3.1

Miscellaneous Exercise Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q4.1

Miscellaneous Exercise Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q5.1

Miscellaneous Exercise Class 11 Maths Question-6
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q6.1

Miscellaneous Exercise Class 11 Maths Question-7
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Miscellaneous Ex Q7.1

Q.1: State whether the following sentences are statements or not, and justify your answers.

(a) A month has 35 days.

(b) Mathematics is very tough

(c) Addition of two numbers such as 5 & 7 is larger than 10.

(d) The resultant of a square of a number is always an even number.

(e) The arms of a quadrilateral are having equal length.

(f) Answer the following questions.

(g) The multiplication result of two numbers such as 8 and (-1) is 8

(h) The interior angles summed up together results in 1800 in a triangle.

(i) Yesterday was a cloudy day.

(j) The numbers which are real are always complex numbers.

Q.2: Give 3 examples of each sentence which are not statements. Give justified reasons for the answers.

Exercise 14.2

Q.1: Write the opposite of the below mentioned statements:

(a). New Delhi is the capital of India.

(b). √3+1 is a complex number.

(c). All quadrilaterals are not squares.

(d). 9 is lesser than 7

(e). The square of every natural number is a even number

Q.2: State whether the following statements are opposite to each other or not.

(a). The number 2 is not an even number

      The number 2 is not an odd number.

(b). The number 2 is an even number.

       The number 2 is an odd number.

Q.3: Find out the component sentences from the below-mentioned compound sentences, and determine whether they are true/ false.

(a). Number 5 is odd or it is a prime number.

(b). All integers are positive and negative.

(c). 1000 is divisible by 9 or 10

Exercise 14.3

Q.1:

(i). Every real number is not complex number and every rational number is a real number.

(ii).  Square of any integer is negative or positive.

(iii).  The sand easily heats up due to the sun but does not cool down easily at night

(iv).  The roots for the equation x + 10 = 3x2 are x = 3 and x = 2

Q.2: Write negation for the statements after identifying the quantifier for the statements

(i).  There exits one number that is equal to the square of the number

(ii).  For every number that is real ‘x’, x < x + 1

(iv).  There exist one capital for each state of India.

Q.3: Check if the following statements are negation for each other. Justify your answer

(i).  y + x = x + y is true for real numbers x and y

(ii).  There exist real numbers x, y such that y + x = x + y

Q.4: State if the “Or” in the statements is inclusive or exclusive. Justify the answer

(i) Moon sets or sun rises

(ii) You must have ration card or passport for applying a driving license.

(iii) Integers are negative or positive

Exercise – 14.4

Q.1: Rewrite the statements with ‘if & then’ in 5 different ways but the sentence should convey the meaning as before.

A natural number is odd implies that its square is odd.

Q.2: Rewrite the following sentences as the converse/contrapositive of the followings:

(a).  A quadrilateral is said to be parallelogram if the diagonals bisect each other.

(b).  y is an odd number that is y is divisible by 3

(c).  If 2 lines do not intersect in the same plane, then they are said to be parallel.

(d).  If something is having a low temperature then it implies that is cold

(e).  If you are not able to deduct the reason, then you will not be able to comprehend geometry.

Q.3: Rewrite the following sentences with “if- then”:

(a).  You have visited Qutub Minar implies that you live in Delhi

(b).  You will pass the exam if you study hard.

(c).  In order to get A+ in the class test, you have to do all the problems of that chapter.

(d).  Parallel lines do not intersect each other in the same plane

Q.4: Identify the contrapositive/converse from the following sentences:

(i)  If you live in Agra, then you have visited Taj Mahal

(a) If you have not visited Taj Mahal then you do not live in Agra.

(b)  If you have visited Taj Mahal then you live in Agra.

(ii) If the diagonals of the quadrilateral bisect each other then that quadrilateral is a parallelogram.

(a)   quadrilateral is not said to be a parallelogram if the diagonals of a quadrilateral do not bisect each other.

(b)  quadrilateral is said to be a parallelogram if the diagonals of a quadrilateral bisect each other.

Exercise 14.5

Q.1: Prove that p: “If a is real such that a3+ 4a = 0, then a is  0″ is true 

(i). by direct method

(ii). by method of contradiction

(iii). by method of contra positive

Q.2: Prove the statement “For real numbers b and a, b2 = a2 implies that b = a” isn’t true. Give a counter example.

Q3: By using contrapositive method prove the following statement is true

p: if a is an integer and a2 is even, then a is even.

NCERT Solutions for Class 11 Maths All Chapters

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives

Limits and Derivatives Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives All Exercises were prepared by Experienced LearnCBSE.in Teachers.

Free download NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1, Ex 13.2, and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives

Topics and Sub Topics in Class 11 Maths Chapter 13 Limits and Derivatives:

Section NameTopic Name
13Limits and Derivatives
13.1Introduction
13.2Intuitive Idea of Derivatives
13.3Limits
13.4Limits of Trigonometric Functions
13.5Derivatives

NCERT Solutions for Class 11 Maths Chapter 13 Exercise.13.1

Ex 13.1 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q1.1

Ex 13.1 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q2.1

More Resources for CBSE Class 11

Ex 13.1 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q3.1

Ex 13.1 Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q4.1

Ex 13.1 Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q5.1

Ex 13.1 Class 11 Maths Question-6
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q6.1

Ex 13.1 Class 11 Maths Question-7
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q7.1

Ex 13.1 Class 11 Maths Question-8
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q8
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q8.1

Ex 13.1 Class 11 Maths Question-9
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q9
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q9.1

Ex 13.1 Class 11 Maths Question-10
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q10
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q10.1

Ex 13.1 Class 11 Maths Question-11
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q11
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q11.1

Ex 13.1 Class 11 Maths Question-12
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q12
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q12.1

Ex 13.1 Class 11 Maths Question-13
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q13
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q13.1

Ex 13.1 Class 11 Maths Question-14
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q14
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q14.1

Ex 13.1 Class 11 Maths Question-15
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q15
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q15.1

Ex 13.1 Class 11 Maths Question-16
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q16
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q16.1

Ex 13.1 Class 11 Maths Question-17
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q17
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q17.1

Ex 13.1 Class 11 Maths Question-18
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q18
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q18.1

Ex 13.1 Class 11 Maths Question-19
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q19
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q19.1

Ex 13.1 Class 11 Maths Question-20
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q20
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q20.1

Ex 13.1 Class 11 Maths Question-21
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q21
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q21.1

Ex 13.1 Class 11 Maths Question-22
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q22
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q22.1

Ex 13.1 Class 11 Maths Question-23
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q23
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q23.1

Ex 13.1 Class 11 Maths Question-24
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q24
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q24.1

Ex 13.1 Class 11 Maths Question-25
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q25
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q25.1

Ex 13.1 Class 11 Maths Question-26
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q26
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q26.1

Ex 13.1 Class 11 Maths Question-27
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q27
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q27.1

Ex 13.1 Class 11 Maths Question-28
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q28
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q28.1

Ex 13.1 Class 11 Maths Question-29
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q29
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q29.1

Ex 13.1 Class 11 Maths Question-30
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q30
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q30.2

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q30.1

Ex 13.1 Class 11 Maths Question-31
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q31
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q31.1

Ex 13.1 Class 11 Maths Question-32
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q32
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.1 Q32.1

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives (सीमा और अवकलज) Hindi medium Ex 13.1

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Exercise 13.1 in PDF form
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Exercise 13.1 in english medium
11 Maths Exercise 13.1
11 Maths Chapter 13 Exercise 13.1 sols in hindi medium
11 Maths Chapter 13 Exercise 13.1 free guide for all answers
11 Maths Chapter 13 Exercise 13.1 for up, gujrat and mp board
11 Maths Chapter 13 Limits and Derivatives Exercise 13.1 sols
11 Maths Chapter 13 Limits and Derivatives Exercise 13.1 in pdf form free download guide
11 Maths Chapter 13 Limits and Derivatives Exercise 13.1 all question answers
Class 11 Maths Chapter 13 Exercise 13.1
Class 11 Maths Chapter 13 Exercise 13.1 sols in hindi medium
Class 11 Maths Chapter 13 Exercise 13.1 download in pdf free
Class 11 Maths Chapter 13 Exercise 13.1 all question answers
11 Maths Chapter 13 Limits and Derivatives Exercise 13.1 all answers guide free
11 Maths ex. 13.1 in english medium
11 Maths ex. 13.1 in Hindi medium
NCERT Solutions for Class 9 Maths Chapter 13 Limits and Derivatives Exercise 13.1 in Hindi medium

NCERT Solutions for Class 11 Maths Chapter 13  Exercise.13.2

Ex 13.2 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q1.1

Ex 13.2 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q2.1

Ex 13.2 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q3.1

Ex 13.2 Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q4.1

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q4.2
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q4.3

Ex 13.2 Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q5.1

Ex 13.2 Class 11 Maths Question-6
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q6.1

Ex 13.2 Class 11 Maths Question-7
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q7.1

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q7.2

Ex 13.2 Class 11 Maths Question-8
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q8
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q8.1

Ex 13.2 Class 11 Maths Question-9
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q9
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q9.1

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q9.2
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q9.3
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q9.4

Ex 13.2 Class 11 Maths Question-10
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q10
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q10.1

Ex 13.2 Class 11 Maths Question-11
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q11
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q11.1

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q11.2
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q11.3
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q11.4
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q11.5
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q11.6
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q11.7
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q11.8
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q11.9
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Q11.10

Class 11 Maths NCERT Solutions – Miscellaneous Questions

Miscellaneous Exercise Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q1.1

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q1.2
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q1.3
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q1.4

Miscellaneous Exercise Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q2.1

Miscellaneous Exercise Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q3.1

Miscellaneous Exercise Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q4.1

Miscellaneous Exercise Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q5.1

Miscellaneous Exercise Class 11 Maths Question-6
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q6.1

Miscellaneous Exercise Class 11 Maths Question-7
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q7.1

Miscellaneous Exercise Class 11 Maths Question-8
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q8
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q8.1

Miscellaneous Exercise Class 11 Maths Question-9
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q9
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q9.1

Miscellaneous Exercise Class 11 Maths Question-10
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q10
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q10.1

Miscellaneous Exercise Class 11 Maths Question-11
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q11
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q11.1

Miscellaneous Exercise Class 11 Maths Question-12
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q12
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q12.1

Miscellaneous Exercise Class 11 Maths Question-13
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q13
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q13.1

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q13.2

Miscellaneous Exercise Class 11 Maths Question-14
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q14
Ans.
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Miscellaneous Ex Q14.1

NCERT Solutions for Class 11 Maths All Chapters

NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry

Introduction to Three Dimensional Geometry Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry All Exercises were prepared by Experienced LearnCBSE.in Teachers.

Free download NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry Ex 12.1, Ex 12.2, Ex 12.3, and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry

Topics and Sub Topics in Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry:

Section NameTopic Name
12Introduction to Three Dimensional Geometry
12.1Introduction
12.2Coordinate Axes and Coordinate Planes in Three Dimensional Space
12.3Coordinates of a Point in Space
12.4Distance between Two Points
12.5Section Formula

NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1

Ex 12.1 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1 Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1 Q1.1
Ex 12.1 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1 Q2.1

More Resources for CBSE Class 11

Ex 12.1 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1 Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1 Q3.1
Ex 12.1 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1 Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1 Q4.1

NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry (त्रिविमीय ज्यामिति का परिचय) Hindi Medium Ex 12.1

NCERT Solutions for Class 9 Maths Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.1 in Hindi medium
NCERT Solutions for Class 9 Maths Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.1 in pdf

NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.2

Ex 12.2 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q1.1
Ex 12.2 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q2.1
Ex 12.2 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q3.1

NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q3.2

NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q3.3
Ex 12.2 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q4.1
Ex 12.2 Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 Q5.1

NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.3

Ex 12.3 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.3 Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.3 Q1.1
Ex 12.3 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.3 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.3 Q2.1
Ex 12.3 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.3 Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.3 Q3.1
Ex 12.3 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.3 Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.3 Q4.1
Ex 12.3 Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.3 Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.3 Q5.1

Class 11 Maths NCERT Solutions – Miscellaneous Questions

Miscellaneous Exercise Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q1.1
Miscellaneous Exercise Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q2.1
Miscellaneous Exercise Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q3
Ans:
Miscellaneous Exercise Class 11 Maths 
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q3.1
Miscellaneous Exercise Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q4.1
Miscellaneous Exercise Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q5.1
Miscellaneous Exercise Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q6
Ans:
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Miscellaneous Ex Q6.1

Exercise 12.1

For any given point, the sign of its coordinates determines the octant in which it will lie.

Now, from the following table it can be easily determined in which coordinates the point lies.

Q.1: A point is lying on y – axis. What are its ‘x‘ coordinates and ‘z’ coordinates?

Q.2: A point is lying on YZ – plane. What are its ‘x‘ coordinates?

Q.3: In which of the octant the following points lie:

(2, 3, 4), (8, -1, -1), (-4, 9, -8), (-1, -2, -3), (4, -5, 6), (7, -1, -4), (-3, -5, 1), (0, 0, -3)

 Q.4: Answer the following questions:

(i). What is the name of a plane determined by the Z-axis and the Y-axis when taken together?

(ii). What is the general form of coordinates of points in the XZ-plane?

(iii). Coordinate plane divides the space into how many octants?

Exercise: 12.2

Q.1: Find the distance between two points whose coordinates are given below:

(i).     (2, 8, 9) and (4, 5, 8)

(ii).    (-3, 4, 5) and (2, 6, -1)

(iii).   (-6, -4, 1) and (5, -2, 6)

(iv).   (-1, 9, 8) and (6, 5, -3)

Q.2: Show that the points (7, 0, -1), (-2, 3, 5) and (1, 2, 3) are collinear.

Q.3: Prove the following statements:

(i). (-4, 9, 6), (0, 7, 10) and (-1, 6, 6) are the vertices of a right angled triangle.

(ii). (4, 9, -6), (0, 7, -10) and (1, 6, -6) are the vertices of an isosceles triangle.

(iii). (2, -3, 4), (1, -2, 5), (-1, 2, 1) and (4, -7, 8) are the vertices of a parallelogram.

Q.4: Find the equation of the set of points P which are equidistant from point  A (3, 2, 1) and point B (-1, 2, 3).

Q.5: The sum of distance of point P from point A (3, 0, 0) and point B (-3, 0, 0) is equal to 12 units. Find the equation of the set of points.

Exercise 12.3

Q.1: Find the coordinates of the point which divides the line segment joining the points (-2, 1, 0) and (1, 3, 6) internally in the ratio of 1:4 and externally in the ratio of 1:4.

Q.2: Given that the points A (3, 2, -4) B (5, 4, -6) and C (9, 8, -10), are collinear. Find the ratio in which line AC is divided by B.

Q.3: Find the ratio in which XZ – plane divides the line segment AB formed by joining the points (3, -5, 8) and (-2, 4, 7).

Q.4: By using the section formula; Show that the points P (-1, 2, 1), Q (0, 13, 2) and R (2, -3, 4) are collinear.

Q.5: The line segment joining points A (5, 3, -6) and B (9, 15, 7) is trisected by the points P and Q, Find the coordinates of points P and Q.

NCERT Solutions for Class 11 Maths All Chapters

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections

Conic Sections Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections All Exercises were prepared by Experienced LearnCBSE.in Teachers.

Free download NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1, Ex 11.2, Ex 11.3, Ex 11.4 and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections

Topics and Sub Topics in Class 11 Maths Chapter 11 Conic Sections:

Section NameTopic Name
11Conic Sections
11.1Introduction
11.2Sections of a Cone
11.3Circle
11.4Parabola
11.5Ellipse
11.6Hyperbola

National Council of Educational Research and Training (NCERT) Book Solutions for class 11th
Subject: Maths
Chapter: Chapter 11 Conic Sections

Class 11th Maths Chapter 11 Conic Sections NCERT Solution is given below.

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1

Ex 11.1 Class 11 Question 1:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q1.1

Ex 11.1 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q2.1

RD Sharma Class 11 Maths Solutions

Ex 11.1 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q3.1

Ex 11.1 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q4.1

Ex 11.1 Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q5.1

Ex 11.1 Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q6

More Resources for CBSE Class 11

Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q6.1

Ex 11.1 Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q7.1
Ex 11.1 Class 11 Maths Question 8:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q8
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q8.1

Ex 11.1 Class 11 Maths Question 9:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q9
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q9.1

Ex 11.1 Class 11 Maths Question 10:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q10
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q10.1

Ex 11.1 Class 11 Maths Question 11:
Find the equation of the circle passing through the points (2, 3) and (-1, 1) and whose centre is on the line x – 3y – 11 = 0.
Solution:
The equation of the circle is,
(x – h)2 + (y – k)2 = r2 ….(i)
Since the circle passes through point (2, 3)
∴ (2 – h)2 + (3 – k)2 = r2
⇒ 4 + h2 – 4h + 9 + k2 – 6k = r2
⇒ h2+ k2 – 4h – 6k + 13 = r2 ….(ii)
Also, the circle passes through point (-1, 1)
∴ (-1 – h)2 + (1 – k)2 = r2
⇒ 1 + h2 + 2h + 1 + k2 – 2k = r2
⇒ h2 + k2 + 2h – 2k + 2 = r2 ….(iii)
From (ii) and (iii), we have
h2 + k2 – 4h – 6k + 13 = h2 + k2 + 2h – 2k + 2
⇒ -6h – 4k = -11 ⇒ 6h + 4k = 11 …(iv)
Since the centre (h, k) of the circle lies on the line x – 3y-11 = 0.
∴ h – 3k – 11 = 0 ⇒ h -3k = 11 …(v)
Solving (iv) and (v), we get
h = 72 and k = −52
Putting these values of h and k in (ii), we get
(72)2+(−52)2−4×72−6×−52+13=r2
⇒ 494+254−14+15+13 ⇒ r2=652
Thus required equation of circle is
⇒ (x−72)2+(y+52)2=652
⇒ x2+494−7x+y2+254+5y=652
⇒ 4×2 + 49 – 28x + 4y2 + 25 + 20y = 130
⇒ 4×2 + 4y2 – 28x + 20y – 56 = 0
⇒ 4(x2 + y2 – 7x + 5y -14) = 0
⇒ x2 + y2 – 7x + 5y -14 = 0.
Ex 11.1 Class 11 Maths Question 12:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q12
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q12.1

Ex 11.1 Class 11 Maths Question 13:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q13
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q13.1

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q13.2

Ex 11.1 Class 11 Maths Question 14:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q14
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q14.1

Ex 11.1 Class 11 Maths Question 15:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q15
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.1 Q15.1

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections (शंकु परिच्छेद) Hindi Medium Ex 11.1

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections - शंकु परिच्छेद
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections
NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1
NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1 in english medium
NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1 in pdf
11 Maths Conic Sections Exercise 11.1 in hindi medium
11 Maths Exercise 11.1 solutions in hindi medium
11 Maths Exercise 11.1 in pdf form solutions
11 Maths Exercise 11.1 pdf download

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.2

Ex 11.2 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q1.1

Ex 11.2 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q2.1

Ex 11.2 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q3.1

Ex 11.2 Class 11 Maths Question 4:

Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q4.1
Ex 11.2 Class 11 Maths Question 5:

Ans:

Ex 11.2 Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q6
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q6.1
Ex 11.2 Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q7.1
Ex 11.2 Class 11 Maths Question 8:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q8
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q8.1

Ex 11.2 Class 11 Maths Question 9:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q9
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q9.1
Ex 11.2 Class 11 Maths Question 10:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q10
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q10.1
Ex 11.2 Class 11 Maths Question 11:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q11
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q11.1
Ex 11.2 Class 11 Maths Question 12:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q12
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.2 Q12.1

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.3

Ex 11.3 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q1
Ans:

Ex 11.3 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q2.1

Ex 11.3 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q3.1
Ex 11.3 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q4.1

Ex 11.3 Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q5.1

Ex 11.3 Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q6
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q6.1
Ex 11.3 Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q7.1
Ex 11.3 Class 11 Maths Question 8:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q8
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q8.1
Ex 11.3 Class 11 Maths Question 9:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q9
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q9.1
Ex 11.3 Class 11 Maths Question 10:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q10
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q10.1
Ex 11.3 Class 11 Maths Question 11:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q11
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q11.1
Ex 11.3 Class 11 Maths Question 12:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q12
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q12.1
Ex 11.3 Class 11 Maths Question 13:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q13
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q13.1
Ex 11.3 Class 11 Maths Question 14:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q14
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q14.1
Ex 11.3 Class 11 Maths Question 15:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q15
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q15.1

Ex 11.3 Class 11 Maths Question 16:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q16
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q16.1

Ex 11.3 Class 11 Maths Question 17:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q17
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q17.1
Ex 11.3 Class 11 Maths Question 18:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q18
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q18.1
Ex 11.3 Class 11 Maths Question 19:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q19
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q19.1
Ex 11.3 Class 11 Maths Question 20:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q20
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 Q20.1

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.4

Ex 11.4 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q1.1

Ex 11.4 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q2.1
Ex 11.4 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q3.1
Ex 11.4 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q4.1
Ex 11.4 Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q5.1
Ex 11.4 Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q6
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q6.1
Ex 11.4 Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q7.1

Ex 11.4 Class 11 Maths Question 8.
Vertices (0, ±5), foci (0, ±8)
Solution:
Vertices are (0, ±5) which lie on x-axis. So the equation of hyperbola in standard form
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q8

Ex 11.4 Class 11 Maths Question 9.
Vertices (0, ±3), foci (0, ±5)
Solution:
Vertices are (0, ±3) which lie on x-axis. So the equation of hyperbola in standard form
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q9
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q9.1

Ex 11.4 Class 11 Maths Question 10:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q10
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q10.1
Ex 11.4 Class 11 Maths Question 11:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q11
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q11.1

Ex 11.4 Class 11 Maths Question 12:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q12
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q12.1

Ex 11.4 Class 11 Maths Question 13:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q13
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q13.1
Ex 11.4 Class 11 Maths Question 14:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q14
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q14.1
Ex 11.4 Class 11 Maths Question 15:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q15
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q15.1

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 Q15.2

Class 11 Maths NCERT Solutions – Miscellaneous Questions

Miscellaneous Exercise Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q1.1

Miscellaneous Exercise Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q2.1

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q2.2

Miscellaneous Exercise Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q3.1

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q3.2

Miscellaneous Exercise Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q4.1

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q4.2
Miscellaneous Exercise Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q5.1
Miscellaneous Exercise Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q6
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q6.1
Miscellaneous Exercise Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q7.1

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q7.2
Miscellaneous Exercise Class 11 Maths Question 8:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q8
Ans:
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Ex Q8.1

Exercise 11.1

Q.1: A circle is given with centre (0, 3) and radius 3. Obtain the equation of the given circle.

Q.2: A circle is given with centre (-1, 2) and radius 4. Find the equation of the circle.

Q.4: A circle is given with centre (2, 2) and radius √5

Q.6: The equation of a given circle is given as (a + 5)2 + (b – 3)2 = 36. Find the centre and radius of the circle.. Obtain the equation of the given circle.

Q.7: The equation of a given circle is given as a+ b2 – 4a – 4b + 3 = 0

Find the radius and centre of the circle.

Q.8: The equation of a given circle is given as a+ b2 – 6a + 8b – 14 = 0

Find the centre and radius of the circle.

Q.9: The equation of a given circle is given as 2a+ 2b2 – 8a = 0

Find the centre and radius of the circle.

Q.10: The circle passing through the points (6, 2) and (4, 3) and whose centre lies on the line 2a + y = 8. Find the equation of the circle.

Q.11: The circle passing through the points (3, 2) and (-2, 2) and whose centre lies on the line a – 3y – 13 = 0. Find the equation of the circle.

Q.12: The radius of the circle is 6 whose centre lies on x – axis and passes through the point (3, 2). Find the equation.

Q.13: The circle passing through (0, 0) and making intercepts a and b on the coordinate axes. Find the equation of the circle.

Q.14: The circle with centre (3, 3) and passes through the point (6, 5), find the equation of a circle?

Q.15: Check whether the point (–2.0, 3.0) lies inside, outside or on the circle x 2 + y 2 = 25?

Exercise 11.2

Q.1: For the equation y2 = 16x, determine the focus coordinates, the directrix equation, the length of the latus rectum and the axis of the parabola.

Q.2: For the equation x2 = 8y, determine the focus coordinates, the directrix equation, the length of the latus rectum and the axis of the parabola.

Q.3: For the equation y2 = – 12x, determine the focus coordinates, the directrix equation, the length of the latus rectum and the axis of the parabola.

Q.4: For the equation x2 = – 20y, determine the focus coordinates,  the directrix equation, the length of the latus rectum and the axis of the parabola.

Q.5: For the equation y2 = 24x, determine the focus coordinates, the directrix equation, the length of the latus rectum and the axis of the parabola.

Q.6: For the equation x2 = – 7y, determine the focus coordinates,  the directrix equation, the length of the latus rectum and the axis of the parabola.

Q7. Obtain the equation of the parabola which satisfies the given conditions below:

(i) Focus coordinates = (8, 0)

(ii) Directrix (x) = – 8

Q.8: Obtain the equation of the parabola which satisfies the given conditions below:

(i) Focus coordinates = (0, – 5)

(ii) Directrix (y) = 5

Q.9: Obtain the equation of the parabola which satisfies the given conditions below:

(i) Vertex is at origin.

(ii) Focus coordinates = (4, 0)

Q.10: Obtain the equation of the parabola which satisfies the given conditions below:

(i) Vertex is at origin.

(ii) Focus coordinates = (- 3, 0)

Q.11: Obtain the equation of the parabola which satisfies the given conditions below:

(i) Vertex is at origin.

(ii) Passing through coordinates = (3, 5)

The axis of the parabola is on x – axis.

Q.12: Obtain the equation of the parabola which satisfies the given conditions below:

(i) Vertex is at the origin.

(ii) Passing through coordinates = (6, 4)

The equation is symmetric as considered with y-axis.

Exercise 11.3

Q.7: Obtain the coordinates of the vertices, the foci, the major and the minor axis, the length of the latus rectum and the eccentricity of the ellipse 49x2 + 9y= 441

Q.8: Obtain the coordinates of the vertices, the foci, the major and the minor axis, the length of the latus rectum and the eccentricity of the ellipse 4x2 + 16y= 64

Q.9: Obtain the coordinates of the vertices, the foci, the major and the minor axis, the length of the latus rectum, and the eccentricity of the ellipse 4x2 + y= 4

Q.10: For the given condition obtain the equation of the ellipse.

(i) Vertices (±6, 0)

(ii) Foci (±3, 0)

Q.11: For the given condition obtain the equation of the ellipse.

(i) Vertices (0, ±8)

(ii) Foci ( 0, ±4)

Q.12: For the given condition obtain the equation of the ellipse.

(i) Vertices (±5, 0)

(ii) Foci (±3, 0)

Q.13: For the given condition obtain the equation of the ellipse.

(i) Coordinates of major axis (±5, 0)

(ii) Coordinates of minor axis (0, ±3)

Q.14: For the given condition obtain the equation of the ellipse.

(i) Coordinates of major axis (0, ±2)

(ii) Coordinates of minor axis (±√3, 0)

Q.15: For the given condition obtain the equation of the ellipse.

(i) Length of major axis 30

(ii) Coordinates of foci (±4, 0)

Q.16: For the given condition obtain the equation of the ellipse.

(i) Length of minor axis 26

(ii) Coordinates of foci (0, ±9)

Q.17: For the given condition obtain the equation of the ellipse.

(i) Coordinates of foci (±4, 0)

(ii) m = 6

Q.18: For the given condition obtain the equation of the ellipse.

(i) n = 2, c = 3 (on the x – axis)

(ii) Coordinates of centre (0, 0)

Q.19: For the given condition obtain the equation of the ellipse.

(i) Centre is at origin and major axis is along the y – axis

(ii) It passes through the points (1, 6) and (3, 2)

Q.20: For the given condition obtain the equation of the ellipse.

(i) Major axis is represented along x – axis

(ii) It passes through the points (6, 2) and (4, 3)

Exercise 11.4

Q.3: Obtain the coordinates of the vertices, the foci, the length of the latus rectum and the eccentricity of the hyperbola 25 y2 – 4 x2 = 100

Q.4: Obtain the coordinates of the vertices, the foci, the length of the latus rectum and the eccentricity of the hyperbola 9 x2 – 4 y2 = 36

Q.5: Obtain the coordinates of the vertices, the foci, the length of the latus rectum and the eccentricity of the hyperbola 6 y2 – 16 x2 = 96

Q.6: Obtain the coordinates of the vertices, the foci, the length of the latus rectum and the eccentricity of the hyperbola 64 y2 – 9 x2 = 96

Q.7: For the given condition obtain the equation of the hyperbola.

(i) Coordinates of the vertices (±3, 0)

(ii) Coordinates of the foci (±4, 0)

Q.8: For the given condition obtain the equation of the hyperbola.

 (i) Coordinates of the vertices (0, ±7)

(ii) Coordinates of the foci (0, ±9)

Q.9: For the given condition obtain the equation of the hyperbola.

 (i) Coordinates of the vertices (0, ±8)

(ii) Coordinates of the foci (0, ±11)

Q.10: For the given condition obtain the equation of the hyperbola.

 (i) Coordinates of the foci (±7, 0),

(ii) The length of the transverse axis is 12

Q.11: For the given condition obtain the equation of the hyperbola.

(i) Coordinates of the foci (0, ±8)

(ii) The length of the conjugate axis is 16

Q.12: For the given condition obtain the equation of the hyperbola.

(i) Coordinates of the foci (±2√3, 0 )

(ii) The length of the latus rectum is 8

Q.13: For the given condition obtain the equation of the hyperbola.

(i) Coordinates of the foci (±2√6, 0)

(ii) The length of the latus rectum is 10

Q.15: For the given condition obtain the equation of the hyperbola.

(i) Coordinates of the foci (0, ± √10)

(ii) It passes through (2, 3)

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines prepared by the Mathematics subject experts. All the important topics in Straight Lines are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These Class 11 Maths NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Exercise.10.1

Topics and Sub Topics in Class 11 Maths Chapter 10 Straight Lines:

Section NameTopic Name
10Straight Lines
10.1Introduction
10.2Slope of Line
10.3Various Forms of the Equation of Line
10.4General Equation of Line
10.5Distance of a Point From a Line

Ex 10.1 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q1.1
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q1.2

LearnCBSE.in Updated Straight Lines exercise wise to make it user-friendly, check out now NCERT Solutions for Class 10 Straight Lines Exercise 10.2, Ex 10.3 and Miscellaneous Questions. If you face any difficulty please give us feedback in the comment section. Check it Now:

Ex 10.1 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q2.1
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q2.2

More Resources for CBSE Class 11

Ex 10.1 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q3.1

Ex 10.1 Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q4.1

Ex 10.1 Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q5.1

Ex 10.1 Class 11 Maths Question-6
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q6.1

Ex 10.1 Class 11 Maths Question-7
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q7.1

Ex 10.1 Class 11 Maths Question-8
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q8
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q8.1

Ex 10.1 Class 11 Maths Question-9
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q9
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q9.1

Ex 10.1 Class 11 Maths Question-10
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q10
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q10.1

Ex 10.1 Class 11 Maths Question-11
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q11
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q11.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q11.2

Ex 10.1 Class 11 Maths Question-12
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q12
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q12.1

Ex 10.1 Class 11 Maths Question-13
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q13
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q13.1

Ex 10.1 Class 11 Maths Question-14
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q14
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.1 Q14.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines (सरल रेखाएँ) Hindi Medium Ex 10.1

NCERT Solutions for Class 1 Maths Chapter 10 Straight Lines (सरल रेखाएँ)
NCERT Solutions for Class 1 Maths Chapter 10 Straight Lines Exercise 10.1
11 Maths Exercise 10.1
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Exercise 10.1Hindi Medium
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Exercise 10.1 in Hindi Medium
11 Maths Exercise 10.1 in Hindi
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Exercise 10.1 in pdf form free download
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Exercise 10.1 in english medium
11 Maths Exercise 10.1 Pdf in Hindi Medium
11 Maths Exercise 10.1 in hindi medium
11 Maths Exercise 10.1 free
11 Maths Exercise 10.1 in hindi medium
11 Maths Exercise 10.1 for gujrat board
11 Maths Exercise 10.1 free download all answers
11 Maths Exercise 10.1 free guide for up, gujrat, mp board cbse

NCERT Solutions for Class 11 Maths Chapter 10 Exercise.10.2

Ex 10.2 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q1.1

Ex 10.2 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q2.1

Ex 10.2 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q3.1

Ex 10.2 Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q4.1

Ex 10.2 Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q5.1

Ex 10.2 Class 11 Maths Question-6
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q6.1

Ex 10.2 Class 11 Maths Question-7
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q7.1

Ex 10.2 Class 11 Maths Question-8
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q8
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q8.1

Ex 10.2 Class 11 Maths Question-9
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q9
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q9.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q9.2

Ex 10.2 Class 11 Maths Question-10
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q10
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q10.1

Ex 10.2 Class 11 Maths Question-11
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q11
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q11.1

Ex 10.2 Class 11 Maths Question-12
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q12
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q12.1

Ex 10.2 Class 11 Maths Question-13
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q13
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q13.2

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q13.1

Ex 10.2 Class 11 Maths Question-14
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q14
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q14.1

Ex 10.2 Class 11 Maths Question-15
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q15
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q15.1

Ex 10.2 Class 11 Maths Question-16
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q16
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q16.1

Ex 10.2 Class 11 Maths Question-17
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q17
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q17.1

Ex 10.2 Class 11 Maths Question-18
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q18
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q18.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q18.2

Ex 10.2 Class 11 Maths Question-19
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q19
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q19.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q19.2

Ex 10.2 Class 11 Maths Question-20
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q20
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 Q20.1

NCERT Solutions for Class 11 Maths Chapter 10 Exercise.10.3

Ex 10.3 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q1.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q1.2

Ex 10.3 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q2.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q2.2

Ex 10.3 Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q3.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q3.2
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q3.3

Ex 10.3 Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q4.1

Ex 10.3 Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q5.1

Ex 10.3 Class 11 Maths Question-6
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q6.1

Ex 10.3 Class 11 Maths Question-7
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q7.1

Ex 10.3 Class 11 Maths Question-8
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q8
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q8.1

Ex 10.3 Class 11 Maths Question-9
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q9
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q9.1

Ex 10.3 Class 11 Maths Question-10
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q10
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q10.1

Ex 10.3 Class 11 Maths Question-11
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q11
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q11.1

Ex 10.3 Class 11 Maths Question-12
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q12
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q12.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q12.2
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q12.3

Ex 10.3 Class 11 Maths Question-13
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q13
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q13.1

Ex 10.3 Class 11 Maths Question-14
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q14
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q14.1
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q14.2

Ex 10.3 Class 11 Maths Question-15
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q15
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q15.1

Ex 10.3 Class 11 Maths Question-16
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q16
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q16.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q16.2

Ex 10.3 Class 11 Maths Question-17
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q17
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q17.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q17.2

Ex 10.3 Class 11 Maths Question-18
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q18
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q18.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 Q18.2

NCERT Solutions for Class 11 Maths Chapter 10 Miscellaneous Solutions

Miscellaneous Exercise Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q1
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q1.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q1.2

Miscellaneous Exercise Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q2
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q2.1

Miscellaneous Exercise Class 11 Maths Question-3
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q3
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q3.1

Miscellaneous Exercise Class 11 Maths Question-4
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q4
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q4.1

Miscellaneous Exercise Class 11 Maths Question-5
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q5
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q5.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q5.2

Miscellaneous Exercise Class 11 Maths Question-6
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q6
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q6.1

Miscellaneous Exercise Class 11 Maths Question-7
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q7
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q7.1

Miscellaneous Exercise Class 11 Maths Question-8
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q8
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q8.1

Miscellaneous Exercise Class 11 Maths Question-9
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q9
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q9.1

Miscellaneous Exercise Class 11 Maths Question-10

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q10
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q10.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q10.2

Miscellaneous Exercise Class 11 Maths Question-11
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q11
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q11.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q11.2
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q11.3

Miscellaneous Exercise Class 11 Maths Question-12
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q12
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q12.1

Miscellaneous Exercise Class 11 Maths Question-13
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q13
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q13.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q13.2

Miscellaneous Exercise Class 11 Maths Question-14
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q14
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q14.1

Miscellaneous Exercise Class 11 Maths Question-15
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q15
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q15.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q15.2

Miscellaneous Exercise Class 11 Maths Question-16
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q16
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q16.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q16.2

Miscellaneous Exercise Class 11 Maths Question-17
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q17
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q17.1

Miscellaneous Exercise Class 11 Maths Question-18
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q18
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q18.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q18.2

Miscellaneous Exercise Class 11 Maths Question-19
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q19
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q19.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q19.2

Miscellaneous Exercise Class 11 Maths Question-20
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q20
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q20.1

Miscellaneous Exercise Class 11 Maths Question-21
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q21
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q21.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q21.2

Miscellaneous Exercise Class 11 Maths Question-22
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q22
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q22.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q22.2

Miscellaneous Exercise Class 11 Maths Question-23
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q23
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q23.1

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q23.2

Miscellaneous Exercise Class 11 Maths Question-24
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q24
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q24.1
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Miscellaneous Ex Q24.2

Maths NCERT Solutions Class 11 Maths Chapter 10 Exercise.10.1

Q-1. Construct a quadrilateral in the Cartesian plane with vertices (-2, 5), (0, 6), (4, -4) and (-3, -1). Also, find the area of the quadrilateral.

Q-2. Consider an equilateral triangle, each of whose sides are 2b which lies on the y- axis in such a manner that, the mid-point of each of its base is at the origin. Obtain all the vertices of the equilateral triangle.

Q-3. What is the distance between X (a1, b1) and Y (a2, b2) if:

(a) XY is parallel to x- axis

(b) XY is parallel to y- axis

Q-4. Consider two points (6, 5) and (4, 2). Get a point on the y- axis which is equivalent from the given two points.

Q-5. What is the slope of a line passing through the origin and, the mid- point of the line- segment joining the two points O (0, -5) and A (9, 0)?

Q-6. Prove that the points (5, 5), (4, 6) and (-2, -2) are the vertices of the right- angled triangle, without using Pythagoras theorem.

Q-7. What is the slope of the line which makes an angle 60∘ along the positive direction of the Y- axis which is measured in anticlockwise sequence.

Q-8. What will be the value of a so that the points (a, -2), (3, 2) and (5, 6) get collinear to each other?

Q-9. Prove that the points (-3, -2), (5, 0), (4, 4) and (-4, 2) are the vertices of a parallelogram without using the distance formula.

Q-10. Consider two points (4, -2) and (5, -3). What is the angle between the x- axis and the line joining the given two points?

Q-12. Consider a line passing through two points (a1, b1) and (j, k). Assume that the slope of the line passing through these points is m. Prove that:

k – b1 = m (j – a1).

Q-14. Take the records of the population and year graph given below. What will be the slope of the line XY? By using this, find the population in the year 2005.

NCERT Solutions for Class 11 Maths All Chapters

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series

Ex 9.1 Class 11 Maths 

Sequences and Series Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series All Exercises were prepared by Experienced LearnCBSE.in Teachers.

Free download NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1, Ex 9.2, Ex 9.3, Ex 9.4 and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series

Topics and Sub Topics in Class 11 Maths Chapter 9 Sequences and Series:

Section NameTopic Name
9Sequences and Series
9.1Introduction
9.2Sequences
9.3Series
9.4Arithmetic Progression (A.P.)
9.5Geometric Progression (G.P.)
9.6Relationship Between A.M. and G.M.
9.7Sum to n terms of Special Series

 NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.1

Ex 9.1 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-1
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q1.1

Ex 9.1 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q2.1

More Resources for CBSE Class 11

Ex 9.1 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-5
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q3.1

Ex 9.1 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-7
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q4.1

Ex 9.1 Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q5.1

Ex 9.1 Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-11
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-12

Ex 9.1 Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-13
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q7.1

Ex 9.1 Class 11 Maths Question 8:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q8
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q8.1

Ex 9.1 Class 11 Maths Question 9:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-17
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q9.1

Ex 9.1 Class 11 Maths Question 10:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q10
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q10.1

Ex 9.1 Class 11 Maths Question 11:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-21
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-22

Ex 9.1 Class 11 Maths Question 12:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q12
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 Q12.1

Ex 9.1 Class 11 Maths Question 13:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-25
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-26

Ex 9.1 Class 11 Maths Question 14:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-27
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-28

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series (अनुक्रम तथा श्रेणी) Hindi Medium Ex 9.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Exercise 9.1
11 Maths Chapter 9 Sequences and Series Exercise 9.1 in Hindi Medium
11 Maths Chapter 9 Exercise 9.1 in Hindi Medium
Class 11 Maths Chapter 9 Optional Exercise 9.1 all question answers in hindi
Class 11 Maths Chapter 9 Optional Exercise 9.1 for up, gujrat, mp board cbse
Class 11 Maths Chapter 9 Optional Exercise 9.1 download free pdf

NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.2

Ex 9.2 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-2

Ex 9.2 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-4
Ex 9.2 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-5
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-6
Ex 9.2 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-8
Ex 9.2 Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-9
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-10
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-11
Ex 9.2 Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-12
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-13
Ex 9.2 Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q7.1
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-16

Ex 9.2 Class 11 Maths Question 8:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q8
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q8.1

Ex 9.2 Class 11 Maths Question 9:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-19
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q9.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q9.2

Ex 9.2 Class 11 Maths Question 10:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-22
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-23
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-24

Ex 9.2 Class 11 Maths Question 11:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q11
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q11.1
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-27
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q11.3

Ex 9.2 Class 11 Maths Question 12:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q12
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-30
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-31

Ex 9.2 Class 11 Maths Question 13:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q13
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q13.1
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-34

Ex 9.2 Class 11 Maths Question 14:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q14
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-36

Ex 9.2 Class 11 Maths Question 15:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q15
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-38

Ex 9.2 Class 11 Maths Question 16:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q16
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-40
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-41

Ex 9.2 Class 11 Maths Question 17:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q17
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q17.1

Ex 9.2 Class 11 Maths Question 18:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.2 Q18
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-45

NCERT Solutions for class 11 Maths Chapter 9 Exercise 9.3

Ex 9.3 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q1
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-2

Ex 9.3 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q2
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q2.1

Ex 9.3 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q3.1

Ex 9.3 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q4
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-8

Ex 9.3 Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-9
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q5.1
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-11
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q5.3

Ex 9.3 Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-13
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q6.1

Ex 9.3 Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-15
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q7.1

Ex 9.3 Class 11 Maths Question 8:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q8
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-18
Ex 9.3 Class 11 Maths Question 9:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-19
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q9.1

Ex 9.3 Class 11 Maths Question 10:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q10
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-22
Ex 9.3 Class 11 Maths Question 11:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-23
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-24
Ex 9.3 Class 11 Maths Question 12:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-25
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q12.1
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-27

Ex 9.3 Class 11 Maths Question 13:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-28
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-29
Ex 9.3 Class 11 Maths Question 14:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-30
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-31
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-32
Ex 9.3 Class 11 Maths Question 15:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q15
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q15.1
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-35

Ex 9.3 Class 11 Maths Question 16:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q16
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q16.1
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-38

Ex 9.3 Class 11 Maths Question 17:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-40
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-41
Ex 9.3 Class 11 Maths Question 18:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q18
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q18.1

Ex 9.3 Class 11 Maths Question 19:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q19
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-45
Ex 9.3 Class 11 Maths Question 20:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q20
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-47
Ex 9.3 Class 11 Maths Question 21:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q21
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-49
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-50
Ex 9.3 Class 11 Maths Question 22:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q22
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q22.1

Ex 9.3 Class 11 Maths Question 23:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-53
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-54
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q23.2

Ex 9.3 Class 11 Maths Question 24:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q24
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-57

Ex 9.3 Class 11 Maths Question 25:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q25
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q25.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q25.2

Ex 9.3 Class 11 Maths Question 26:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q26
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q26.1

Ex 9.3 Class 11 Maths Question 27:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-63
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-64
Ex 9.3 Class 11 Maths Question 28:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q28
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q28.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q28.2

Ex 9.3 Class 11 Maths Question 29:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-68
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q29.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q29.2

Ex 9.3 Class 11 Maths Question 30:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q30
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-72

Ex 9.3 Class 11 Maths Question 31:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q31
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-74
Ex 9.3 Class 11 Maths Question 32:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-75
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.3 Q32.1

NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.4

Ex 9.4 Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-1
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-2
Ex 9.4 Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-3
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-4
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-5
Ex 9.4 Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-6
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-7
Ex 9.4 Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-8
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-9
Ex 9.4 Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-10
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.4 Q5.1
Ex 9.4 Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-12
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-13
Ex 9.4 Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-14
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.4 Q7.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.4 Q7.2

Ex 9.4 Class 11 Maths Question 8:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-17
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-18
Ex 9.4 Class 11 Maths Question 9:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-19
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.4 Q9.1
Ex 9.4 Class 11 Maths Question 10:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.4 Q10
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-22

Class 11 Maths NCERT Miscellaneous Solutions

Miscellaneous Exercise Class 11 Maths Question 1:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-1
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q1.1
Miscellaneous Exercise Class 11 Maths Question 2:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-3
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-4
Miscellaneous Exercise Class 11 Maths Question 3:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q3
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q3.1
Miscellaneous Exercise Class 11 Maths Question 4:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-7
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q4.1
Miscellaneous Exercise Class 11 Maths Question 5:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q5
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q5.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q5.2

Miscellaneous Exercise Class 11 Maths Question 6:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q6
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q6.1
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-14

Miscellaneous Exercise Class 11 Maths Question 7:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-16
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q7.2

Miscellaneous Exercise Class 11 Maths Question 8:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q8
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-19
Miscellaneous Exercise Class 11 Maths Question 9:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-20
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q9.1
Miscellaneous Exercise Class 11 Maths Question 10:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-22
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-23
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-24
Miscellaneous Exercise Class 11 Maths Question 11:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q11
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q11.1
Miscellaneous Exercise Class 11 Maths Question 12:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-27
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-28
Miscellaneous Exercise Class 11 Maths Question 13:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-29
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q13.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q13.2

Miscellaneous Exercise Class 11 Maths Question 14:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q14
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q14.1
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-34
Miscellaneous Exercise Class 11 Maths Question 15:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-35
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-36
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-37
Miscellaneous Exercise Class 11 Maths Question 16:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-38
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series-39
Miscellaneous Exercise Class 11 Maths Question 17:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q17
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q17.1

Miscellaneous Exercise Class 11 Maths Question 18:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q18
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q18.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q18.2

Miscellaneous Exercise Class 11 Maths Question 19:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q19
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q19.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q19.2

Miscellaneous Exercise Class 11 Maths Question 20:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q20
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q20.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q20.2

Miscellaneous Exercise Class 11 Maths Question 21:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q21
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q21.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q21.2

Miscellaneous Exercise Class 11 Maths Question 22:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q22
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q22.1

Miscellaneous Exercise Class 11 Maths Question 23:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q23
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q23.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q23.2

Miscellaneous Exercise Class 11 Maths Question 24:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q24
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q24.1
Miscellaneous Exercise Class 11 Maths Question 25:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q25
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q25.1

Miscellaneous Exercise Class 11 Maths Question 26:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q26
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q26.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q26.2

Miscellaneous Exercise Class 11 Maths Question 27:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q27
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q27.1

Miscellaneous Exercise Class 11 Maths Question 28:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q28
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q28.1

Miscellaneous Exercise Class 11 Maths Question 29:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q29
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q29.1

Miscellaneous Exercise Class 11 Maths Question 30:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q30
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q30.1

Miscellaneous Exercise Class 11 Maths Question 31:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q31
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q31.1

Miscellaneous Exercise Class 11 Maths Question 32:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q32
Ans:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Miscellaneous Ex Q32.1

NCERT Solutions for Class 11 Maths All Chapters

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem

Binomial Theorem Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem All Exercises were prepared by Experienced LearnCBSE.in Teachers.

Free download NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1, Ex 8.2, and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem

Topics and Sub Topics in Class 11 Maths Chapter 8 Binomial Theorem:

Section NameTopic Name
8Binomial Theorem
8.1Introduction
8.2Binomial Theorem for Positive Integral Indices
8.3General and Middle Terms

NCERT Solutions for Class 11 Maths Chapter 8 Exercise.8.1

Ex 8.1 Class 6 Maths Question-1

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q1

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q1.1

Ex 8.1 Class 6 Maths Question-2

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q2

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q2.1

More Resources for CBSE Class 11

Ex 8.1 Class 6 Maths Question-3

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q3

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q3.1

Ex 8.1 Class 6 Maths Question-4

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q4

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q4.1

Ex 8.1 Class 6 Maths Question-5

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q5

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q5.1

Ex 8.1 Class 6 Maths Question-6

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q6

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q6.1

Ex 8.1 Class 6 Maths Question-7

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q7

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q7.1

Ex 8.1 Class 6 Maths Question-8

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q8

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q8.1

Ex 8.1 Class 6 Maths Question-9

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q9

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q9.1

Ex 8.1 Class 6 Maths Question-10

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q10

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q10.1

Ex 8.1 Class 6 Maths Question-11

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q11

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q11.1

Ex 8.1 Class 6 Maths Question-12

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q12

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q12.1

Ex 8.1 Class 6 Maths Question-13

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q13

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q13.1

Ex 8.1 Class 6 Maths Question-14

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q14

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.1 Q14.1

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem (द्विपद प्रमेय) Hindi medium Ex 8.1

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem
NCERT Solutions for Class 11 Maths Chapter 8 Exercise 8.1
NCERT Solutions for Class 11 Maths Chapter 8 Exercise 8.1 in Hindi medium
11 Maths Exercise 8.1 solutions11 Maths Exercise 8.1 solutions
11 Maths Exercise 8.1 Binomial Theorem solutions
Class 11 Maths Binomial Theorem Exercise 8.1 all question answers

NCERT Solutions for Class 11 Maths Chapter 8 Exercise.8.2

Ex 8.2 Class 11 Maths Question-1

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q1

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q1.1

Ex 8.2 Class 11 Maths Question-2

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q2

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q2.1

Ex 8.2 Class 11 Maths Question-3

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q3

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q3.1

Ex 8.2 Class 11 Maths Question-4

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q4

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q4.1

Ex 8.2 Class 11 Maths Question-5

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q5

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q5.1

Ex 8.2 Class 11 Maths Question-6

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q6

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q6.1

Ex 8.2 Class 11 Maths Question-7

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q7

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q7.1

Ex 8.2 Class 11 Maths Question-8

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q8

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q8.1

Ex 8.2 Class 11 Maths Question-9

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q9

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q9.1

Ex 8.2 Class 11 Maths Question-10

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q10

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q10.1
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q10.2

Ex 8.2 Class 11 Maths Question-11

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q11

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q11.1
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q11.2

Ex 8.2 Class 11 Maths Question-12

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q12

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 Q12.1

NCERT Solutions for Class 11 Maths Chapter 8 Miscellaneous Solutions

Miscellaneous Exercise Class 11 Maths Question-1

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q1

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q1.1
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q1.2

Miscellaneous Exercise Class 11 Maths Question-2

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q2

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q2.1
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q2.2

Miscellaneous Exercise Class 11 Maths Question-3

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q3

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q3.1

Miscellaneous Exercise Class 11 Maths Question-4

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q4

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q4.1

Miscellaneous Exercise Class 11 Maths Question-5

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q5

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q5.1

Miscellaneous Exercise Class 11 Maths Question-6

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q6

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q6.1

Miscellaneous Exercise Class 11 Maths Question-7

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q7

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q7.1

Miscellaneous Exercise Class 11 Maths Question-8

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q8

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q8.1
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q8.2

Miscellaneous Exercise Class 11 Maths Question-9

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q9

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q9.1
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q9.2

Miscellaneous Exercise Class 11 Maths Question-10

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q10

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Miscellaneous Ex Q10.1

NCERT Solutions for Class 11 Maths All Chapters

NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combinations

Permutations and Combinations Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations All Exercises were prepared by Experienced LearnCBSE.in Teachers.

Free download NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Ex 7.1, Ex 7.2, Ex 7.3 , Ex 7.4 and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combinations

Topics and Sub Topics in Class 11 Maths Chapter 7 Permutation and Combinations:

Section NameTopic Name
7Permutations and Combinations
7.1Introduction
7.2Lundamental Principle of Counting
7.3Permutations
7.4Combinations

NCERT Solutions for Class 11 Maths Chapter 7 Exercise.7.1

Ex 7.1 Class 6 Maths Question-1
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Ex 7.1 Class 6 Maths Question-2
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Ex 7.1 Class 6 Maths Question-3
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Ex 7.1 Class 6 Maths Question-4
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Ex 7.1 Class 6 Maths Question-5
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Ex 7.1 Class 6 Maths Question-6
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NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations (क्रमचय और संचयं) Hindi medium Ex 7.1

NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations (क्रमचय और संचयं)
NCERT Solutions for class 11 Maths Exercise 7.1 in English medium updated for 2018-19
NCERT Solutions for class 11 Maths Exercise 7.1 in Hindi medium
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NCERT Solutions for Class 11 Maths Chapter 7 Exercise.7.2

Ex 7.2 Class 11 Maths Question-1
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Ex 7.2 Class 11 Maths Question-2
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Ex 7.2 Class 11 Maths Question-3
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Ex 7.2 Class 11 Maths Question-4
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Ex 7.2 Class 11 Maths Question-5
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NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.3

Ex 7.3 Class 11 Maths Question-1
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Ex 7.3 Class 11 Maths Question-2
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Ex 7.3 Class 11 Maths Question-3
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Ex 7.3 Class 11 Maths Question-4
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Ex 7.3 Class 11 Maths Question-5
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Ex 7.3 Class 11 Maths Question-6
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Ex 7.3 Class 11 Maths Question-7
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NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combinations Ex 7.3 Q7.2

Ex 7.3 Class 11 Maths Question-8
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Ex 7.3 Class 11 Maths Question-9
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Ex 7.3 Class 11 Maths Question-10
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Ex 7.3 Class 11 Maths Question-11
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NCERT Solutions for Class 11 Maths Chapter 7 Exercise.7.4

Ex 7.4 Class 11 Maths Question-1
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Ex 7.4 Class 11 Maths Question-2
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Ex 7.4 Class 11 Maths Question-3
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Ex 7.4 Class 11 Maths Question-4
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Ex 7.4 Class 11 Maths Question-5
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Ex 7.4 Class 11 Maths Question-6
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Ex 7.4 Class 11 Maths Question-7
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Ex 7.4 Class 11 Maths Question-8
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Ex 7.4 Class 11 Maths Question-9
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NCERT Solutions for Class 11 Maths Chapter 7  Miscellaneous Solutions

Miscellaneous Exercise Class 11 Maths Question-1
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Miscellaneous Exercise Class 11 Maths Question-2
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Miscellaneous Exercise Class 11 Maths Question-3
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Miscellaneous Exercise Class 11 Maths Question-4
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Miscellaneous Exercise Class 11 Maths Question-5
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Miscellaneous Exercise Class 11 Maths Question-6
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Miscellaneous Exercise Class 11 Maths Question-7
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Miscellaneous Exercise Class 11 Maths Question-8
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Miscellaneous Exercise Class 11 Maths Question-9
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Miscellaneous Exercise Class 11 Maths Question-10
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Miscellaneous Exercise Class 11 Maths Question-11
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NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Ex 7.1 in Hindi Medium

प्रश्नावली 7.1

Ex 7.1 Class 11 Maths प्रश्न 1.
अंक 1, 2, 3, 4 और 5 से कितनी 3 अंकीय संख्याएँ बनाई जा सकती हैं, यदि
(i) अंकों की पुनरावृत्ति की अनुमति हो।
(ii) अंकों की पुनरावृत्ति की अनुमति नहीं हो।
हल:
3 अंकीय संख्या में 3 स्थान होते हैं : इकाई, दहाई और सैकड़ा।
(i) इकाई का स्थान 5 तरीकों से भरा जा सकता है क्योंकि 1, 2, 3, 4, 5 में से कोई भी एक अंक लिया जा सकता है।
दहाई का स्थान भी 5 तरीकों से भरा जा सकता है क्योंकि पुनरावृत्ति की अनुमति है।
1, 2, 3, 4, 5 में से कोई भी अंक लिया जा सकता है।
इसी प्रकार सैकड़े का स्थान भी 5 तरीकों से भरा जा सकता है।
3 अंकीय संख्याओं की संख्या = 5 x 5 x 5 = 125.

(ii) इकाई का स्थान 1, 2, 3, 4, 5 में से कोई-से एक अंक को लेकर 5 तरीकों से भरा जा सकता है।
दहाई का स्थान 4 तरीकों से भरा जा सकता है क्योंकि एक अंक पहले ही चयनित कर लिया गया। पुनरावृत्ति की अनुमति नहीं है।
सैकड़े का स्थान 3 तरीकों से भरा जा सकता है क्योंकि 2 अंक पहले ही चयनित कर लिए गए हैं।
3 अंकीय संख्याओं की संख्या = 5 x 4 x 3 = 60.

Ex 7.1 Class 11 Maths प्रश्न 2.
अंकः1, 2, 3, 4, 5, 6 से कितनी 3 अंकीय सम संख्याएँ बनाई जा सकती हैं, यदि अंकों की पुनरावृत्ति की जा सकेती है?
हल:
इकाई का स्थान 2, 4, 6 में से एक को लेकर 3 तरीकों से भरा जा सकता है।
क्योंकि पुनरावृत्ति की जा सकती है, दहाई का स्थान 6 तरीकों से भरा जा सकता है।
इसी प्रकार सैकड़े का स्थान भी 6 तरीकों से ही भरा जा सकता है।
3 अंकीय संख्याओं की संख्या = 6 x 6 x 3 = 108.

Ex 7.1 Class 11 Maths प्रश्न 3.
अंग्रेजी वर्णमाला के प्रथम 10 अक्षरों से कितने 4 अक्षरों के कोड बनाए जा सकते हैं, यदि किसी भी अक्षर की पुनरावृत्ति नहीं की जा सकती?
हल:
4 अक्षरों वाले कोड में 4 स्थान हैं। प्रत्येक अक्षर के लिए एक स्थान चाहिए।
पहले स्थान को 10 तरीकों से, दूसरे स्थान को 9 तरीकों से, तीसरे स्थान को 8 तरीकों से और चौथे स्थान को 7 तरीकों से भर सकते हैं क्योंकि पुनरावृत्ति की अनुमति नहीं है।
एक अक्षर दुबारा नहीं लिखा जा सकता।
चार अक्षर वाले कोडों की संख्या = 10 x 9 x 8 x 7 = 5040.

Ex 7.1 Class 11 Maths प्रश्न 4.
0 से 9 तक के अंकों का प्रयोग करके कितने 5 अंकीय टेलीफोन नम्बर बनाए जा सकते हैं, यदि प्रत्येक नम्बर 67 से आरम्भ होता है और कोई अंक एक बार से अधिक नहीं आता है?
हल:
पांच अंकीय नम्बर में 5 स्थान हैं जिसमें पहले और दूसरे को I और II से निरूपित किया गया है। I और II स्थान पर 6 और 7 को रखा गया है।
शेष 8 अंकों में से एक-एक अंक लेकर I, IV और V स्थान को भरना है। स्थान III को 8 तरीकों से, स्थान IV को 7 तरीकों से तथा स्थान V को 6 तरीकों से भर सकते है।
5 अंकीय टेलीफोन नम्बरों की संख्या = 8 x 7 x 6 = 336 .

Ex 7.1 Class 11 Maths प्रश्न 5.
एक सिक्का तीन बार उछाला जाता है और परिणाम अंकित कर लिए जाते हैं। परिणामों की संभव संख्या क्या है?
हल:
एक बार सिक्का उछालने से दो में से एक भाग ऊपर आता है अर्थात T या H जबकि H चित्त और T पट को निरूपित करते हैं।
एक बार सिक्का उछालने से दो परिणाम होते हैं।
तीन बार सिक्का उछालने से 2 x 2 x 2 = 8 परिणाम होंगे।
ये परिणाम इस प्रकार है :
TTT, TTH, THT, HTT, HHT, HTH, THH, HHH

Ex 7.1 Class 11 Maths प्रश्न 6.
भिन्न-भिन्न रंगों के 5 झंडे दिए हुए हैं। इससे कितने विभिन्न संकेत बनाए जा सकते हैं, यदि प्रत्येक संकेत में 2 झंडों, एक के नीचे दूसरे के प्रयोग की आवश्यक पड़ती है?
हल:
झंडे के ऊपर का स्थान भरने के 5 तरीके हैं। एक झंडा प्रयोग होने के बाद 4 झंडे रह जाते हैं। नीचे का दूसरा स्थान 4 तरीकों से भरा जा सकता है।
कुल संकेतों की संख्या = 5 x 4 = 20.

Exercise- 7.1

Q-1: Form 3- digit numbers by using digits 4, 5, 6, 7 and 8 and assume that

(i) The digits can be repeated.

(ii) Digits can’t be repeated in the 3- digit number.

Q-2: Form a 3- digit number which should be even by using 1, 2, 3, 6, 8, and 9. Note that, repetition of digits is allowed.

Q-3: Find the total number of 4- letter code formed by using the 10 English alphabets, i.e., a, b, c, d, e, f, g, h, i and j. Assume that the repetition of the letters of English alphabet is not allowed.

Q-4: Find the total number of 5- digit telephone numbers formed by using the numbers from 0 to 9. Note that, each of the telephone number will start with 36 and the repetition of the numbers is not allowed.

Q-5: Consider a scenario when a person tosses a coin. He tosses the coin for two times and every time the outcome of the toss is recorded by one of his friend. Find the total number of possible outcomes of the coin his friend will record.

Q-6: Consider 5 flags which are of different colors. Find the total possibility of getting different signals. Note that, each of the signals requires the use of any two flags at the same time, one after the other.

EXERCISE- 7.2

Q-1: Evaluate:

(i). 8!                                                                    (ii). 4! – 3!

Q-2: Is 3! + 4! = 7! ?

EXERCISE – 7.3

Q-1: If there is no repetition of numbers, then find the total of 3- digit numbers formed by using digits from 2 to 9.

Q-2: Find the total number of 4- digits numbers where there is no repetition of digits.

Q-3: Find the total number of 3- digit number which is even and is formed by using the digits 2, 3, 4, 5, 6, 7 and 8. Note that repetition of digit is restricted.

Q-4: How many 4- digit numbers will be formed by using the digits 2, 3, 4, 5 and 6. Note that, repetition of digits is not allowed. Find among those numbers, how many numbers will be even number?

Q-5: Consider a committee with 9 persons, in how many ways can we choose a chairman and a vice chairman? Note that, a person can hold only one position at a time.

Q-8: Get all the number of ways, with or without the meaning, which might be formed by using the letters from the word EQUATION. Note that, repetition of the word is restricted.

Q-9: Find the number of words, with or without the meaning, which might be formed by using the letters from the word MONDAY. Note that, repetition of the word is restricted, if

(i) At a time, 3 letters can be used.

(ii) All the letters can be used at a time.

(iii) First letter is a vowel and all the letters are being used.

Q-10: Find the number of distinct permutations such that 4 I’s does not come together in the word MISSISSIPPI.

Q-11: Arrange the letters of the word PERMUTATIONS and observe the number of ways of the permutation if,

(i). the new word starts with P and ends with S.

(ii). when the vowels are taken all together.

(iii). there will always be 4 letters between P and S.

EXERCISE – 7.4

Q-3: Find total number of chords which can be drawn through 21 points on the circle.

Q-4: Find the number of ways in which a team of 2 boys and 2 girls can be selected from the group of 5 boys and 4 girls.

Q-5: In how many ways will 9 balls be selected from 7 red balls, 6 blue balls and 5 white balls if every time 3 balls of different colors be selected?

Q-6: Find out the number of combinations of 5 cards from a deck of 52 cards. Assume that there is at least one ace in each of the combinations.

Q-7: Find the number of ways by which one can select a cricket team of 11 players from a bunch of 17 players among which only 5 players can bowl if every cricket team of 11 players must have exactly 4 bowlers.

Q-8: There are 6 black and 5 red balls. Find the number of ways through which 3 black and 3 red balls will be selected.

Q-9: Find the number of ways by which a student can choose a program of 5 courses, if there are options of 10 courses and for every student 2 courses are made compulsory.

MISCELLANEOUS EXERCISE

Q-1: Find the number of words, having meaning or meaningless, each of 2 vowels and 4 consonants will be formed by the letters of the word DAUGHTER?

Q-2: Find the number of words, which can be either meaningful or meaningless, which will be formed by using all of the letters of the word EQUATION at a time such that both the vowel and the consonant will occur together.

Q-3: There are 10 boys and 5 girls through which a committee with 7 members has to be formed. Now, find the number of ways in which this might be created when the committee formed consists of:

(i) Exactly 4 girls                          (ii) at least 4 girls                            (iii) almost 4 girls?

Q-4: In a dictionary, the permutation of the letters of the word EXAMINATION is listed, then find the total number of words in the list of dictionary before the first letter of the word start with E.

Q-5: Find the total number of 6- digit numbers formed by using the digits 0, 2, 3, 4, 5 and 6 which should be divisible by 10. Note that, the repetition of digit is not allowed.

Q-6: It is known that the English alphabet has 21 consonants and 5 vowels. Find the number of words formed with 4 different consonants and 3 different vowels from the English alphabet.

Q-7: There are 12 questions in the question paper of an examination which is mainly divided into two parts, say, part-I and part-II, each having 4 and 8 questions, respectively. There is a condition given in the question paper that the student has to attempt at least 8 questions for sure, selection 3 from each section. Now, find the number of ways in which a student can select the questions in the question paper.

Q-8: Find the number of ways of 5- card combinations from a deck of 52 cards. Note that, among those 5 cards, there must be exactly one king in the combination.

Q-9: Consider a situation in which 7 men and 6 women needs to be seated in a row in such a way that the women will occupy the even places.

Q-10: There are 20 students in a class from which 8 students will be chosen for an exclusion party. 3 students from the class decided that either they will join combinely or none of them will go for the exclusion party. Find the number of ways by which the exclusion party will be chosen.

Q-11: Arrange ASSASSINATION in such a way that all the S’s are filled together. Find the number ways for the arrangement of S’s together.

NCERT Solutions for Class 11 Maths All Chapters