ncert solutions class 12 maths

NCERT Solutions for Class 12 Maths has been written to help students like you who are appearing for different board exams as well as the JEE. It provides sound knowledge and understanding of all important concepts covered in each chapter in the Class 12 Maths NCERT textbook. There are 13 important chapters from the NCERT textbook. Both problems and their detailed solutions are provided. The solutions have been devised by India’s best teachers to help students grasp basic concepts better and faster.

NCERT Solutions For Class 12 Maths Chapter 13 Probability

NCERT Solutions for Class 12 Maths Chapter 13 Probability is designed and prepared by the best teachers across India. All the important topics are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

Chapter 13 Probability Solutions covers multiple exercises. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. This will prove to be most helpful to you in your home assignments as well as practice sessions.
The topics and sub-topics included in Chapter 13 Probability the following:

Section NameTopic Name
13Probability
13.1Introduction
13.2Conditional Probability
13.3Multiplication Theorem on Probability
13.4Independent Events
13.5Bayes’ Theorem
13.6Random Variables and its Probability Distributions
13.7Bernoulli Trials and Binomial Distribution

NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.1

Ex 13.1 Class 12 Maths Question 1
Given that E and Fare events such that
P (E) = 0.6, P (F) = 0.3 and P(E∩F) = 0.2
find P(E|F) and P (F|E).
Solution:
NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.1 Q 1

Ex 13.1 Class 12 Maths Question 2
Compute P(A|B) if P(B)=0.5 and P (A∩B) = 0.32.
Solution:
NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.1 Q 2

Class 12 Maths Probability Solutions

Ex 13.1 Class 12 Maths Question 3.
If P (A)=0.8, P (B)=0.5 and P(B/A)=0.4, find
(i) P(A∩B)
(ii) P(A/B)
(iii)P(A∪B)
Solution:
NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.1 Q 3

Ex 13.1 Class 12 Maths Question 4.
Evaluate P(A∪B) if 2P(A) = P(B) = 513 and P(A|B) = 25.
Solution:
NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.1 Q 4

Ex 13.1 Class 12 Maths Question 5.
If P(A) = 611,P(B) =511 and P(A∪B) = 711,
Find
(i) P(A∩B)
(ii) P(A|B)
(iii) P(B|A)
Solution:
NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.1 Q 5

Ex 13.1 Class 12 Maths Question 6.
Determine P(E/F) in question 6 to 9:
A coin is tossed three times, where
(i) E: head on third toss F: heads on first two tosses.
(ii) E: at least two heads F : at most two heads
(iii) E: at most two tails F: at least one tail
Solution:
NCERT Solutions Class 12 Maths Chapter 13 Probability Ex 13.1 Q 6

Ex 13.1 Class 12 Maths Question 7.
Two coins are tossed once
(i) E: tail appears on one coin F: one coin shows head
(ii) E: no tail appears F: no head appears.
Solution:
NCERT Solutions Class 12 Maths Chapter 13 Probability Ex 13.1 Q 7

Ex 13.1 Class 12 Maths Question 8.
A die is thrown three times.
E: 4 appears on the third toss
F: 6 and 5 appears respectively on first two tosses.
Solution:
Class 12 Maths NCERT Solutions Chapter 13 Probability Ex 13.1 Q 8

Ex 13.1 Class 12 Maths Question 9.
Mother, father and son line up at random for a family picture:
E: son on one end, F: father in middle
Solution:
Class 12 Maths NCERT Solutions Chapter 13 Probability Ex 13.1 Q 9

Ex 13.1 Class 12 Maths Question 10.
A Mack and a red die are rolled.
(a) Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
(b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
Solution:
Class 12 Maths NCERT Solutions Chapter 13 Probability Ex 13.1 Q 10

Ex 13.1 Class 12 Maths Question 11
A fair die is rolled. Consider events E = {1,3,5} F = {2,3} and G = {2,3,4,5}, Find
(i) P(E|F) and P(F|E)
(ii) P(E|G) and P(G|E)
(iii) P((E ∪ F) |G) and P (E ∩ F)|G)
Solution:
Probability Class 12 Maths NCERT Solutions Chapter 13 Ex 13.1 Q 11

Ex 13.1 Class 12 Maths Question 12.
Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that
(i) the youngest is a girl,
(ii) at least one is girl?
Solution:
Probability Class 12 Maths NCERT Solutions Chapter 13 Ex 13.1 Q 12

Ex 13.1 Class 12 Maths Question 13.
An instructor has a question bank consisting of300 easy True/ False questions, 200 difficult True/ False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
Solution:
Probability Class 12 Maths NCERT Solutions Chapter 13 Ex 13.1 Q 13

Ex 13.1 Class 12 Maths Question 14.
Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.
Solution:
Probability Class 12 Maths NCERT Solutions Chapter 13 Ex 13.1 Q 14

Ex 13.1 Class 12 Maths Question 15.
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’ given that ‘at least one die shows a 3’.
Solution:
Probability Class 12 Maths NCERT Solutions Chapter 13 Ex 13.1 Q 15
Probability Maths Class 12 NCERT Solutions Chapter 13 Ex 13.1 Q 15-i
Probability Maths Class 12 NCERT Solutions Chapter 13 Ex 13.1 Q 15-ii

In each of the following choose the correct answer:

Ex 13.1 Class 12 Maths Question 16.
If P(A) = 12, P (B) = 0 then P (A | B) is
(a) 0
(b) 12
(c) not defined
(d) 1
Solution:
Probability Maths Class 12 NCERT Solutions Chapter 13 Ex 13.1 Q 16

Ex 13.1 Class 12 Maths Question 17.
If A and B are events such that P(A | B) = P(B | A) then
(a) A⊂B but A≠B
(b) A = B
(c) A∩B = φ
(d) P(A) = P(B)
Solution:
Probability Maths Class 12 NCERT Solutions Chapter 13 Ex 13.1 Q 17

Class 12 Maths NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming is designed and prepared by the best teachers across India. All the important topics are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

Chapter 12 – Linear Programming covers multiple exercises. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. This will prove to be most helpful to you in your home assignments as well as practice sessions.
The topics and sub-topics included in the Linear Programming chapter are the following:

Section NameTopic Name
12Linear Programming
12.1Introduction
12.2Linear Programming Problem and its Mathematical Formulation
12.3Different Types of Linear Programming Problems
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 1
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 2
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 3
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 4
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 5
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 6
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 7
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 8
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 9
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 10

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Hindi Medium Ex 12.1

NCERT Solutions for Class 12 Maths Exercise 12.1 of Linear Programming
NCERT Solutions for Class 12 Maths Exercise 12.1
12 Maths Exercise 12.1 Linear Programming
12 Maths Exercise 12.1 solutions
12 Maths Exercise 12.1 all answers
12 Maths Exercise 12.1 in Hindi Medium
Class 12 Maths Exercise 12.1 in Hindi medium
Class 12 Maths Exercise 12.1 for 2019-20
Class 12 Maths Exercise 12.1 updated
NCERT Solutions for Class 12 Maths Exercise 12.1 in PDF
NCERT Solutions for Class 12 Maths Exercise 12.1 for up board
NCERT Solutions for Class 12 Maths Exercise 12.1 in Hindi medium

Class 12 Maths NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry

NCERT Solutions for Class 12 Maths – Chapter 11 – Three Dimensional Geometry– is designed and prepared by the best teachers across India. All the important topics are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

Chapter 11 – Three Dimensional Geometry covers multiple exercises. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. This will prove to be most helpful to you in your home assignments as well as practice sessions.
The topics and sub-topics included in the Three Dimensional Geometry chapter are the following:

Section NameTopic Name
11Three Dimensional Geometry
11.1Introduction
11.2Direction Cosines and Direction Ratios of a Line
11.3Equation of a Line in Space
11.4Angle between Two Lines
11.5Shortest Distance between Two Lines
11.6Plane
11.7Coplanarity of Two Lines
11.8Angle between Two Lines
11.9Distance of a Point from a P
11.10Angle between a L ine and a Plane
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 1
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 2
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 3
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 4
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 5
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 6
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 7
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 8
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 9
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 10
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 11

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Hindi Medium Ex 11.1

NCERT Solutions for Class 12 Maths Exercise 11.1 of Three Dimensional Geometry
NCERT Solutions for Class 12 Maths Exercise 11.2 in Hindi Medium PDF
12 Maths exercise 11.1

Class 12 Maths NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

NCERT Solutions for Class 12th Maths Chapter 10 Vector Algebra

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra is designed and prepared by the best teachers across India. All the important topics are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

Chapter 10 – Vector Algebra covers multiple exercises. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. This will prove to be most helpful to you in your home assignments as well as practice sessions.
The topics and sub-topics included in the Vector Algebra chapter are the following:

Section NameTopic Name
10Vector Algebra
10.1Introduction
10.2Some Basic Concepts
10.3Types of Vectors
10.4Addition of Vectors
10.5Multiplication of a Vector by a Scalar
10.6Product of Two Vectors
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 1
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 2
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 3
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 4
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 5
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 6
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 7
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra 8

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Hindi Medium Ex 10.1

NCERT Solutions for Class 12 Maths Exercise 10.1 of Vector Algebra
NCERT Solutions for Class 12 Maths Exercise 10.1 in Hindi Medium PDF
12 Maths exercise 10.1
12 Maths Exercise 10.1 in Hindi Medium PDF

Class 12 Maths NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations– is designed and prepared by the best teachers across India. All the important topics are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

Chapter 9 – Differential Equations covers multiple exercises. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. This will prove to be most helpful to you in your home assignments as well as practice sessions.

The topics and sub-topics included in the Differential Equations chapter are the following:

Section NameTopic Name
9Differential Equations
9.1Introduction
9.2Basic Concepts
9.3General and Particular Solutions of a Differential Equation
9.4Formation of a Differential Equation whose General Solution is given
9.5Methods of Solving First order, First Degree Differential Equations
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 1
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 2
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 3
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 4
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 5
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 6
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 7
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 8

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Hindi Medium Ex 9.1

NCERT Solutions for Class 12 Maths Exercise 9.1 of Differential Equations
NCERT Solutions for Class 12 Maths Exercise 9.1 in PDF
12 Maths exercise 9.1
NCERT Solutions for Class 12 Maths Exercise 9.1 in Hindi Medium PDF

Class 12 Maths NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

NCERT Solutions for Class 12 Maths – Chapter 8 – Application of Integrals– is designed and prepared by the best teachers across India. All the important topics are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

Chapter 8 – Application of Integrals covers multiple exercises. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. This will prove to be most helpful to you in your home assignments as well as practice sessions.
The topics and sub-topics included in the Integrals chapter are the following:

Section NameTopic Name
8Application of Integrals
8.1Introduction
8.2Area under Simple Curves
8.3Area between Two Curves
NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals 1
NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals 2
NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals 3
NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals 4
NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals 5
NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals 6
NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals 7
NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals 8

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Hindi Medium Ex 8.1

NCERT Solutions for class 12 Maths Chapter 8
NCERT Solutions for class 12 Maths Chapter 8 Exercise 8.1
NCERT Solutions for class 12 Maths Chapter 8 Exercise 8.1 in pdf form
NCERT Solutions for class 12 Maths Chapter 8 Exercise 8.1 in english medium
NCERT Solutions for class 12 Maths Chapter 8 Exercise 8.1 download free
NCERT Solutions for class 12 Maths Chapter 8 Exercise 8.1 for intermediate up board
NCERT Solutions for class 12 Maths Chapter 8 Exercise 8.1 for final year +2
NCERT Solutions for class 12 Maths Chapter 8 Exercise 8.1 inter second year
NCERT Solutions for class 12 Maths Chapter 8 Exercise 8.1 all question answers
class 12 Maths Chapter 8 Exercise 8.1 for final year +2
12 Maths Chapter 8 Exercise 8.1 for intermediate up board

Class 12 Maths NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 7 Integrals

The topics and sub-topics included in the Integrals chapter are the following:

Section NameTopic Name
7Integrals
7.1Introduction
7.2Integration as an Inverse Process of Differentiation
7.3Methods of Integration
7.4Integrals of some Particular Functions
7.5Integration by Partial Fractions
7.6Integration by Parts
7.7Definite Integral
7.8Fundamental Theorem of Calculus
7.9Evaluation of Definite Integrals by Substitution
7.10Some Properties of Definite Integrals

NCERT Solutions for Class 12 Maths Chapter 7  Integrals: Engineering aspirants and students appearing for CBSE Class 12 board exams must take the NCERT Mathematics textbooks seriously and finish them from top to bottom. They must also go through the NCERT solutions for Class 12 Maths and Class 11 Maths to have a better understanding of the various concepts. In this article, we will provide you with NCERT Solutions for Class 12 Maths Chapter 7 – Integrals which have been designed by the best teachers in India.

Free download NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11, Ex 7.10, Ex 7.9, Ex 7.8, Ex 7.7, Ex 7.6, Ex 7.5, Ex 7.4, Ex 7.3, Ex 7.2, Ex 7.1 Integrals 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.

Class 12 Maths Chapter 7 NCERT Solutions Integrals

NCERT Solutions for Class 12 Maths Chapter 7 – Integrals contains step-by-step and detailed solutions for every question.

  1. Introduction
  2. Integration as an Inverse Process of Differentiation
  3. Geometrical interpretation of indefinite integral
  4. Some properties of indefinite integral
  5. Comparison between differentiation and integration
  6. Methods of Integration
  7. Integration by substitution
  8. Integration using trigonometric identities
  9. Integrals of Some Particular Functions
  10. Integration by Partial Fractions
  11. Integration by Parts
  12. Integral of the type
  13. Integrals of some more types
  14. Definite Integral
  15. Definite integral as the limit of a sum
  16. Fundamental Theorem of Calculus
  17. Area function
  18. First fundamental theorem of integral calculus
  19. Second fundamental theorem of integral calculus
  20. Evaluation of Definite Integrals by Substitution
  21. Some Properties of Definite Integrals

Integrals Ex 7.1 Class 12

Ex 7.1 Class 12 Maths Question 1.
sin 2x
Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 1
Ex 7.1 Class 12 Maths Question 2.
cos 3x
Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 2
Ex 7.1 Class 12 Maths Question 3.
e2x
Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 3
Ex 7.1 Class 12 Maths Question 4.
(ax + c)²
Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 4
Ex 7.1 Class 12 Maths Question 5.
sin2x−4e3x
Ex 7.1 Class 12 Maths Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 5
Find the following integrals in Exercises 6 to 20 :

Ex 7.1 Class 12 Maths Question 6.
∫(4e3x+1)dx
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q 6
Ex 7.1 Class 12 Maths Question 7.
∫x2(1−1×2)dx
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q 7
Ex 7.1 Class 12 Maths Question 8.
∫(ax2+bx+c)dx
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q 8
Ex 7.1 Class 12 Maths Question 9.
∫(2×2+ex)dx
Solution:
Integrals Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 9
Ex 7.1 Class 12 Maths Question 10.
∫[x−−√−1x√]2dx
Solution:
Integrals Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 10
Ex 7.1 Class 12 Maths Question 11.
∫x3+5×2−4x2dx
Solution:
Integrals Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 11
Ex 7.1 Class 12 Maths Question 12.
∫x3+3x+4x√dx
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 12
Ex 7.1 Class 12 Maths Question 13.
∫x3−x2+x−1x−1dx
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 13
Ex 7.1 Class 12 Maths Question 14.
∫(1−x)x−−√dx
Solution:
Class 12 Maths NCERT Solutions Chapter 7 Ex 7.1 Q 14
Ex 7.1 Class 12 Maths Question 15.
∫x−−√(3×2+2x+3)dx
Solution:
Class 12 Maths NCERT Solutions Chapter 7 Ex 7.1 Q 15
Ex 7.1 Class 12 Maths Question 16.
∫(2x−3cosx+ex)dx
Solution:
Maths NCERT Class 12 Solutions Chapter 7 Integrals Ex 7.1 Q 16
Ex 7.1 Class 12 Maths Question 17.
∫(2×2−3sinx+5x−−√)dx
Solution:
Maths NCERT Class 12 Solutions Chapter 7 Integrals Ex 7.1 Q 17
Ex 7.1 Class 12 Maths Question 18.
∫secx(secx+tanx)dx
Solution:
Maths NCERT Class 12 Solutions Chapter 7 Integrals Ex 7.1 Q 18
Ex 7.1 Class 12 Maths Question 19.
∫sec2xcosec2xdx
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 19
Ex 7.1 Class 12 Maths Question 20.
∫2−3sinxcos2xdx
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 20

Choose the correct answer in Exercises 21 and 22.
Ex 7.1 Class 12 Maths Question 21.
The antiderivative (x−−√+1x√) equals
(a) 13×13+2×12+c
(b) 23×23+12×2+c
(c) 23×32+2×12+c
(d) 32×32+12×12+c
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 21
Ex 7.1 Class 12 Maths Question 22.
If ddxf(x)=4×3−3×4 such that f(2)=0 then f(x) is
(a) x4+1×3−1298
(b) x3+1×4+1298
(c) x4+1×3+1298
(d) x3+1×4−1298
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 22

Move to Top → Class 12 Integrals Chapter 7

Integrals Ex 7.2 Class 12

Integrate the functions in Exercises 1 to 37:

Ex 7.2 Class 12 Maths Question 1.
2×1+x2
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2 Q 1
Ex 7.2 Class 12 Maths Question 2.
(logx)2x
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2 Q 2
Ex 7.2 Class 12 Maths Question 3.
1x+xlogx
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2 Q 3
Ex 7.2 Class 12 Maths Question 4.
sinx sin(cosx)
Solution:
ncert solutions class 12 maths Chapter 7 Integrals Ex 7.2 Q 4
Ex 7.2 Class 12 Maths Question 5.
sin(ax+b) cos(ax+b)
Solution:
class 12 integration NCERT Solutions Chapter 7 Ex 7.2 Q 5
Ex 7.2 Class 12 Maths Question 6.
ax+b−−−−−√
Solution:
class 12 integration NCERT Solutions Chapter 7 Ex 7.2 Q 6
Ex 7.2 Class 12 Maths Question 7.
xx+2−−−−−√
Solution:
class 12 integration NCERT Solutions Chapter 7 Ex 7.2 Q 7
Ex 7.2 Class 12 Maths Question 8.
x1+2×2−−−−−−√
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 8

Ex 7.2 Class 12 Maths Question 9.
(4x+2)x2+x+1−−−−−−−−√
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 9
Ex 7.2 Class 12 Maths Question 10.
1x−x√
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 10
Ex 7.2 Class 12 Maths Question 11.
xx+4√,x>0
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 11
Ex 7.2 Class 12 Maths Question 12.
(x3−1)13.x5
Solution:
ncert class 12 maths solutions Integrals Ex 7.2 Q 12
Ex 7.2 Class 12 Maths Question 13.
x2(2+3×3)3
Solution:
ncert class 12 maths solutions Integrals Ex 7.2 Q 13
Ex 7.2 Class 12 Maths Question 14.
1x(logx)m,x>0
Solution:
ncert class 12 maths solutions Integrals Ex 7.2 Q 14
Ex 7.2 Class 12 Maths Question 15.
x9−4×2
Solution:
ncert class 12 maths solutions Integrals Ex 7.2 Q 14
Ex 7.2 Class 12 Maths Question 16.
e2x+3
Solution:
ncert maths solutions class 12 Integration Chapter 7 Ex 7.2 Q 16
Ex 7.2 Class 12 Maths Question 17.
xex2
Solution:
ncert maths solutions class 12 Integration Chapter 7 Ex 7.2 Q 17
Ex 7.2 Class 12 Maths Question 18.
etan−1×1+x2
Solution:
ncert maths solutions class 12 Integration Chapter 7 Ex 7.2 Q 18
Ex 7.2 Class 12 Maths Question 19.
e2x−1e2x+1
Solution:
integration ncert solutions Class 12 chapter 7 Ex 7.2 Q 19
Ex 7.2 Class 12 Maths Question 20.
e2x−e2xe2x+e−2x
Solution:
integration ncert solutions Class 12 chapter 7 Ex 7.2 Q 20
Ex 7.2 Class 12 Maths Question 21.
tan²(2x-3)
Solution:
∫tan²(2x-3)dx = ∫[sec²(2x-3)-1]dx = I
put 2x-3 = t
so that 2dx = dt
I = 12 ∫sec²t dt-x+c
= 12t−x+c
= 12tan(2x−3)−x+c
Ex 7.2 Class 12 Maths Question 22.
sec²(7-4x)
Solution:
maths class 12 ncert solutions Chapter 7 Integration Ex 7.2 Q 22
Ex 7.2 Class 12 Maths Question 23.
sin−1×1−x2√
Solution:
maths class 12 ncert solutions Chapter 7 Integration Ex 7.2 Q 23
Ex 7.2 Class 12 Maths Question 24.
2cosx−3sinx6cosx+4sinx
Solution:
Ex 7.2 class 12 maths NCERT Solutions Q 24
Ex 7.2 Class 12 Maths Question 25.
1cos2x(1−tanx)2
Solution:
Ex 7.2 class 12 maths NCERT Solutions Q 25
Ex 7.2 Class 12 Maths Question 26.
cosx√x√
Solution:
Ex 7.2 class 12 maths NCERT Solutions Q 26
Ex 7.2 Class 12 Maths Question 27.
sin2x−−−−−√cos2x
Solution:
Ex 7.2 class 12 maths NCERT Solutions Q 27
Ex 7.2 Class 12 Maths Question 28.
cosx1+sinx√
Solution:
Integration Solutions class 12 Maths Chapter 7 Ex 7.2 Q 28
Ex 7.2 Class 12 Maths Question 29.
cotx log sinx
Solution:
Integration Solutions class 12 Maths Chapter 7 Ex 7.2 Q 29
Ex 7.2 Class 12 Maths Question 30.
sinx1+cosx
Solution:
Integration Solutions class 12 Maths Chapter 7 Ex 7.2 Q 30
Ex 7.2 Class 12 Maths Question 31.
sinx(1+cosx)2
Solution:
NCERT Maths Class 12 Solutions Chapter 7 Ex 7.2 Q 31
Ex 7.2 Class 12 Maths Question 32.
11+cotx
Solution:
NCERT Maths Class 12 Solutions Chapter 7 Ex 7.2 Q 32
Ex 7.2 Class 12 Maths Question 33.
11−tanx
Solution:
NCERT Maths Class 12 Solutions Chapter 7 Ex 7.2 Q 33
Ex 7.2 Class 12 Maths Question 34.
tanx√sinxcosx
Solution:
NCERT Integration Solutions Ex 7.2 Q 34
Ex 7.2 Class 12 Maths Question 35.
(1+logx)2x
Solution:
NCERT Integration Solutions Ex 7.2 Q 35
Ex 7.2 Class 12 Maths Question 36.
(x+1)(x+logx)2x
Solution:
NCERT Integration Solutions Ex 7.2 Q 36
Ex 7.2 Class 12 Maths Question 37.
x3sin(tan−1×4)1+x8dx
Solution:
NCERT Integration Solutions Ex 7.2 Q 37
Choose the correct answer in exercises 38 and 39

Ex 7.2 Class 12 Maths Question 38.
∫10×9+10xloge10x10+10xdx
(a) 10x – x10 + C
(b) 10x + x10 + C
(c) (10x – x10) + C
(d) log (10x + x10) + C
Solution:
NCERT Integration Solutions Ex 7.2 Q 38
Ex 7.2 Class 12 Maths Question 39.
∫dxsin2xcos2x=
(a) tanx + cotx + c
(b) tanx – cotx + c
(c) tanx cotx + c
(d) tanx – cot2x + c
Solution:
NCERT Solutions for Class 12 Maths integrals Ex 7.2 Q 39

Move to Top → Class 12 Integrals Chapter 7

Integrals Ex 7.3 Class 12

Find the integrals of the functions in Exercises 1 to 22.
Ex 7.3 Class 12 Maths Question 1.
sin²(2x+5)
Solution:
Ex 7.3 Class 12 Maths NCERT Solutions Q 1
Ex 7.3 Class 12 Maths Question 2.
sin3x cos4x
Solution:
Ex 7.3 Class 12 Maths NCERT Solutions Q 2
Ex 7.3 Class 12 Maths Question 3.
∫cos2x cos4x cos6x dx
Solution:
Ex 7.3 Class 12 Maths NCERT Solutions Q 3
Ex 7.3 Class 12 Maths Question 4.
∫sin3(2x+1)dx
Solution:
Ex 7.3 Class 12 Maths NCERT Solutions Q 4
Ex 7.3 Class 12 Maths Question 5.
sin3x cos3x
Solution:
NCERT Solutions Integration Chapter 7 Ex 7.3 Q 5
Ex 7.3 Class 12 Maths Question 6.
sinx sin2x sin3x
Solution:
NCERT Solutions Integration Chapter 7 Ex 7.3 Q 6
Ex 7.3 Class 12 Maths Question 7.
sin 4x sin 8x
Solution:
NCERT Solutions Integration Chapter 7 Ex 7.3 Q 7
Ex 7.3 Class 12 Maths Question 8.
1−cosx1+cosx
Solution:
chapter 7 maths class 12 NCERT Solutions Ex 7.3 Q 8
Ex 7.3 Class 12 Maths Question 9.
cosx1+cosx
Solution:
Class 12 Maths Chapter 7 Solutions Ex 7.3 Q 9
Ex 7.3 Class 12 Maths Question 10.
∫sinx4 dx
Solution:
Class 12 Maths Chapter 7 Solutions Ex 7.3 Q 10
Ex 7.3 Class 12 Maths Question 11.
cos4 2x
Solution:
Class 12 Maths Chapter 7 Solutions Ex 7.3 Q 11
Ex 7.3 Class 12 Maths Question 12.
sin2x1+cosx
Solution:
Class 12 Maths Chapter 7 Solutions Ex 7.3 Q 12
Ex 7.3 Class 12 Maths Question 13.
cos2x−cos2αcosx−cosα
Solution:
Class 12 Maths Chapter 7 Solutions Ex 7.3 Q 13
Ex 7.3 Class 12 Maths Question 14.
cosx−sinx1+sin2x
Solution:
Chapter 7 Class 12 Maths NCERT Solutions Ex 7.3 Q 14
Ex 7.3 Class 12 Maths Question 15.
∫tan32xsec2xdx=I
Solution:
Chapter 7 Class 12 Maths NCERT Solutions Ex 7.3 Q 15
Ex 7.3 Class 12 Maths Question 16.
tan4x
Solution:
NCERT Solutions for Class 12 Maths Ex 7.3 Q 16
Ex 7.3 Class 12 Maths Question 17.
sin3x+cos3xsin2xcos2x
Solution:
NCERT Solutions for Class 12 Maths Ex 7.3 Q 17
Ex 7.3 Class 12 Maths Question 18.
cos2x+2sin2xcos2x
Solution:
NCERT Solutions for Class 12 Maths Ex 7.3 Q 18
Ex 7.3 Class 12 Maths Question 19.
1sinxcos3x
Solution:
NCERT Solutions for Class 12 Maths Ex 7.3 Q 19
Ex 7.3 Class 12 Maths Question 20.
cos2x(cosx+sinx)2
Solution:
Class 12 Maths NCERT Solutions Chapter 7 Ex 7.3 Q 20
Ex 7.3 Class 12 Maths Question 21.
sin-1 (cos x)
Solution:
Class 12 Maths NCERT Solutions Chapter 7 Ex 7.3 Q 21
Class 12 Maths NCERT Solutions Chapter 7 Ex 7.3 Q 21 - i
Ex 7.3 Class 12 Maths Question 22.
∫1cos(x−a)cos(x−b)dx
Solution:
Class 12 Maths NCERT Solutions Chapter 7 Ex 7.3 Q 22
Ex 7.3 Class 12 Maths Question 23.
∫sin2x−cos2xsin2xcos2xdxisequalto
(a) tanx+cotx+c
(b) tanx+cosecx+c
(c) -tanx+cotx+c
(d) tanx+secx+c
Solution:
NCERT Solution Class 12 Maths Ex 7.3 Q 23
Ex 7.3 Class 12 Maths Question 24.
∫ex(1+x)cos2(ex.x)dxisequalto
(a) -cot(e.xx)+c
(b) tan(xex)+c
(c) tan(ex)+c
(d) cot ex+c
Solution:
NCERT Solution Class 12 Maths Ex 7.3 Q 24

Move to Top → Class 12 Integrals Chapter 7

Integrals Class 12 Ex 7.4

Ex 7.4 Class 12 Maths Question 1.
3x2x6+1
Solution:
Class 12 Integrals NCERT Solutions Ex 7.4 Q 1
Ex 7.4 Class 12 Maths Question 2.
11+4×2√
Solution:
Class 12 Integrals NCERT Solutions Ex 7.4 Q 2
Ex 7.4 Class 12 Maths Question 3.
1(2−x)2+1√
Solution:
Class 12 Integrals NCERT Solutions Ex 7.4 Q 3
Ex 7.4 Class 12 Maths Question 4.
19−25×2√
Solution:
Class 12 Integrals NCERT Solutions Ex 7.4 Q 4
Ex 7.4 Class 12 Maths Question 5.
3×1+2×4
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 PDF Ex 7.4 Q 5
Ex 7.4 Class 12 Maths Question 6.
x21−x6
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 PDF Ex 7.4 Q 6
Ex 7.4 Class 12 Maths Question 7.
x−1×2−1√
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 PDF Ex 7.4 Q 7
Ex 7.4 Class 12 Maths Question 8.
x2x6+a6√
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 PDF Ex 7.4 Q 8
Ex 7.4 Class 12 Maths Question 9.
sec2xtan2x+4√
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 9
Ex 7.4 Class 12 Maths Question 10.
1×2+2x+2√
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 10
Ex 7.4 Class 12 Maths Question 11.

19×2+6x+5
Solution:
miscellaneous exercise on chapter 7 class 12 Q 11
Ex 7.4 Class 12 Maths Question 12.
17−6x−x2√
Solution:
miscellaneous exercise on chapter 7 class 12 Q 12
Ex 7.4 Class 12 Maths Question 13.
1(x−1)(x−2)√
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 13
Ex 7.4 Class 12 Maths Question 14.
18+3x−x2√
Solution:
miscellaneous exercise on chapter 7 class 12 Q 14
Ex 7.4 Class 12 Maths Question 15.
1(x−a)(x−b)√
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 15
Ex 7.4 Class 12 Maths Question 16.
4x+12×2+x−3√
Solution:
Class 12 Maths Solutions Ex 7.4 Q 16
Ex 7.4 Class 12 Maths Question 17.
x+2×2−1√
Solution:
Class 12 Maths Solutions Ex 7.4 Q 17
Class 12 Maths Solutions Ex 7.4 Q 17 - i
Ex 7.4 Class 12 Maths Question 18.
5x−21+2x+3×2
Solution:
put 5x-2=Addx(1+2x+3x²)+B
⇒ 6A=5, A=56−2=2A+B, B=−113
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q18

Ex 7.4 Class 12 Maths Question 19.
6x+7(x−5)(x−4)√
Solution:
Class 12 Maths Solutions Ex 7.4 Q 18
Class 12 Maths Solutions Ex 7.4 Q 18 - i
Class 12 Maths Solutions Ex 7.4 Q 18 - ii
Ex 7.4 Class 12 Maths Question 20.
x+24x−x2√
Solution:
Class 12 Maths Solutions Ex 7.4 Q 19
Class 12 Maths Solutions Ex 7.4 Q 19 - i
Class 12 Maths Solutions Ex 7.4 Q 19 - ii
Ex 7.4 Class 12 Maths Question 21.
x+2×2+2x+3√
Solution:
Class 12 Maths Solutions Ex 7.4 Q 20
Class 12 Maths Solutions Ex 7.4 Q 20 - i
Ex 7.4 Class 12 Maths Question 22.
x+3×2−2x−5
Solution:
NCERT Maths Class 12 Ex 7.4 Q 21
NCERT Maths Class 12 Ex 7.4 Q 21 -i
Ex 7.4 Class 12 Maths Question 23.
5x+3×2+4x+10√
Solution:
NCERT Maths Class 12 Ex 7.4 Q 22
NCERT Maths Class 12 Ex 7.4 Q 22 - i
Ex 7.4 Class 12 Maths Question 24.
∫dxx2+2x+2equals
(a) xtan-1(x+1)+c
(b) (x+1)tan-1x+c
(c) tan-1(x+1)+c
(d) tan-1x+c
Solution:
NCERT Maths Class 12 Ex 7.4 Q 23
Ex 7.4 Class 12 Maths Question 25.
∫dx9x−4×2√equals
(a) 19sin−1(9x−88)+c
(b) 12sin−1(8x−99)+c
(c) 13sin−1(9x−88)+c
(d) sin−1(9x−89)+c
Solution:
NCERT Maths Class 12 Ex 7.4 Q 24

Move to Top → Class 12 Integrals Chapter 7

Integrals Class 12 Ex 7.5

Ex 7.5 Class 12 Maths Question 1.
x(x+1)(x+2)
Solution:
NCERT Solutions Maths Class 12 Ex 7.5 Q 1
Ex 7.5 Class 12 Maths Question 2.
1×2−9
Solution:
NCERT Solutions Maths Class 12 Ex 7.5 Q 2
Ex 7.5 Class 12 Maths Question 3.
3x−1(x−1)(x−2)(x−3)
Solution:
NCERT Solutions Maths Class 12 Ex 7.5 Q 3
Ex 7.5 Class 12 Maths Question 4.
x(x−1)(x−2)(x−3)
Solution:
NCERT Solutions Maths Class 12 Ex 7.5 Q 4
Ex 7.5 Class 12 Maths Question 5.
2xx2+3x+2
Solution:
Chapter 7 Class 12 Maths Ex 7.5 Q 5
Ex 7.5 Class 12 Maths Question 6.
1−x2x(1−2x)
Solution:
Chapter 7 Class 12 Maths Ex 7.5 Q 6
Ex 7.5 Class 12 Maths Question 7.
x(x2+1)(x−1)
Solution:
Chapter 7 Class 12 Maths Ex 7.5 Q 7
Chapter 7 Class 12 Maths Ex 7.5 Q 7 - i
Ex 7.5 Class 12 Maths Question 8.
x(x−1)2(x+2)
Solution:
Class 12 Integration NCERT Solutions Ex 7.5 Q 8
Ex 7.5 Class 12 Maths Question 9.
3x+5×3−x2−x+1
Solution:
Class 12 Integration NCERT Solutions Ex 7.5 Q 9
Ex 7.5 Class 12 Maths Question 10.
2x−3(x2−1)(2x+3)
Solution:
Class 12 Integration NCERT Solutions Ex 7.5 Q 10
Ex 7.5 Class 12 Maths Question 11.
5x(x−1)(x2−4)
Solution:
Class 12 Integration NCERT Solutions Ex 7.5 Q 11
Ex 7.5 Class 12 Maths Question 12.
x3+x+1×2−1
Solution:
Class 12 Integration NCERT Solutions Ex 7.5 Q 12
Ex 7.5 Class 12 Maths Question 13.
2(1−x)(1+x2)
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Miscellaneous Exercise Q 13
Ex 7.5 Class 12 Maths Question 14.
3x−1(x+2)2
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Miscellaneous Exercise Q 14
Ex 7.5 Class 12 Maths Question 15.
1×4−1
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Miscellaneous Exercise Q 15
Ex 7.5 Class 12 Maths Question 16.
1x(xn+1)
[Hint : multiply numerator and denominator by xn-1 and put xn = t ]
Solution:
Class 12 Maths Ex 7.5 Q 16
Class 12 Maths Ex 7.5 Q 16 - i
Ex 7.5 Class 12 Maths Question 17.
cosx(1−sinx)(2−sinx)
Solution:
Class 12 Maths Ex 7.5 Q 17
Ex 7.5 Class 12 Maths Question 18.
(x2+1)(x2+2)(x2+3)(x2+4)
Solution:
Class 12 Maths Ex 7.5 Q 18
Class 12 Maths Ex 7.5 Q 18 - i
Ex 7.5 Class 12 Maths Question 19.
2x(x2+1)(x2+3)
Solution:
NCERT Class 12 Maths Ex 7.5 Q 19
Ex 7.5 Class 12 Maths Question 20.
1x(x4−1)
Solution:
NCERT Class 12 Maths Ex 7.5 Q 20
Ex 7.5 Class 12 Maths Question 21.
1ex−1
Solution:
NCERT Class 12 Maths Ex 7.5 Q 21
Ex 7.5 Class 12 Maths Question 22.
choose the correct answer in each of the following :
∫xdx(x−1)(x−2)equals
(a) log∣∣∣(x−1)2x−2∣∣∣+c
(b) log∣∣∣(x−2)2x−1∣∣∣+c
(c) log∣∣(x−12x−2)∣∣+c
(d) log|(x-1)(x-2)|+c
Solution:
NCERT Class 12 Maths Ex 7.5 Q 22
Ex 7.5 Class 12 Maths Question 23.
∫dxx(x2+1)equals
(a) log|x|−12log(x2+1)+c
(b) log|x|+12log(x2+1)+c
(c) −log|x|+12log(x2+1)+c
(d) 12log|x|+log(x2+1)+c
Solution:
NCERT Class 12 Maths Ex 7.5 Q 23

Move to Top → Class 12 Integrals Chapter 7

Integrals Class 12 Ex 7.6

Ex 7.6 Class 12 Maths Question 1.
x sinx
Solution:
Maths Class 12 NCERT Solutions Chapter 7 Ex 7.6 Q 1
Ex 7.6 Class 12 Maths Question 2.
x sin3x
Solution:
Maths Class 12 NCERT Solutions Chapter 7 Ex 7.6 Q 2
Ex 7.6 Class 12 Maths Question 3.
x2ex
Solution:
Maths Class 12 NCERT Solutions Chapter 7 Ex 7.6 Q 3
Ex 7.6 Class 12 Maths Question 4.
x logx
Solution:
Maths Class 12 NCERT Solutions Chapter 7 Ex 7.6 Q 4
Ex 7.6 Class 12 Maths Question 5.
x log2x
Solution:
NCERT Maths Solution Class 12 Ex 7.6 Q 5
Ex 7.6 Class 12 Maths Question 6.
x2logx
Solution:
NCERT Maths Solution Class 12 Ex 7.6 Q 6
Ex 7.6 Class 12 Maths Question 7.
xsin−1x
Solution:
NCERT Maths Solution Class 12 Ex 7.6 Q 7
Ex 7.6 Class 12 Maths Question 8.
xtan−1x
Solution:
NCERT Maths Solution Class 12 Ex 7.6 Q 8
Ex 7.6 Class 12 Maths Question 9.
xcos−1x
Solution:
Class 12 Maths NCERT Solution Ex 7.6 Q 9
Class 12 Maths NCERT Solution Ex 7.6 Q 9 - i
Ex 7.6 Class 12 Maths Question 10.
(sin−1x)2
Solution:
Class 12 Maths NCERT Solution Ex 7.6 Q 10
Ex 7.6 Class 12 Maths Question 11.
xcos−1×1−x2√
Solution:
Class 12 Maths NCERT Solution Ex 7.6 Q 11
Ex 7.6 Class 12 Maths Question 12.
x sec²x
Solution:
Class 12 Maths NCERT Solution Ex 7.6 Q 12
Ex 7.6 Class 12 Maths Question 13.
tan−1x
Solution:
Class 12 Maths NCERT Solution Q 13
Ex 7.6 Class 12 Maths Question 14.
x(logx)²
Solution:
Class 12 Maths NCERT Solution Q 14
Ex 7.6 Class 12 Maths Question 15.
(x²+1)logx
Solution:
Class 12 Maths NCERT Solution Q 15
Class 12 Maths NCERT Solution Q 15 - i
Ex 7.6 Class 12 Maths Question 16.
ex(sinx+cosx)
Solution:
Class 12 Maths NCERT Solution Q 16
Ex 7.6 Class 12 Maths Question 17.
xex(1+x)2
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 17
Ex 7.6 Class 12 Maths Question 18.
ex(1+sinx)1+cosx
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 18
Ch 7 Maths Class 12 Ex 7.6 Q 18 - i
Ex 7.6 Class 12 Maths Question 19.
ex(1x−1×2)
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 19
Ex 7.6 Class 12 Maths Question 20.
(x−2)ex(x−1)3
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 20
Ex 7.6 Class 12 Maths Question 21.
e2xsinx
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 21
Ex 7.6 Class 12 Maths Question 22.
sin−1(2×1+x2)
Solution:
Maths Class 12 Chapter 7 NCERT Solutions Ex 7.6 Q 22

Choose the correct answer in exercise 23 and 24

Ex 7.6 Class 12 Maths Question 23.
∫x2ex3dxequals
(a) 13ex3+c
(b) 13+ex2+c
(c) 12ex3+c
(d) 12ex2+c
Solution:
Maths Class 12 Chapter 7 NCERT Solutions Ex 7.6 Q 23
Ex 7.6 Class 12 Maths Question 24.
∫exsecx(1+tanx)dxequals
(a) excosx+c
(b) exsecx+c
(c) exsinx+c
(d) extanx+c
Solution:
NCERT Maths Solutions for Class 12 Ex 7.6 Q 24

Move to Top → Class 12 Integrals Chapter 7

Class 12 Integrals Ex 7.7

Integral the function in exercises 1 to 9

Ex 7.7 Class 12 Maths Question 1.
4−x2−−−−−√
Solution:
Maths NCERT Class 12 Ex 7.7 Q 1
Ex 7.7 Class 12 Maths Question 2.
1−4×2−−−−−−√
Solution:
Maths NCERT Class 12 Ex 7.7 Q 2
Ex 7.7 Class 12 Maths Question 3.
x2+4x+6−−−−−−−−−√
Solution:
Maths NCERT Class 12 Ex 7.7 Q 3
Ex 7.7 Class 12 Maths Question 4.
x2+4x+1−−−−−−−−−√
Solution:
Maths NCERT Class 12 Ex 7.7 Q 4
Ex 7.7 Class 12 Maths Question 5.
1−4x−x2−−−−−−−−−√
Solution:
Maths NCERT Class 12 Ex 7.7 Q 5
Ex 7.7 Class 12 Maths Question 6.
x2+4x−5−−−−−−−−−√
Solution:
NCERT Solutions Class 12 Ex 7.7 Q 6
Ex 7.7 Class 12 Maths Question 7.
1+3x−x2−−−−−−−−−√
Solution:
NCERT Solutions Class 12 Ex 7.7 Q 7
Ex 7.7 Class 12 Maths Question 8.
x2+3x−−−−−−√
Solution:
NCERT Solutions Class 12 Ex 7.7 Q 8
Ex 7.7 Class 12 Maths Question 9.
1+x29−−−−−√
Solution:
NCERT Solutions Class 12 Ex 7.7 Q 9
Choose the correct answer in the Exercises 10 to 11:

Ex 7.7 Class 12 Maths Question 10.
∫1+x2−−−−−√dxisequalto
(a) x21+x2−−−−−√+12log|x+1+x2−−−−−√|+c
(b) 23(1+x2)32+c
(c) 23x(1+x2)32+c
(d) x221+x2−−−−−√+12x2log∣∣x+1+x2−−−−−√∣∣+c
Solution:
Exercise 7.7 Class 12 Maths Q 10
Ex 7.7 Class 12 Maths Question 11.
∫x2−8x+7−−−−−−−−−√dxisequalto
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.7 Q11
Solution:
Exercise 7.7 Class 12 Maths Q 11

Move to Top → Class 12 Integrals Chapter 7

Class 12 Integrals Ex 7.8

Ex 7.8 Class 12 Maths Question 1.
∫baxdx
Solution:
Maths NCERT Class 12 Ex 7.8 Q 1
Maths NCERT Class 12 Ex 7.8 Q 1 - i

Ex 7.8 Class 12 Maths Question 2.
∫50(x+1)dx
Solution:
Maths NCERT Class 12 Ex 7.8 Q 2
Maths NCERT Class 12 Ex 7.8 Q 2 - i

Ex 7.8 Class 12 Maths Question 3.
∫32x2dx
Solution:
Maths NCERT Class 12 Ex 7.8 Q 3
Maths NCERT Class 12 Ex 7.8 Q 3 -i

Ex 7.8 Class 12 Maths Question 4.
∫41(x2−x)dx
Solution:
NCERT Solutions Class 12 Ex 7.8 Q 4
NCERT Solutions Class 12 Ex 7.8 Q 4 - i
NCERT Solutions Class 12 Ex 7.8 Q 4 - ii

Ex 7.8 Class 12 Maths Question 5.
∫1−1exdx
Solution:
Maths NCERT Class 12 Ex 7.8 Q 5
Maths NCERT Class 12 Ex 7.8 Q 5 - i

Ex 7.8 Class 12 Maths Question 6.
∫40(x+e2x)dx
Solution:
Maths NCERT Class 12 Ex 7.8 Q 6
Maths NCERT Class 12 Ex 7.8 Q 6 - i

Move to Top → Class 12 Integrals Chapter 7

Class 12 Integrals Ex 7.9

Ex 7.9 Class 12 Maths Question 1.
∫1−1(x+1)dx
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Ex 7.9 Q 1

Ex 7.9 Class 12 Maths Question 2.
∫321xdx
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Ex 7.9 Q 2

Ex 7.9 Class 12 Maths Question 3.
∫21(4×3−5×2+6x+9)dx
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Ex 7.9 Q 3

Ex 7.9 Class 12 Maths Question 4.
∫π40sin2xdx
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Ex 7.9 Q 4

Ex 7.9 Class 12 Maths Question 5.
∫π20cos2xdx
Solution:
NCERT Integration Ex 7.9 Q 5

Ex 7.9 Class 12 Maths Question 6.
∫54exdx
Solution:
NCERT Integration Ex 7.9 Q 6

Ex 7.9 Class 12 Maths Question 7.
∫π40tanxdx
Solution:
NCERT Integration Ex 7.9 Q 7

Ex 7.9 Class 12 Maths Question 8.
∫π4π6cosecxdx
Solution:
NCERT Integration Ex 7.9 Q 8

Ex 7.9 Class 12 Maths Question 9.
∫10dx1−x2√
Solution:
NCERT Class 12 Maths Solution Ex 7.9 Q 9

Ex 7.9 Class 12 Maths Question 10.
∫10dx1+x2
Solution:
NCERT Class 12 Maths Solution Ex 7.9 Q 10

Ex 7.9 Class 12 Maths Question 11.
∫32dxx2−1
Solution:
NCERT Class 12 Maths Solution Ex 7.9 Q 11

Ex 7.9 Class 12 Maths Question 12.
∫π20cos2xdx
Solution:
NCERT Class 12 Maths Solution Ex 7.9 Q 12

Ex 7.9 Class 12 Maths Question 13.
∫32xx2+1dx
Solution:
Ex 7.9 Class 12 Q 13

Ex 7.9 Class 12 Maths Question 14.
∫102x+35×2+1dx
Solution:
Ex 7.9 Class 12 Q 14

Ex 7.9 Class 12 Maths Question 15.
∫10xex2dx
Solution:
Ex 7.9 Class 12 Q 15

Ex 7.9 Class 12 Maths Question 16.
∫215x2x2+4x+3dx
Solution:
Ex 7.9 Class 12 Q 16
Ex 7.9 Class 12 Q 16 - i

Ex 7.9 Class 12 Maths Question 17.
∫π40(2sec2x+x3+2)dx
Solution:
Ex 7.9 Class 12 Q 17

Ex 7.9 Class 12 Maths Question 18.
∫π0(sin2x2−cos2x2)dx
Solution:
Maths NCERT Class 12 Solutions Ex 7.9 Q 18

Ex 7.9 Class 12 Maths Question 19.
∫206x+3×2+4dx
Solution:
Maths NCERT Class 12 Solutions Ex 7.9 Q 19

Ex 7.9 Class 12 Maths Question 20.
∫10(xex+sinπx4)dx
Solution:
Maths NCERT Class 12 Solutions Ex 7.9 Q 20

Ex 7.9 Class 12 Maths Question 21.
∫3√1dx1+x2equals
(a) π3
(b) 2π3
(c) π6
(d) π12
Solution:
Maths NCERT Class 12 Solutions Ex 7.9 Q 21

Ex 7.9 Class 12 Maths Question 22.
∫230dx4+9x2equals
(a) π6
(b) π12
(c) π24
(d) π4
Solution:
Maths NCERT Class 12 Solutions Ex 7.9 Q 22

Move to Top → Class 12 Integrals Chapter 7

Integration Class 12 Ex 7.10

Ex 7.10 Class 12 Maths Question 1:
Ex 7.10 Integrals Class 12 NCERT Solutions Ex 7.10 Q 1
Solution:
NCERT Solutions of Class 12 Maths Chapter 7 Integrals Ex 7.10 Q 1
Ex 7.10 Class 12 Maths Question 2:
Ex 7.10 Integrals Class 12 NCERT Solutions Ex 7.10 Q 2
Solution:
NCERT Solutions of Class 12 Maths Chapter 7 Integrals Ex 7.10 Q 2
Ex 7.10 Class 12 Maths Question 3:
Ex 7.10 Integrals Class 12 NCERT Solutions Ex 7.10 Q 3
Solution:
NCERT Solutions of Class 12 Maths Chapter 7 Integrals Ex 7.10 Q 3
Ex 7.10 Class 12 Maths Question 4:
Integration Class 12 Ex 7.10 Q 4
Solution:
NCERT Solutions of Class 12 Maths Chapter 7 Integrals Ex 7.10 Q 4
Ex 7.10 Class 12 Maths Question 5:
Integration Class 12 Ex 7.10 Q 5
Solution:
NCERT Solutions of Class 12 Maths Chapter 7 Integrals Ex 7.10 Q 5
NCERT Solutions of Class 12 Maths Chapter 7 Integrals Ex 7.10 Q 5 - i
Ex 7.10 Class 12 Maths Question 6:
Integration Class 12 Ex 7.10 Q 6
Solution:
NCERT Class 12 Solutions Integrals Ex 7.10 Q 6
NCERT Class 12 Solutions Integrals Ex 7.10 Q 6 - i
Ex 7.10 Class 12 Maths Question 7:
Integration Class 12 Ex 7.10 Q 7
Solution:
NCERT Class 12 Solutions Integrals Ex 7.10 Q 7
Ex 7.10 Class 12 Maths Question 8:
Integrals Class 12 Ex 7.10 8
Solution:
NCERT Class 12 Solutions Integrals Ex 7.10 Q 8
Ex 7.10 Class 12 Maths Question 9:
Integration Class 12 Ex 7.10 Q 9
Solution:
ncert solution of maths class 12 Chapter 7 Ex 7.10 Q 9
Ex 7.10 Class 12 Maths Question 10:
Integrals Class 12 Ex 7.10 10
Solution:
ncert solution of maths class 12 Chapter 7 Ex 7.10 Q 10
Ex 7.10 Class 12 Maths Question 11:
Integrals Class 12 Ex 7.10 11
Solution:
ncert solution of maths class 12 Chapter 7 Ex 7.10 Q 11
ncert solution of maths class 12 Chapter 7 Ex 7.10 Q 11 - i
ncert solution of maths class 12 Chapter 7 Ex 7.10 Q 11 - ii
ncert solution of maths class 12 Chapter 7 Ex 7.10 Q 11 - iii
Ex 7.10 Class 12 Maths Question 12:
integrals class 12 ncert solutions Ex 7.10 Q 12
Solution:
NCERT Class 12 Solutions Ex 7.10 Q 12
NCERT Class 12 Solutions Ex 7.10 Q 12 - i
NCERT Class 12 Solutions Ex 7.10 Q 12 - ii
Ex 7.10 Class 12 Maths Question 13:
integrals class 12 ncert solutions Ex 7.10 Q 13
Solution:
NCERT Class 12 Solutions Ex 7.10 Q 13
Ex 7.10 Class 12 Maths Question 14:
integrals class 12 ncert solutions Ex 7.10 Q 14
Solution:
NCERT Class 12 Solutions Ex 7.10 Q 14
Ex 7.10 Class 12 Maths Question 15:
integrals class 12 ncert solutions Ex 7.10 Q 15
Solution:
NCERT Class 12 Solutions Ex 7.10 Q 15
Ex 7.10 Class 12 Maths Question 16:
maths ncert solutions class 12 Ex 7.10 Q 16
Solution:
NCERT Maths 12 Solutions Ex 7.10 Q 16
Ex 7.10 Class 12 Maths Question 17:
maths ncert solutions class 12 Ex 7.10 Q 17
Solution:
NCERT Maths 12 Solutions Ex 7.10 Q 17
NCERT Maths 12 Solutions Ex 7.10 Q 17 - i
Ex 7.10 Class 12 Maths Question 18:
maths ncert solutions class 12 Ex 7.10 Q 18
Solution:
NCERT Maths 12 Solutions Ex 7.10 Q 18
NCERT Maths 12 Solutions Ex 7.10 Q 18 - i
Ex 7.10 Class 12 Maths Question 19:
maths ncert solutions class 12 Ex 7.10 Q 19
maths ncert solutions class 12 Ex 7.10 Q 19 - i
Solution:
NCERT Maths 12 Solutions Ex 7.10 Q 19
Ex 7.10 Class 12 Maths Question 20:
maths ncert solutions class 12 Ex 7.10 Q 20
maths ncert solutions class 12 Ex 7.10 Q 20 - i
Solution:
NCERT Maths 12 Solutions Ex 7.10 Q 20

Move to Top → Class 12 Integrals Chapter 7

NCERT Solutions for Class 2 Maths Integration Class 12 Ex 7.11

class 12 maths ncert solutions Ex 7.11 Q 1
Ex 7.11 Integrals Class 12 Maths NCERT Solutions Sol 1
class 12 maths ncert solutions Ex 7.11 Q 2
Ex 7.11 Integrals Class 12 Maths NCERT Solutions Sol 2
class 12 maths ncert solutions Ex 7.11 Q 3
Ex 7.11 Integrals Class 12 Maths NCERT Solutions Sol 3
class 12 maths ncert solutions Ex 7.11 Q 4
Ex 7.11 Integrals Class 12 Maths NCERT Solutions Sol 4
integrals ncert solutions Ex 7.11 Q 5
Ex 7.11 Integrals Class 12 Maths NCERT Solutions Sol 5
integrals ncert solutions Ex 7.11 Q 6
Ex 7.11 Integration Class 12 Maths NCERT Solutions Sol 6
Ex 7.11 Integration Class 12 Maths NCERT Solutions Sol 6
integrals ncert solutions Ex 7.11 Q 7
Ex 7.11 Integration Class 12 Maths NCERT Solutions Sol 7
integrals ncert solutions Ex 7.11 Q 8
Ex 7.11 Integration Class 12 Maths NCERT Solutions Sol 8
integrals ncert solutions Ex 7.11 Q 9
Ex 7.11 Integration Class 12 Maths NCERT Solutions Sol 9
integrals ncert solutions Ex 7.11 Q 10
Ex 7.11 Integration Class 12 Maths NCERT Solutions Sol 10
integrals ncert solutions Ex 7.11 Q 11
NCERT maths solutions class 12 Ex 7.11 Sol 11
integration class 12 ncert solutions Ex 7.11 Q 12
NCERT maths solutions class 12 Ex 7.11 Sol 12
integration class 12 ncert solutions Ex 7.11 Q 13
NCERT maths solutions class 12 Ex 7.11 Sol 13
integration class 12 ncert solutions Ex 7.11 Q 14
NCERT maths solutions class 12 Ex 7.11 Sol 14
integration class 12 ncert solutions Ex 7.11 Q 15
NCERT maths solutions class 12 Ex 7.11 Sol 15
integration class 12 ncert solutions Ex 7.11 Q 16
NCERT solutions for class 12 maths Ex 7.11 Sol 16
integration class 12 ncert solutions Ex 7.11 Q 17
NCERT solutions for class 12 maths Ex 7.11 Sol 17
integration class 12 ncert solutions Ex 7.11 Q 18
NCERT solutions for class 12 maths Ex 7.11 Sol 18
integration class 12 ncert solutions Ex 7.11 Q 19
NCERT solutions for class 12 maths Ex 7.11 Sol 19
integration class 12 ncert solutions Ex 7.11 Q 20
NCERT solutions for class 12 maths Ex 7.11 Sol 20
integration class 12 ncert solutions Ex 7.11 Q 21
NCERT solutions for class 12 maths Ex 7.11 Sol 21
integration class 12 ncert solutions Ex 7.11 Q 22
NCERT solutions for class 12 maths Ex 7.11 Sol 22
integration class 12 ncert solutions Ex 7.11 Q 23
NCERT solutions for class 12 maths Ex 7.11 Sol 23
integration class 12 ncert solutions Ex 7.11 Q 24
NCERT solutions for class 12 maths Ex 7.11 Sol 24
integration class 12 ncert solutions Ex 7.11 Q 25
NCERT solutions for class 12 maths Ex 7.11 Sol 25
integration class 12 ncert solutions Ex 7.11 Q 26
Maths NCERT Solution Class 12 Ex 7.11 Q 26
integration class 12 ncert solutions Ex 7.11 Q 27
Maths NCERT Solution Class 12 Ex 7.11 Q 27
integration class 12 ncert solutions Ex 7.11 Q 28
Maths NCERT Solution Class 12 Ex 7.11 Q 28
integration class 12 ncert solutions Ex 7.11 Q 29
Maths NCERT Solution Class 12 Ex 7.11 Q 29
integration class 12 ncert solutions Ex 7.11 Q 30
Maths NCERT Solution Class 12 Ex 7.11 Q 30
Maths NCERT Solution Class 12 Ex 7.11 Q 30 - i
integration class 12 ncert solutions Ex 7.11 Q 31
Maths NCERT Solution Class 12 Ex 7.11 Q 31
Maths NCERT Solution Class 12 Ex 7.11 Q 31 - i
integration class 12 ncert solutions Ex 7.11 Q 32
Maths NCERT Solution Class 12 Ex 7.11 Q 32
integration class 12 ncert solutions Ex 7.11 Q 33
Maths NCERT Solution Class 12 Ex 7.11 Q 33
integration class 12 ncert solutions Ex 7.11 Q 34
Maths NCERT Solution Class 12 Ex 7.11 Q 34
integration class 12 ncert solutions Ex 7.11 Q 35
Maths NCERT Solution Class 12 Ex 7.11 Q 35
integration class 12 ncert solutions Ex 7.11 Q 36
Maths NCERT Solution Class 12 Ex 7.11 Q 36
integration class 12 ncert solutions Ex 7.11 Q 37
Maths NCERT Solution Class 12 Ex 7.11 Q 37
integration class 12 ncert solutions Ex 7.11 Q 38
integration class 12 ncert solutions Ex 7.11 Q 38 - i
Maths NCERT Solution Class 12 Ex 7.11 Q 38
integration class 12 ncert solutions Ex 7.11 Q 39
Maths NCERT Solution Class 12 Ex 7.11 Q 39
integration class 12 ncert solutions Ex 7.11 Q 40
integration class 12 ncert solutions Ex 7.11 Q 40 - i
Maths NCERT Solution Class 12 Ex 7.11 Q 40
integration class 12 ncert solutions Ex 7.11 Q 41
integration class 12 ncert solutions Ex 7.11 Q 41- i
Maths NCERT Solution Class 12 Ex 7.11 Q 41

Move to Top → Class 12 Integrals Chapter 7

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise

Miscellaneous Exercise Class 11 Maths Question 1:
ncert solutions class 12 maths Miscellaneous Questions Q 1
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 1 - i
ncert solutions class 12 maths Miscellaneous Questions Q 1 - ii

Miscellaneous Exercise Class 11 Maths Question 2:
ncert solutions class 12 maths Miscellaneous Questions Q 2
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 2 - i

Miscellaneous Exercise Class 11 Maths Question 3:
miscellaneous exercise on chapter 7 class 12 Q 3
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 3 - i

vMiscellaneous Exercise Class 11 Maths Question 4:
ncert solutions class 12 maths Miscellaneous Questions Q 4
Solution:
miscellaneous exercise on chapter 7 class 12 Q 4 - i
ncert solutions class 12 maths Miscellaneous Questions Q 4 - ii

Miscellaneous Exercise Class 11 Maths Question 5:
ncert solutions class 12 maths Miscellaneous Questions Q 5
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 5 - i

Miscellaneous Exercise Class 11 Maths Question 6:
ncert solutions class 12 maths Miscellaneous Questions Q 6
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 6 - i

Miscellaneous Exercise Class 11 Maths Question 7:
ncert solutions class 12 maths Miscellaneous Question Q 7
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 7 - i

Miscellaneous Exercise Class 11 Maths Question 8:
ncert solutions class 12 maths Miscellaneous Questions Q 8
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 8 - i

Miscellaneous Exercise Class 11 Maths Question 9:
ncert solutions for class 12 maths chapter 7 miscellaneous exercise Q 9
Solution:
ncert solutions for class 12 maths miscellaneous Q 9 - i

Miscellaneous Exercise Class 11 Maths Question 10:
ncert solutions class 12 maths Miscellaneous Questions Q 10
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 10 - i
Miscellaneous Exercise Class 11 Maths Question 11:
ncert solutions class 12 maths Miscellaneous Questions Q 11
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 11 - i

Miscellaneous Exercise Class 11 Maths Question 12:
ncert solutions class 12 maths Miscellaneous Questions Q 12
Solution:
ncert miscellaneous solutions class 12 Q 12 - i

Miscellaneous Exercise Class 11 Maths Question 13:
ncert solutions class 12 maths Miscellaneous Questions Q 13
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 13 - i

Miscellaneous Exercise Class 11 Maths Question 14:
ncert solutions class 12 maths Miscellaneous Questions Q 14
Solution:
ncert solutions for class 12 maths chapter 7 miscellaneous Q 14
ncert solutions class 12 maths Miscellaneous Questions Q 14 - i

Miscellaneous Exercise Class 11 Maths Question 15:
ncert solutions class 12 maths Miscellaneous Questions Q 15
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 15 - i

Miscellaneous Exercise Class 11 Maths Question 16:
ncert integrals miscellaneous solutions Q 16
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 16 - i

Miscellaneous Exercise Class 11 Maths Question 17:
ncert solutions class 12 maths Miscellaneous Questions Q 17
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 17 - i

Miscellaneous Exercise Class 11 Maths Question 18:
ncert solutions class 12 maths Miscellaneous Questions Q 18
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 18 - i

Miscellaneous Exercise Class 11 Maths Question 20:
ncert solutions class 12 maths Miscellaneous Questions Q 20
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 20 -i
ncert solutions class 12 maths Miscellaneous Questions Q 20 - ii

Miscellaneous Exercise Class 11 Maths Question 21:
ncert solutions class 12 maths Miscellaneous Questions Q 21
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 21 - i

Miscellaneous Exercise Class 11 Maths Question 22:
ncert solutions class 12 maths Miscellaneous Questions Q 22
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 22 - i

Miscellaneous Exercise Class 11 Maths Question 23:
ncert solutions class 12 maths Miscellaneous Questions Q 23
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 23 - i

Miscellaneous Exercise Class 11 Maths Question 24:
ncert solutions class 12 maths Miscellaneous Questions Q 24
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 24 - i
ncert miscellaneous solutions class 12 Q 24 - ii

Miscellaneous Exercise Class 11 Maths Question 25:
ncert solutions class 12 maths Miscellaneous Questions Q 25
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 25 - i

Miscellaneous Exercise Class 11 Maths Question 26:
ncert solutions class 12 maths Miscellaneous Questions Q 26
Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 26 - i

Miscellaneous Exercise Class 11 Maths Question 27:
maths class 12 ncert solutions miscellaneous exercise 27
Solution:
maths class 12 ncert solutions miscellaneous exercise 27 - i
maths class 12 ncert solutions miscellaneous exercise 27 - ii

Miscellaneous Exercise Class 11 Maths Question 28:
maths class 12 ncert solutions miscellaneous exercise 28
Solution:
maths class 12 ncert solutions miscellaneous exercise 28 - i
maths class 12 ncert solutions miscellaneous exercise 28 - ii

Miscellaneous Exercise Class 11 Maths Question 29:
maths class 12 ncert solutions miscellaneous exercise 29
Solution:
maths class 12 ncert solutions miscellaneous exercise 29 - i

Miscellaneous Exercise Class 11 Maths Question 30:
maths class 12 ncert solutions miscellaneous exercise 30
maths class 12 ncert solutions miscellaneous exercise 30 - i

Miscellaneous Exercise Class 11 Maths Question 31:
maths class 12 ncert solutions miscellaneous exercise 31
Solution:
maths class 12 ncert solutions miscellaneous exercise 31 - i

Miscellaneous Exercise Class 11 Maths Question 32:
maths class 12 ncert solutions miscellaneous exercise 32
Solution:
maths class 12 ncert solutions miscellaneous exercise 32- i
maths class 12 ncert solutions miscellaneous exercise 32- ii

Miscellaneous Exercise Class 11 Maths Question 33:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 33
Solution:

Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 33 - ii

Miscellaneous Exercise Class 11 Maths Question 34:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 34
Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 34 - i
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 34 - ii

Question 35:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 35
Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 35 -i

Miscellaneous Exercise Class 11 Maths Question 36:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 36
Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 36 -i

Miscellaneous Exercise Class 11 Maths Question 37:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 37
Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 37 - i

Miscellaneous Exercise Class 11 Maths Question 38:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 38
Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 38 -i

Miscellaneous Exercise Class 11 Maths Question 39:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 39
Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 39-i

Miscellaneous Exercise Class 11 Maths Question 40:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 40
Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 40 -i
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 40 -ii

Miscellaneous Exercise Class 11 Maths Question 41:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 41
Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 41 -i
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 41 -ii

Miscellaneous Exercise Class 11 Maths Question 42:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 42
Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 42 - i
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 42 - ii

Miscellaneous Exercise Class 11 Maths Question 43:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 43
Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 43-i
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 43-ii

Miscellaneous Exercise Class 11 Maths Question 44:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 44
Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 44 -i
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 44 -ii

Move to Top → Class 12 Integrals Chapter 7

Integration Formulas

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Integration Formulas 1
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Integration Formulas 2
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Integration Formulas 3
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Integration Formulas 4
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Integration Formulas 5
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Integration Formulas 6
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Integration Formulas 7

Move to Top → Class 12 Integrals Chapter 7

गणित कक्षा 12 समाकलन प्रश्नावली 7.1

निम्नलिखित फलनों के प्रतिअवकलज ( समाकलन) निरीक्षण विधि द्वारा ज्ञात कीजिए।

Ex 7.1 Class 11 Maths प्रश्न 1.
sin 2x
हल-
∫sin 2x dx
हम जानते हैं कि, ddx cos2x = -2 sin 2x
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 1

Ex 7.1 Class 11 Maths प्रश्न 2.
cos 3x
हल-
∫cos 3x dx
हम जानते हैं कि, ddx sin 3x = 3 cos 3x
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q2
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 2.1

Ex 7.1 Class 11 Maths प्रश्न 3.
e2x
हल-
∫e2x dx
हम जानते हैं कि,
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q3

Ex 7.1 Class 11 Maths प्रश्न 4.
(ax + b)²
हल-
∫(ax + b)² dx
हम जानते हैं कि,
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q4

Ex 7.1 Class 11 Maths प्रश्न 5.
sin 2x – 4e3x
हल-
∫(sin 2x -4e3x) dx = ∫sin 2x dx – 4∫e3x …(1)
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 5

निम्नलिखित समाकलनों को ज्ञात कीजिए।

Ex 7.1 Class 11 Maths प्रश्न 6.
∫(4e3x + 1) dx
हल-
∫(4e3x + 1) dx = 4∫e3xdx + ∫1 dx
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q6

Ex 7.1 Class 11 Maths प्रश्न 7.
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q7
हल-
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 7-i

Ex 7.1 Class 11 Maths प्रश्न 8.
∫(ax² + bx + c) dx
हल-
∫(ax² + bx + c) dx = a∫x²dx + b∫xdx + c∫1 dx
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q8

Ex 7.1 Class 11 Maths प्रश्न 9.
∫(2x² + ex) dx
हल-
∫(2x² + ex) dx = 2∫x² dx + ∫ex dx
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q9

Ex 7.1 Class 11 Maths प्रश्न 10.
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q10
हल-
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 10.1

Ex 7.1 Class 11 Maths प्रश्न 11.
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q11
हल-
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 11.1

Ex 7.1 Class 11 Maths प्रश्न 12.
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 12
हल-
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q12

Ex 7.1 Class 11 Maths प्रश्न 13.
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q13
हल-
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q13.1

Ex 7.1 Class 11 Maths प्रश्न 14.
∫(1-x)√x dx
हल-
∫(1-x)√x dx
=∫(√x-x√x)dx
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q14

Ex 7.1 Class 11 Maths प्रश्न 15.
∫√x(3x² + 2x + 3)dx
हल-
∫√x(3x² + 2x + 3)dx
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q15

Ex 7.1 Class 11 Maths प्रश्न 16.
∫(2x – 3cosx + ex)dx
हल-
∫(2x – 3cosx + ex)dx
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 16

प्रश्न 17.
∫(2x² – 3sinx + 5√x)dx
हल-
∫(2x² – 3sinx + 5√x)dx
= 2∫x² dx – 3 ∫ sinx dx + 5∫√x dx
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q17

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q17.1

Ex 7.1 Class 11 Maths प्रश्न 18.
∫secx (sec x + tan x) dx
हल-
∫sec x (sec x + tan x) dx
= ∫(sec² x + sec x tan x) dx
= ∫(sec² x dx
= ∫sec x tan x dx
tan x + sec x + C

Ex 7.1 Class 11 Maths प्रश्न 19.
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q19
हल-
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 19.1

Ex 7.1 Class 11 Maths प्रश्न 20.
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 20
हल-
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q20

प्रश्न 21 एवं 22 में सही उत्तर का चयन कीजिए

Ex 7.1 Class 11 Maths प्रश्न 21
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q21
हल-
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q21.1

Ex 7.1 Class 11 Maths प्रश्न 22
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q22
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22.1
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q22.1

Move to Top → Class 12 Integrals Chapter 7

Class 12 Maths NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives: Students preparing for Class 12 board exams and JEE (Main and Advanced) must finish the NCERT Maths textbooks thoroughly. You must understand the theory behind every concept and then solve the questions at the end of every chapter. Once you have finished the entire syllabus and are revising. you must go through the solutions of every question. In this article, we will provide you with NCERT Solutions for Class 12 Maths Chapter 6 – Applications of Derivatives.

Class 12 Maths Chapter 6 NCERT Solutions– Applications of Derivatives

NCERT Solutions for Class 12 Maths Chapter 6 – Applications of Derivatives have been designed by top and experienced teachers. Go through them and get a clear idea about how to approach the problems so that you can solve them in the most efficient way.

RD Sharma Solutions HC Verma Concepts of Physics

The topics and sub-topics included in the Applications of Derivatives chapter are the following:

Section NameTopic Name
6Applications of Derivatives
6.1Introduction
6.2Rate of Change of Quantities
6.3Increasing and Decreasing Functions
6.4Tangents and Normals
6.5Approximations
6.6Maxima and Minima
6.7Maximum and Minimum Values of a Function in a Closed Interval
6.8Summary
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives 1
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives 2
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives 3
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives 4
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives 5
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives 6
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives 7
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives 8
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives 9
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives 10
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives 11

NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives Hindi Medium Ex 6.1

NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.1 in English Medium
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.1 AOD updated for 2018-2019.
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.1 Rate of change
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.1 in English for CBSE and UP Board
NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.1 sols of all questions
Class 12 Maths Chapter 6 Exercise 6.1 solutions in Hindi medium free
Class 12 Maths Chapter 6 Exercise 6.1 sols for CBSE and UP Board 2018-2019.
Class 12 Maths Chapter 6 Exercise 6.1 in Hindi me
Class 12 Maths Chapter 6 Exercise 6.1 full guide in hindi
Class 12 Maths Chapter 6 Exercise 6.1 ke sabhi prashano ke uttar hindi me
12 Maths Chapter 6 Exercise 6.1 sols for CBSE and UP Board 2018-2019.

Class 12 Maths NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability is designed and prepared by the best teachers across India. All the important topics are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

Did you try solving RD Sharma Class 12 Maths Continuity and Differtiability?

Chapter 5 Continuity and Differentiability Maths NCERT Solutions cover eight exercises. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. This will prove to be most helpful to you in your home assignments as well as practice sessions.

The topics and sub-topics included in the Continuity and Differentiability chapter are the following:

  • Continuity and Differentiability
  • Introduction
  • Algebra of continuous functions
  • Differentiability
  • Derivatives of composite functions
  • Derivatives of implicit functions
  • Derivatives of inverse trigonometric functions
  • Exponential and Logarithmic Functions
  • Logarithmic Differentiation
  • Derivatives of Functions in Parametric Forms
  • Second-Order Derivative
  • Mean Value Theorem
  • Summary

There are total eight exercises and one misc exercise(144 Questions fully solved) in the class 12th maths chapter 5 Continuity and Differentiability.

Class 12 Maths Continuity and Differentiability Exercise 5.1

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 1
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 2

Class 12 Maths Continuity and Differentiability Exercise 5.2 and 5.3

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 3

Class 12 Maths Continuity and Differentiability Exercise 5.4

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 4

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NCERT Class 12 Maths Solutions

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

NCERT Solutions for Class 12 Maths Chapter 4 Determinants: For both CBSE Class 12 board exams and competitive entrance exams like JEE and NEET, NCERT textbooks must be thoroughly finished. These books not only help in having your basics clear but also help in improving your problem-solving abilities. In order to make the best use of these books, you need to solve all the problems at the end of every chapter. Then you need to go through their solutions. In this article, we will provide you with NCERT Solutions for Class 12 Maths Chapter 4 Determinants.

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Class 12 Maths NCERT Solutions Chapter 4 Determinants

NCERT Maths is especially important for engineering aspirants. So, students must finish the NCERT Maths textbooks as early as possible and then move onto some other reference books. To clear any doubts, they must go through the solutions of the questions at the end of every chapter. Find out the NCERT Solutions for Class 12 Maths Chapter 4 Determinants which is designed by some of India’s best teachers.

The topics and sub-topics included in the Determinants chapter are the following:

Section NameTopic Name
4Determinants
4.1Introduction
4.2Determinant
4.3Properties of Determinants
4.4Area of a Triangle
4.5Adjoint and Inverse of a Matrix
4.6Applications of Determinants and Matrices
4.7Summary
NCERT Solutions for Class 12 Maths Chapter 4 Determinants 1
NCERT Solutions for Class 12 Maths Chapter 4 Determinants 2
NCERT Solutions for Class 12 Maths Chapter 4 Determinants 3
NCERT Solutions for Class 12 Maths Chapter 4 Determinants 4
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Class 12 Maths NCERT Solutions