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### NCERT Solutions for Class 12 Maths

NCERT Math books provide a solid base in every concept for the exams conducted by CBSE board. It includes all the main topics with specific explanation that helps the students with better understanding. NCERT books also play a vital role in JEE according to the HRD ministry.

BYJU’S brings you NCERT solutions for class 12, designed by some of the best teachers in India. The solutions for class 12 maths has detailed step-by-step explanation for all the questions of NCERT text book. It acts as a vital tool to many students in their exam preparation along with home assignments.

#### Chapter-7: Integrals

Exercise – 7.1 Question 1: By the method of inspection obtain an integral (or anti – derivative) of the sin ...

#### Chapter-5: Continuity and Differentiability

Exercise 5.1 Q1: Prove that the function f(x)=5x-3 is continuous at x=0, at x=-3 and at x=5. Sol: The given ...

#### Chapter-13: Probability

Exercise – 13.1 Given below are events such as P(Q) = 0.6 , P(R) = 0.3 P(Q\cap R) = 0.2 ...

#### Chapter-6: Applications of Derivative

Excercise 1 Q-1) For a circle, with radius given below, find the rate of change of the area w.r.t raduis’a’ ...

#### Chapter-4: Determinants

Exercise 4.1 Q1: Evaluate the determinants. \begin{vmatrix} 2 & 4\\ -5 & -1 \end{vmatrix} Ans: \begin{vmatrix} 2 & 4\\ -5 ...

## Chapter-7: Integrals

Exercise – 7.1   Question 1: By the method of inspection obtain an integral (or anti – derivative) of the sin 3x.   Answer: As the derivative is sin 3x and x is the function of the anti – derivative of sin 3x.     Question 2: By the method of inspection obtain an integral […]

## Chapter-5: Continuity and Differentia...

Exercise 5.1   Q1: Prove that the function is continuous at , at and at . Sol: The given function is At , So, f is continuous at x=0 At   So , f is continuous at x=-3 At x=5,f(x)=f(5)= (5×5) – 3=25-3=22 So , f is continuous at x=5     Q2 : Examine […]

## Chapter-13: Probability

Exercise – 13.1 Given below are events such as P(Q) = 0.6 , P(R) = 0.3 P() = 0.2. Determine the value of P() and P( Sol: According to the Q., it is given that P(Q) = 0.6 , P(R) = 0.3, P () = 0.2 P() = = = P() = = =   […]

## Chapter-6: Applications of Derivative

Excercise 1 Q-1) For a circle, with radius given below, find the rate of change of the area w.r.t raduis’a’.  i) a = 2mm, ii) a = 5mm Ans.) We know that the area of circle with radius ‘a’ is . i.e. A = The rate of change of area w.r.t ‘a’ is, a = […]

## Chapter-4: Determinants

Exercise 4.1   Q1: Evaluate the determinants.   Ans: = 2 ( -1 ) – 4 ( -5 ) = – 2 + 20 = 18     Q2: Evaluate the determinant. (i) (ii)   Ans: (i) (cos Ɵ )(cos Ɵ ) – ( -sin Ɵ ) (sin Ɵ ) = cos2 Ɵ + sin2 […]

## Chapter-10: Vector Algebra

Exercise – 10.1 Question 1: Graphically represent a 40 km displacement towards 30 o east of north. Answer 1: Vector represent a 40 km displacement towards 30o east of north.   Question 2: Categorize the following measures as vectors and scalars. (a)  20 kg                                          (b)  4 meters north – south           (c) 80o (d)  70 watt                                      […]

## Chapter-3: Matrices

EXERCISE – 3.1 Q-1: In a matrix given below: A = , write (a) the order of the matrix. (b) the number of element. (c) Write the elements of a13, a21, a23, a24, a33   Solution: (a) In the matrix given in the question, there are 3 rows and 4 columns. Hence, the order of […]

## Chapter-12: Linear Programming

Exercise – 12.1 Q1: Maximize Z = 3x + 4y Subject to the constraints: x + y ≤ 4, 0 ≤ x, 0 ≤ y Sol: The feasible region determined by the constraints, x + y ≤ 4, x ≥ 0, y ≥ 0, is as follows: The corner points of the feasible region are […]

## Chapter-9: Differential Equations

Exercise : 9.1 Q.1: Find the degree and order of the differential equation +sin (ym) = 0.   Solution: + sin (y”’) = 0 y”” + sin (y”’) = 0 y”” is the highest order derivative present in the differential equation. Therefore, the order is four. The given differential equation is not a polynomial equation […]

## Chapter-11: Three Dimensional Geometr...

Exercise 1.1  Q1. Find the cosine directions, if a line makes angles 90°, 135°, 45° with x, y and z- axes respectively.   Sol: Let, the direction cosines of the line be p, q and r p = cos 90° = 0 q = cos 135° = r = cos 45° = Therefore, the direction […]