NCERT mathematics solutions provide well-explained solutions for each question provided in the textbook and clear the basic fundamental concept of students. The solution to every question in this NCERT Mathematics solution is explained step by step with simple language so that students can easily understand. Students who are weak in mathematics can obtain good marks in the upcoming examination with the help of NCERT solutions.

We are providing chapter wise NCERT mathematics solutions for class 12. Students will get solutions to each chapter like Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Applications of Derivatives, Integrals, Applications of Integrals, Differential Equations, Vector Algebra, etc in PDF format. Students can download this PDF by clicking the link provided below.

Class 12 Mathematics chapter 1 is Relation and Function. This chapter is basic and root of all other chapters. Almost topic in class 12 mathematics is linked with Chapter 1 Relation and Function. In this chapter, we study the different types of function and their existence and relation between them. This chapter is a little bit confusing but if you make all the questions of this NCERT test book then your all concept will be clear. You can take help from the NCERT Mathematics solution provided on this website. This NCERT mathematics solution will help you during solving questions and this will clear your concept about chapter 1 "Relation and function".

**EXERCISE - 1.1 Q-1:**

** Check each and every relation whether the following are symmetric, reflexive and transitive: (i) The relation R of the set S = {2, 3, 4, 5, 6, 7, 8, 9 ........ 15} is defined as R = {(a, b): 2a - b = O} (ii) The relation R of the set S having natural numbers is defined as R = {(a, b): b = 2a + 6 and a < 5} (iii) The relation R of the set S = {2, 3, 4, 5, 6, 7} is defined as R = {(a, b): b is divisible by a} (iv) The relation R of the set S having only the Integers is defined as R = {(a, b): a - b is an integer} (v) The relation R from the set H having human beings at a particular time in the town is given by: (a) R = {(a, b): a and bis working at the same place} (b) R = {(a, b): a and b are living in the same society} (c) R = {(a, b): a is exactly 6 cm taller than b} (d) R = {(a, b): b is husband of a} (e) R = {(a, b): a is the father of b} **

Class 12 NCERT Mathematics Chapter 2 is Inverse Trigonometric Functions. This chapter deals with the Inverse of a trigonometric function. This chapter is basic for trigonometric function. You can solve all the questions of class 12 NCERT mathematics test book with the help of NCERT mathematics solution of Chapter 2 Inverse Trigonometric Functions which is given below.

Class 12 NCERT Mathematics Chapter 3 is Matrices. Matrix is a rectangular array that is used to solve a complex linear equation. Class 12 NCERT mathematics solution of chapter 3 Matrices will help you to solve all the questions of the textbook and you will become a master in Matrix.

**Q2: Examine the continuity of the function f(x) = 2x2 -1 at x = 3.**

**Sol:** The given function is f(x) = 2x2-1

At x = 3, f(x)=f(3) =2x 3A(A{2}}-1=17

limx_,3f(x) = limx➔3(2x2 -1) = 2 x 3' -1 = 17

therefore limx_,3f(x) = f(3) Thus, f is continuous at x = 3

**Q-3) For a circle, determine the rate of change of area when radius 'y' is 20mm. The radius of circle is increase at the rate of 6mm/s.**

**Question 1: By the method of inspection obtain an integral (or anti - derivative) of the sin 3x.**

**Q.2: Find the degree and order of differential equation y' + Sy = 0**

Solution: Given: y' + Sy = 0 y' is the highest order derivative present in the differential equation

Therefore, the order is one. The given differential equation is a polynomial equation in y' The highest degree derivative present in the differential equation is y'

Therefore, the degree is one.

**Question 1: Graphically represent a 40 km displacement towards 30 ° east of north.**

Answer 1: Vector OP represent a 40 km displacement towards 30° east of north.

**Q2. Find the direction cosines of a line which makes equal angles with the coordinate axes**