CBSE 12 Maths Most Expected Questions 2025

1

Relation R on Real Numbers is defined as R = {(a, b): a ≤ b}. The relation is :

2

Let f: [-2,2] → [-2,2] be a function defined by f(x) = x/xl, then f is :

3

For real numbers x and y, we write xRY → x - y + V2 is an irrational number. Then, check the relation R is reflexive, symmetric or

4

Let N denote the set of all natural numbers and R be the relation on N x N defined by (a, b)R(c, d) if ad (b + c) = bc(a + d). Show that R is an equivalence relation.

5

Consider f: R+ → [-5, ∞) given by f(x) = 9x2 + 6x - 5 where R, is the set of all nonnegative real numbers. Prove that f is one- one and onto function.

6

Let N be the set of natural numbers and R be the relation on N x N defined by (a, b)R (c, d) iff ad = bc for all a, b, c, d € N. Show that R is an equivalence relation.

7

If A and B are matrices of order 3 X n and m x 5 respectively, then find the order of matrix 5A - 3B, given that it is defined.

8

Given that matrices A and B are of order 3 x n and m x 5 respectively, then the order of matrix C = 5A +3B is:

9

A is a skew-symmetric matrix of order 3, then prove that det A = 0.

10

The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is

11

If A is a 3 × 2 matrix, B is a 3 x 3 matrix and C is a 2 x 3 matrix, then the elements in A, B and C are respectively

12

If A a non-singular square matrix of order 3 and A2 = 2A, then find the value of | A|.

13

Given that A is a square matrix of order 3 X 3 and |A| = -4. Find | adj A |

14

Let A = [a] be a square matrix of order 3 X 3 and |A| = -7. Find the value of a11 A21 + a12 A22 + a13 A23 where Aij is the cofactor of element aj

15

If A and B are square matrices of the same order 3, such that |A| = 2 and AB = 2l, write the value of | B.