CBSE Class 12 Maths Pre-Board Sample Paper 2025 With Solutions, Download PDF

SECTION A (Multiple Choice Questions)

Each question carries 1 mark

1. If is a singular matrix, then the value of λ is:

(a) λ=5

(b) λ≠5

(c) λ=50/7

(d) λ≠−5

2. If A = [a_ij] is a square matrix of order 3 such that , then the value of |A|+|adj A| is

        (a)                    (b)                       (c)                       (d) 350

3. If A is the set of cities, and a relation R on set A is defined as R={(x,y): xand y are directly connected by a road}, then relation R is:

(a) Reflexive but not symmetric

(b) Symmetric but not transitive

(c) Reflexive and transitive

(d) Equivalence

4. If A is a square matrix of order 2 such that ∣A∣=3, then the value of ∣2A∣ is:

(a) 6

(b) 12

(c) ±12

(d) 24

5. If , α and β are roots of equation |2x x 3x| = 5, then value of is α + β is,

      (a) 2/3          (b) -5/2                (c) 3/2                      (d) -2/5

6. If the function f(x)=∣x−1∣+∣x+2∣ is not differentiable at p and q, then the value of p+q is:

(a) 1

(b) -1

(c) 0

(d) 3

              (a) 1              (b)                 (c) 1/                     (d) -1

8. If then the value of A²+ B² is

                 (a) 2x             (b) 0                  (c) 1                      (d) π

9. The direction cosine of a line equally inclined to the axes is?

           (a) 1, 1, 1        (b) ±1, ±1,±1       (c) ∓1/√3 , ∓1/√3 , ∓1/√3               (d) 1, 0, 0

10. Let A and B be two events. If P(A)=0.3, P(A) P(B)=0.5, P(A∪B)=0.7, then P(A∣B) is:

(a) 0.4

(b) 0.6

(c) 0.2

(d) 0.5

11. If m is the order and n is the degree of given differential equation,  then what is the value of   m + n 

(a) 5             

(b) 9                 

(c) 4                     

(d) 7

12. If then C is equal to

(a) 65/66 

(b) 24/65   

(c) 16/65           

(d)    56/65

13. If magnitude of vector is ‘3 units’ then the value of  is

 (a)  1/3                           

(b) √3                  

(c)  ∓1/√3         

(d) ∓√3

14. The Integrating factor of the differential equation (x log x)+y=2 log x ,is given by

 (a)log(log x ) 

(b)e^x 

(c) log x   

(d)x 

15. The direction ratio of the line is

 (a) 4,  3,  6   

(b) 2, 3, - 6 

(c) 2, -3, 6   

(d) – 2,  -3,  -6

1

2

3

4

5

6

7

8

9

10

C

B

B

C

C

C

A

C

C

C

11

12

13

14

15

A

D

D

C

C

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