Cbse Class 12 Maths Sample Paper

PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 01 FOR BOARD EXAM 2025
(ANSWERS)
SUBJECT: MATHEMATICS (041) MAX. MARKS : 80
CLASS : XII DURATION: 3 HRS
General Instructions:
1. This Question paper contains - five sections A, B, C, D and E. Each section is compulsory.
However, there are internal choices in some questions.
2. Section A has 18 MCQ’s and 02 Assertion-Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each.
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment (4
marks each) with sub parts.

SECTION – A
Questions 1 to 20 carry 1 mark each.

0 1 
1. If A =   , then A2023 is equal to:
0 0
0 1   0 2023 0 0  2023 0 
(a)   (b)  (c)  (d) 
0 0 0 0  
0 0  0 2023
0 0
Ans: (c)  
0 0

2. For any square matrix A, AAT is a
(a) unit matrix (b) symmetric matrix (c) skew-symmetric matrix (d) diagonal matrix
Ans: (b) symmetric matrix

d
3. If [f (x)] =ax +b and f(0) = 0, then f(x) is equal to:
dx
ax 2 ax 2
(a) a + b (b)  bx (c)  bx  c (d) b
2 2
ax 2
Ans: (b)  bx
2

 dy 
4. Degree of the differential equation sin x  cos    y 2 is:
 dx 
(a) 2 (b) 1 (c) not defined (d) 0
Ans: (c) not defined

5. P is a point on the line joining the points (0,5, -2) and (3, -1,2) . If the x-coordinate of P is 6,
then its z-coordinate is
(a) 10 (b) 6 (c) -6 (d) -10
Ans: (b) 6

6. If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number
obtained on one of the dice is 4, is:

Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1-

, (a) 1/9 (b) 4/9 (c) 1/18 (d) 1/2
Ans: (d) 1/2

7. The value of
(a) (b) (c) (d)
Ans: (d)

8. If (a, b), (c, d) and (e, f) are the vertices of ∆ABC and ∆ denotes the area of ∆ABC, then
2
a c e
b d f is equal to:
1 1 1
(a) 2∆² (b) 4∆² (c) 2∆ (d) 4∆
Ans: (b) 4∆²
 x2  9
 ,x 3
9. If the function f(x) defined by f ( x)   x  3 is continuous at x = 3, then the value of k is
 k. x  3

(a) 6 (b) (c) -6 (d) 3
Ans: (a) 6

 x y  dy
10. If tan    k , then dx is equal to:
 x y 
y y  y  y
(a) (b) (c) sec2   (d)  sec 2  
x x x x
y
Ans: (b)
x
11. The corner points of the feasible region of a linear programming problem are (0, 4), (8, 0) and
 20 4 
 ,  . If Z = 30x + 24y is the objective function, then (maximum value of Z – minimum
 3 3
value of Z) is equal to:
(a) 144 (b) 96 (c) 120 (d) 136
Ans: (a) 144
dy
12. The integrating factor of the differential equation (1 – y²) + yx = ay, (– 1 <y < 1) is:
dx
1 1 1 1
(a) 2 (b) (c) 2
(d)
y 1 2
y 1 1 y 1  y2
1
Ans: (d)
1  y2
13. Projection of vector 2i  3 j on the vector 3i  2 j is:
12 12
(a) 0 (b) 12 (c) (d)
13 13
Ans: (a) 0

14. If = 60, = 40 and = 22 then =
(a) 36 (b) 22/60 (c) 46 (d) None of these
Ans: (c) 46

Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2-