Sample question paper class 12 mathematics

SAMPLE QUESTION PAPER
Class:-XII

Session 2023-24

Mathematics (Code-041)

Time: 3 hours Maximum marks: 80

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 of 4 marks each with

sub-parts.
___________________________________________________________________________________________

Section –A
(Multiple Choice Questions)
Each question carries 1 mark

1, when i  j
Q1. If A  aij  is a square matrix of order 2 such that aij   , then A2 is
 0, when i  j
1 0 1 1 1 1   1 0
(a)   (b)   (c)   (d)  
1 0  0 0 1 0  0 1
Q2. If A and B are invertible square matrices of the same order, then which of the following is not correct?
1
(b) det  A  det  A 
1
(a) adjA  A . A 1

(c)  AB   B 1 A 1 (d)  A  B   B 1  A 1
1 1




Q3. If the area of the triangle with vertices   3 , 0  ,  3,0  and  0, k  is 9 squnits, then the value/s of k will
be
(a) 9 (b)  3 (c) -9 (d) 6
 kx
 , if x  0
Q4. If f  x    x is continuous at x  0 , then the value of k is
 3, if x  0

(a) −3 (b) 0 (c) 3 (d) any real number


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,  
   
Q5. The lines r  i  j  k   2i  3 j  6 k and r  2i  j  k   6i  9 j  18 k ; (where  &  are

scalars) are
(a) coincident (b) skew (c) intersecting (d) parallel
3
  dy  2  d2 y 2
Q6. The degree of the differential equation 1      2 is
  dx   dx
3
(a) 4 (b) (c) 2 (d) Not defined
2
Q7. The corner points of the bounded feasible region determined by a system of linear constraints are
 0, 3  ,  1,1  and  3, 0  . Let Z  px  qy , where p , q  0 . The condition on p and q so that the
minimum of Z occurs at  3, 0  and  1,1  is

q
(a) p  2q (b) p  (c) p  3q (d) p  q
2
   
ombus whose diagonals intersect at E . Then EA  EB  EC  ED equals to
Q8. ABCD is a rhombus
   
(a) 0 (b) AD (c) 2BD (d) 2AD

 e sin x cos 3  2n  1 x dx is
2
Q9. For any integer n , the value of
0


(a) -1 (b) 0 (c) 1 (d) 2

 0 2x  1 x 
 
Q10. The value of A , if A  1  2 x 0 2 x  , where x    , is
 
  x 2 x 0 

(a)  2 x  1 (c)  2 x  1
2 3
(b) 0 (d) None of these

Q11. The feasible
easible region corresponding to the linear constraints of a L
Linear Programming
rogramming Problem is given
below.




Which of the following is not a constraint to the given Linear Programming Problem?
(a) x  y  2 (b) x  2 y  10 (c) x  y  1 (d)) x  y  1


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