SAMPLE QUESTION PAPER (2024 - 25)
CLASS- XII
SUBJECT: Mathematics (041)
Time: 3 Hours Maximum Marks: 80
General Instructions:
Read the following instructions very carefully and strictly follow them:
(i) This Question paper contains 38 questions. All questions are compulsory.
(ii) This Question paper is divided into five Sections - A, B, C, D and E.
(iii) In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and Questions no. 19 and
20 are Assertion-Reason based questions of 1 mark each.
(iv) In Section B, Questions no. 21 to 25 are Very Short Answer (VSA)-type questions, carrying 2 marks
each.
(v) In Section C, Questions no. 26 to 31 are Short Answer (SA)-type questions, carrying 3 marks each.
(vi) In Section D, Questions no. 32 to 35 are Long Answer (LA)-type questions, carrying 5 marks each.
(vii) In Section E, Questions no. 36 to 38 are Case study-based questions, carrying 4 marks each.
(viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B,
3 questions in Section C, 2 questions in Section D and one subpart each in 2 questions of Section E.
(ix) Use of calculators is not allowed.
SECTION-A 1 20 20
(This section comprises of multiple choice questions (MCQs) of 1 mark each)
Select the correct option (Question 1 - Question 18):
𝟐𝟎𝟐𝟓 𝟎 𝟎
Q.1. If for a square matrix A, 𝑨. (𝒂𝒅𝒋𝑨) = [ 𝟎 𝟐𝟎𝟐𝟓 𝟎 ], then the value of A adj A is
𝟎 𝟎 𝟐𝟎𝟐𝟓
equal to:
(C) 2025 45 (D) 2025 2025
2 2
(A) 1 (B) 2025 1
Q.2. Assume X , Y , Z , W and P are matrices of order 2 n, 3 k , 2 p, n 3 and p k ,
respectively. Then the restriction on n, k and p so that PY WY will be defined are:
(A) k 3, p n (B) k is arbitrary, p 2
(C) p is arbitrary, k 3 (D) k 2, p 3
Q.3. The interval in which the function f defined by 𝑓(𝑥) = 𝑒 𝑥 is strictly increasing, is
(A) [1, ∞) (B) ,0 (C) (−∞, ∞) (D) (0,∞)
Class-XII/Sample Paper/2024-25/Mathematics/Page 1 of 9
, 𝟐
Q.4. If A and B are non-singular matrices of same order with 𝒅𝒆𝒕(𝑨) = 𝟓, then 𝒅𝒆𝒕(𝑩−𝟏 𝑨𝑩) is equal to
2 4
(A) 5 (B) 5 (C) 5 (D) 5 5
𝒅𝒚
Q.5. The value of ' n ' , such that the differential equation 𝒙𝒏 𝒅𝒙 = 𝒚(𝒍𝒐𝒈𝒚 − 𝒍𝒐𝒈𝒙 + 𝟏);
(𝐰𝐡𝐞𝐫𝐞 𝒙, 𝒚 ∈ 𝑹+ ) is homogeneous, is
(A) 0 (B) 1 (C) 2 (D) 3
Q.6. If the points (𝒙𝟏 , 𝒚𝟏 ), (𝒙𝟐 , 𝒚𝟐 ) and (𝒙𝟏 + 𝒙𝟐 , 𝒚𝟏 + 𝒚𝟐 )are collinear, then 𝒙𝟏 𝒚𝟐 is equal to
(A) x2 y1 (B) x1 y1 (C) x2 y2 (D) x1 x2
0 1 c
Q.7. If A 1 a b is a skew-symmetric matrix then the value of a b c
2 3 0
(A)1 (B) 2 (C) 3 (D) 4
Q.8. For any two events A and B , if P A 1
2
2
3
1
, P B and P A B , then 𝑃 (𝐴⁄ ̅ ) equals:
4
̅
𝐵
3 8 5 1
(A) (B) (C) (D)
8 9 8 4
Q.9. The value of 𝛼 if the angle between 𝑝⃗ = 2𝛼 2 𝑖̂ − 3𝛼𝑗̂ + 𝑘̂ and 𝑞⃗ = 𝑖̂ + 𝑗̂ + 𝛼𝑘̂ is obtuse, is
(A) 𝑅 − [0, 1] (B) (0, 1) (C) [0, ∞) (D) [1, ∞)
Q.10. If |𝑎⃗| = 3, |𝑏⃗⃗| = 4 and |𝑎⃗ + 𝑏⃗⃗| =5, then |𝑎⃗ − 𝑏⃗⃗| =
(A) 3 (B) 4 (C) 5 (D) 8
Q.11. For the linear programming problem (LPP), the objective function is Z 4 x 3 y and the feasible
region determined by a set of constraints is shown in the graph:
Class-XII/Sample Paper/2024-25/Mathematics/Page 2 of 9
CLASS- XII
SUBJECT: Mathematics (041)
Time: 3 Hours Maximum Marks: 80
General Instructions:
Read the following instructions very carefully and strictly follow them:
(i) This Question paper contains 38 questions. All questions are compulsory.
(ii) This Question paper is divided into five Sections - A, B, C, D and E.
(iii) In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and Questions no. 19 and
20 are Assertion-Reason based questions of 1 mark each.
(iv) In Section B, Questions no. 21 to 25 are Very Short Answer (VSA)-type questions, carrying 2 marks
each.
(v) In Section C, Questions no. 26 to 31 are Short Answer (SA)-type questions, carrying 3 marks each.
(vi) In Section D, Questions no. 32 to 35 are Long Answer (LA)-type questions, carrying 5 marks each.
(vii) In Section E, Questions no. 36 to 38 are Case study-based questions, carrying 4 marks each.
(viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B,
3 questions in Section C, 2 questions in Section D and one subpart each in 2 questions of Section E.
(ix) Use of calculators is not allowed.
SECTION-A 1 20 20
(This section comprises of multiple choice questions (MCQs) of 1 mark each)
Select the correct option (Question 1 - Question 18):
𝟐𝟎𝟐𝟓 𝟎 𝟎
Q.1. If for a square matrix A, 𝑨. (𝒂𝒅𝒋𝑨) = [ 𝟎 𝟐𝟎𝟐𝟓 𝟎 ], then the value of A adj A is
𝟎 𝟎 𝟐𝟎𝟐𝟓
equal to:
(C) 2025 45 (D) 2025 2025
2 2
(A) 1 (B) 2025 1
Q.2. Assume X , Y , Z , W and P are matrices of order 2 n, 3 k , 2 p, n 3 and p k ,
respectively. Then the restriction on n, k and p so that PY WY will be defined are:
(A) k 3, p n (B) k is arbitrary, p 2
(C) p is arbitrary, k 3 (D) k 2, p 3
Q.3. The interval in which the function f defined by 𝑓(𝑥) = 𝑒 𝑥 is strictly increasing, is
(A) [1, ∞) (B) ,0 (C) (−∞, ∞) (D) (0,∞)
Class-XII/Sample Paper/2024-25/Mathematics/Page 1 of 9
, 𝟐
Q.4. If A and B are non-singular matrices of same order with 𝒅𝒆𝒕(𝑨) = 𝟓, then 𝒅𝒆𝒕(𝑩−𝟏 𝑨𝑩) is equal to
2 4
(A) 5 (B) 5 (C) 5 (D) 5 5
𝒅𝒚
Q.5. The value of ' n ' , such that the differential equation 𝒙𝒏 𝒅𝒙 = 𝒚(𝒍𝒐𝒈𝒚 − 𝒍𝒐𝒈𝒙 + 𝟏);
(𝐰𝐡𝐞𝐫𝐞 𝒙, 𝒚 ∈ 𝑹+ ) is homogeneous, is
(A) 0 (B) 1 (C) 2 (D) 3
Q.6. If the points (𝒙𝟏 , 𝒚𝟏 ), (𝒙𝟐 , 𝒚𝟐 ) and (𝒙𝟏 + 𝒙𝟐 , 𝒚𝟏 + 𝒚𝟐 )are collinear, then 𝒙𝟏 𝒚𝟐 is equal to
(A) x2 y1 (B) x1 y1 (C) x2 y2 (D) x1 x2
0 1 c
Q.7. If A 1 a b is a skew-symmetric matrix then the value of a b c
2 3 0
(A)1 (B) 2 (C) 3 (D) 4
Q.8. For any two events A and B , if P A 1
2
2
3
1
, P B and P A B , then 𝑃 (𝐴⁄ ̅ ) equals:
4
̅
𝐵
3 8 5 1
(A) (B) (C) (D)
8 9 8 4
Q.9. The value of 𝛼 if the angle between 𝑝⃗ = 2𝛼 2 𝑖̂ − 3𝛼𝑗̂ + 𝑘̂ and 𝑞⃗ = 𝑖̂ + 𝑗̂ + 𝛼𝑘̂ is obtuse, is
(A) 𝑅 − [0, 1] (B) (0, 1) (C) [0, ∞) (D) [1, ∞)
Q.10. If |𝑎⃗| = 3, |𝑏⃗⃗| = 4 and |𝑎⃗ + 𝑏⃗⃗| =5, then |𝑎⃗ − 𝑏⃗⃗| =
(A) 3 (B) 4 (C) 5 (D) 8
Q.11. For the linear programming problem (LPP), the objective function is Z 4 x 3 y and the feasible
region determined by a set of constraints is shown in the graph:
Class-XII/Sample Paper/2024-25/Mathematics/Page 2 of 9
