MATHEMATICS – Code No. 041
SAMPLE QUESTION PAPER
CLASS - XII (2025-26)
Maximum Marks: 80 Time: 3 hours
General Instructions:
Read the following instructions very carefully and strictly follow them:
1. This Question paper contains 38 questions. All questions are compulsory.
2. This Question paper is divided into five Sections - A, B, C, D and E.
3. In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) with only one
correct option and Questions no. 19 and 20 are Assertion-Reason based questions of 1
mark each.
4. In Section B, Questions no. 21 to 25 are Very Short Answer (VSA)-type questions, carrying
2 marks each.
5. In Section C, Questions no. 26 to 31 are Short Answer (SA)-type questions, carrying 3
marks each.
6. In Section D, Questions no. 32 to 35 are Long Answer (LA)-type questions, carrying 5
marks each.
7. In Section E, Questions no. 36 to 38 are Case study-based questions, carrying 4 marks
each.
8. 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.
9. Use of calculator is not allowed.
SECTION-A
This section comprises of multiple choice questions (MCQs) of 1 mark each.
Select the correct option (Question 1 - Question 18)
Q.No. Questions Marks
1. Identify the function shown in the graph 1
𝑥
(A) sin−1 𝑥 (B) sin−1(2𝑥) (C) sin−1 (2) (D) 2 sin−1 𝑥
For Visually Impaired:
1 1
1. Inverse Trigonometric Function, whose domain is [− 3 , 3] , is …
𝑥
(A) cos−1 𝑥 (B) cos −1 (3)
(C) cos−1 (3𝑥) (D) 3 cos−1 𝑥
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e.
2025-26. Page 1 of 10
, 2. If for three matrices 𝐴 = [𝑎𝑖𝑗 ]𝑚×4 , B = [𝑏𝑖𝑗 ]𝑛×3 𝑎𝑛𝑑 C = [𝑐𝑖𝑗 ]𝑝×𝑞 products 𝐴𝐵 and 1
𝐴𝐶 both are defined and are square matrices of same order, then value of 𝑚, 𝑛, 𝑝
and 𝑞 are:
(A) 𝑚 = 𝑞 = 3 𝑎𝑛𝑑 𝑛 = 𝑝 = 4 (B) 𝑚 = 2, 𝑞 = 3 𝑎𝑛𝑑 𝑛 = 𝑝 = 4
(C) 𝑚 = 𝑞 = 4 𝑎𝑛𝑑 𝑛 = 𝑝 = 3 (D) 𝑚 = 4, 𝑝 = 2 𝑎𝑛𝑑 𝑛 = 𝑞 = 3
3. 0 𝑟 −2 1
𝑞+𝑡
If the matrix 𝐴 = [3 𝑝 𝑡 ] is skew-symmetric, then value of is….
𝑝+𝑟
𝑞 −4 0
(A)−2 (B) 0 (C) 1 (D) 2
4. If 𝐴 is a square matrix of order 4 and |𝑎𝑑𝑗 𝐴| = 27, then 𝐴 (𝑎𝑑𝑗 𝐴) is equal to 1
(A) 3 (B) 9 (C) 3 𝐼 (D) 9 𝐼
5. 3 0 0 1
The inverse of the matrix [0 2 0] is…
0 0 5
1
0 0
0 0 3 3
1
(A) [0 2 0] (B) 0 2
0
5 0 0 1
[0 0 5]
1
−3 0 0
−3 0 0
1
(C) 0 −2 0 (D) [ 0 −2 0 ]
1 0 0 −5
[0 0 − 5]
6. cos 67𝑜 sin 67𝑜 1
Value of the determinant | | is
sin 23𝑜 cos 23𝑜
1 √3
(A) 0 (B) (C) (D) 1
2 2
7. If a function defined by 𝑓(𝑥) = {
𝑘𝑥 + 1, 𝑥 ≤ 𝜋 1
cos 𝑥 , 𝑥 > 𝜋
is continuous at 𝑥 = 𝜋, then the value of 𝑘 is
−1 −2
(A) 𝜋 (B) (C) 0 (D)
𝜋 𝜋
8. If 𝑓(𝑥) = 𝑥 tan−1 𝑥 , then 𝑓 ′ (1)is equal to 1
𝜋 1 𝜋 1 𝜋 1 𝜋 1
(A) 4 − (B) 4 + (C) − − (D) − 4 +
2 2 4 2 2
9. A function 𝑓(𝑥) = 10 − 𝑥 − 2𝑥 2 is increasing on the interval 1
1 1 1 1 1
(A) (−∞, − 4] (B) (−∞, 4) (C) [− 4 , ∞) (D)[− 4 , 4]
10. The solution of the differential equation 𝑥𝑑𝑥 + 𝑦𝑑𝑦 = 0 represents a family of 1
(A) straight lines (B) parabolas (C) Circles (D) Ellipses
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e.
2025-26. Page 2 of 10
SAMPLE QUESTION PAPER
CLASS - XII (2025-26)
Maximum Marks: 80 Time: 3 hours
General Instructions:
Read the following instructions very carefully and strictly follow them:
1. This Question paper contains 38 questions. All questions are compulsory.
2. This Question paper is divided into five Sections - A, B, C, D and E.
3. In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) with only one
correct option and Questions no. 19 and 20 are Assertion-Reason based questions of 1
mark each.
4. In Section B, Questions no. 21 to 25 are Very Short Answer (VSA)-type questions, carrying
2 marks each.
5. In Section C, Questions no. 26 to 31 are Short Answer (SA)-type questions, carrying 3
marks each.
6. In Section D, Questions no. 32 to 35 are Long Answer (LA)-type questions, carrying 5
marks each.
7. In Section E, Questions no. 36 to 38 are Case study-based questions, carrying 4 marks
each.
8. 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.
9. Use of calculator is not allowed.
SECTION-A
This section comprises of multiple choice questions (MCQs) of 1 mark each.
Select the correct option (Question 1 - Question 18)
Q.No. Questions Marks
1. Identify the function shown in the graph 1
𝑥
(A) sin−1 𝑥 (B) sin−1(2𝑥) (C) sin−1 (2) (D) 2 sin−1 𝑥
For Visually Impaired:
1 1
1. Inverse Trigonometric Function, whose domain is [− 3 , 3] , is …
𝑥
(A) cos−1 𝑥 (B) cos −1 (3)
(C) cos−1 (3𝑥) (D) 3 cos−1 𝑥
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e.
2025-26. Page 1 of 10
, 2. If for three matrices 𝐴 = [𝑎𝑖𝑗 ]𝑚×4 , B = [𝑏𝑖𝑗 ]𝑛×3 𝑎𝑛𝑑 C = [𝑐𝑖𝑗 ]𝑝×𝑞 products 𝐴𝐵 and 1
𝐴𝐶 both are defined and are square matrices of same order, then value of 𝑚, 𝑛, 𝑝
and 𝑞 are:
(A) 𝑚 = 𝑞 = 3 𝑎𝑛𝑑 𝑛 = 𝑝 = 4 (B) 𝑚 = 2, 𝑞 = 3 𝑎𝑛𝑑 𝑛 = 𝑝 = 4
(C) 𝑚 = 𝑞 = 4 𝑎𝑛𝑑 𝑛 = 𝑝 = 3 (D) 𝑚 = 4, 𝑝 = 2 𝑎𝑛𝑑 𝑛 = 𝑞 = 3
3. 0 𝑟 −2 1
𝑞+𝑡
If the matrix 𝐴 = [3 𝑝 𝑡 ] is skew-symmetric, then value of is….
𝑝+𝑟
𝑞 −4 0
(A)−2 (B) 0 (C) 1 (D) 2
4. If 𝐴 is a square matrix of order 4 and |𝑎𝑑𝑗 𝐴| = 27, then 𝐴 (𝑎𝑑𝑗 𝐴) is equal to 1
(A) 3 (B) 9 (C) 3 𝐼 (D) 9 𝐼
5. 3 0 0 1
The inverse of the matrix [0 2 0] is…
0 0 5
1
0 0
0 0 3 3
1
(A) [0 2 0] (B) 0 2
0
5 0 0 1
[0 0 5]
1
−3 0 0
−3 0 0
1
(C) 0 −2 0 (D) [ 0 −2 0 ]
1 0 0 −5
[0 0 − 5]
6. cos 67𝑜 sin 67𝑜 1
Value of the determinant | | is
sin 23𝑜 cos 23𝑜
1 √3
(A) 0 (B) (C) (D) 1
2 2
7. If a function defined by 𝑓(𝑥) = {
𝑘𝑥 + 1, 𝑥 ≤ 𝜋 1
cos 𝑥 , 𝑥 > 𝜋
is continuous at 𝑥 = 𝜋, then the value of 𝑘 is
−1 −2
(A) 𝜋 (B) (C) 0 (D)
𝜋 𝜋
8. If 𝑓(𝑥) = 𝑥 tan−1 𝑥 , then 𝑓 ′ (1)is equal to 1
𝜋 1 𝜋 1 𝜋 1 𝜋 1
(A) 4 − (B) 4 + (C) − − (D) − 4 +
2 2 4 2 2
9. A function 𝑓(𝑥) = 10 − 𝑥 − 2𝑥 2 is increasing on the interval 1
1 1 1 1 1
(A) (−∞, − 4] (B) (−∞, 4) (C) [− 4 , ∞) (D)[− 4 , 4]
10. The solution of the differential equation 𝑥𝑑𝑥 + 𝑦𝑑𝑦 = 0 represents a family of 1
(A) straight lines (B) parabolas (C) Circles (D) Ellipses
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e.
2025-26. Page 2 of 10
