SET 1
KENDRIYA VIDYALAYA SANGATHAN SILCHAR REGION
PRE – BOARD EXAMINATION 2025 –2026
SUBJECT – MATHEMATICS (041)
CLASS - XII
Time Allowed : 3 Hours Maximum Marks : 80
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 Question no. 19 and 20 are Assertion – Reason based questions of 1 mark each.
4. In Section B, Question no. 21 to 25 are Very Short Answer (VSA) – type questions, carrying 2 marks
each.
5. In Section C, Question no. 26 to 31 are Short Answer (SA) – type questions, carrying 3 marks each.
6. In Section D, Question no. 32 to 35 are Long Answer (LA) – type questions, carrying 5 marks each.
7. In Section E, Question 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 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(MCQ)s of 1 mark each
Select the correct option(Question 1 – Question 18):
Q.No. Question Marks
1 -1 17𝜋 1
The value of sin [sin ( 8 ) ] is
17𝜋 𝜋 𝜋 13𝜋
(𝑎 ) (b) 8 (c) - 8 (d)
8 8
2 If the order of matrix A is m × p and the order of B is p × n. Then the order of matrix AB is? 1
(a ) n × p (b) m × n (c) n × p (d) n × m
3 Let A be a skew symmetric matrix of order 3. If |A| = x, then (2023)x is 1
1
(a ) 2023 (b) 2023 (c) 20232 (d) 1
4 If A is a non-singular square matrix of order 3 such that |𝑎𝑑𝑗𝐴 | = 64 then the value of |𝐴| is 1
(a ) 8 (b) –8 (c) ± 8 (d) 4
5 If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k. 1
7 40
(a ) 4 (b) 140 (c) 47 (d) 7
6 Let A be a square matrix of order 3 x 3 such that |𝐴| = 2 the value of |4𝐴|? 1
(a ) 128 (b) 64 (c) 8 (d) 16
2
7 𝑘𝑥 , 𝑖𝑓 𝑥 ≤ 2 1
What value of k, the function f(x) = { , is continuous at x=2.
3, 𝑖𝑓 𝑥 > 2
3 3
(a ) 0 (b) 1 (c) 4 (d) 2
8 1 𝑥 𝑑𝑦 1
If 𝑦 = (1 + 𝑥) , then 𝑑𝑥 =
1 1 1 1 1
(a) (1 + 𝑥)𝑥 [log (1+𝑥) – ] (b) (1 + 𝑥)𝑥 [log(1+𝑥)]
𝑥+1
(c) 0 (d) 1
, SET 1
9 The interval on which the function 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 6 is strictly increasing is 1
(a ) (−∞, 2) ∪ (2, ∞) (b) (2, ∞)
(c) (−∞, 2) (d) (−∞, 2] ∪ (2, ∞)
10 𝑑𝑦 1
Integrating factor of the differential equation 𝑑𝑥 + 𝑦 𝑡𝑎𝑛𝑥 − 𝑠𝑒𝑐𝑥 = 0 𝑖𝑠
(a ) 𝑐𝑜𝑠𝑥 (b) 𝑠𝑒𝑐𝑥 (c) 𝑒 𝑐𝑜𝑠𝑥 (d) 𝑒 𝑠𝑒𝑐𝑥
11 𝑑 1
If 𝑑𝑥 [ f(x)] = ax + b and f(0) = 0 , then f(x) is equal to
𝑎𝑥 2 𝑎𝑥 2
(a ) a+b (b) + bx (c) + bx + C (d) b
2 2
π
12 2 1
9
What is the value of ∫ sin x dx
π
–
2
(𝑎 ) 0 (𝑏)1 (𝑐) − 1 (𝑑) 2
13 The projection of the vector ⃗⃗⃗⃗𝑎 = 2𝑖̂ − 𝑗̂ + 𝑘̂ on 𝑏⃗ = 𝑖̂ − 2𝑗̂ + 𝑘̂ is : 1
√5 5 5 √6
(a ) (b) (c) √6 (d)
2 √2 5
14 The value of (𝑖̂ × 𝑗̂) ∙ 𝑗̂ + (𝑗̂ × 𝑖̂) ∙ 𝑘̂ is 1
(a ) 2 (b) 0 (c) 1 (d) -1
15 ̂ ̂
The value of p for which the vectors 2𝑖̂ + 𝑝𝑗̂ + 𝑘 and -4𝑖̂ − 6𝑗̂ + 26𝑘 are perpendicular to 1
each other, is
−17 17
(a ) 3 (b) -3 (c) 3 (d) 3
16 The solution set of the inequality 3𝑥 + 4𝑦 < 4 is 1
(a ) An open half-plane not containing the origin
(b ) An open half-plane containing the origin
(c ) The whole 𝑥𝑦 plane not containing the line 3𝑥 + 4𝑦 = 4
(d ) A closed half-plane containing the origin
17 Objective function of an LPP is _____ 1
(a ) a constraint (b) a function which is to be optimized.
(c ) a relation between variables. (d) none of these.
18 If P(A ∩ B) = 70% and P(B) = 85%, then P(A/B) is equal to 1
14 17 7 1
(a ) 17 (b) 20 (c) 8 (d) 8
ASSERTION-REASON BASED QUESTIONS
(Question numbers 19 and 20 are Assertion-Reason based questions carrying 1 mark each. Two statements are
given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options
(a), (b), (c) and (d) as given below.
(a ) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b ) Both (A) and (R) are true but (R) is not the correct explanation of (A).
(c ) (A) is true but (R) is false.
(d ) (A) is false but (R) is true.
19 Assertion(A): All trigonometric functions have their inverses over their respective domains.
Reason(R): The inverse of tan-1x exists for some x ϵ R 1
20 Assertion(A): The area of parallelogram with diagonals 𝑎 and 𝑏⃗ is |𝑎 × 𝑏⃗ |.
1
Reason(R): If 𝑎 and 𝑏⃗ represent the adjacent sides of a triangle, then the area of a triangle,
KENDRIYA VIDYALAYA SANGATHAN SILCHAR REGION
PRE – BOARD EXAMINATION 2025 –2026
SUBJECT – MATHEMATICS (041)
CLASS - XII
Time Allowed : 3 Hours Maximum Marks : 80
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 Question no. 19 and 20 are Assertion – Reason based questions of 1 mark each.
4. In Section B, Question no. 21 to 25 are Very Short Answer (VSA) – type questions, carrying 2 marks
each.
5. In Section C, Question no. 26 to 31 are Short Answer (SA) – type questions, carrying 3 marks each.
6. In Section D, Question no. 32 to 35 are Long Answer (LA) – type questions, carrying 5 marks each.
7. In Section E, Question 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 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(MCQ)s of 1 mark each
Select the correct option(Question 1 – Question 18):
Q.No. Question Marks
1 -1 17𝜋 1
The value of sin [sin ( 8 ) ] is
17𝜋 𝜋 𝜋 13𝜋
(𝑎 ) (b) 8 (c) - 8 (d)
8 8
2 If the order of matrix A is m × p and the order of B is p × n. Then the order of matrix AB is? 1
(a ) n × p (b) m × n (c) n × p (d) n × m
3 Let A be a skew symmetric matrix of order 3. If |A| = x, then (2023)x is 1
1
(a ) 2023 (b) 2023 (c) 20232 (d) 1
4 If A is a non-singular square matrix of order 3 such that |𝑎𝑑𝑗𝐴 | = 64 then the value of |𝐴| is 1
(a ) 8 (b) –8 (c) ± 8 (d) 4
5 If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k. 1
7 40
(a ) 4 (b) 140 (c) 47 (d) 7
6 Let A be a square matrix of order 3 x 3 such that |𝐴| = 2 the value of |4𝐴|? 1
(a ) 128 (b) 64 (c) 8 (d) 16
2
7 𝑘𝑥 , 𝑖𝑓 𝑥 ≤ 2 1
What value of k, the function f(x) = { , is continuous at x=2.
3, 𝑖𝑓 𝑥 > 2
3 3
(a ) 0 (b) 1 (c) 4 (d) 2
8 1 𝑥 𝑑𝑦 1
If 𝑦 = (1 + 𝑥) , then 𝑑𝑥 =
1 1 1 1 1
(a) (1 + 𝑥)𝑥 [log (1+𝑥) – ] (b) (1 + 𝑥)𝑥 [log(1+𝑥)]
𝑥+1
(c) 0 (d) 1
, SET 1
9 The interval on which the function 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 6 is strictly increasing is 1
(a ) (−∞, 2) ∪ (2, ∞) (b) (2, ∞)
(c) (−∞, 2) (d) (−∞, 2] ∪ (2, ∞)
10 𝑑𝑦 1
Integrating factor of the differential equation 𝑑𝑥 + 𝑦 𝑡𝑎𝑛𝑥 − 𝑠𝑒𝑐𝑥 = 0 𝑖𝑠
(a ) 𝑐𝑜𝑠𝑥 (b) 𝑠𝑒𝑐𝑥 (c) 𝑒 𝑐𝑜𝑠𝑥 (d) 𝑒 𝑠𝑒𝑐𝑥
11 𝑑 1
If 𝑑𝑥 [ f(x)] = ax + b and f(0) = 0 , then f(x) is equal to
𝑎𝑥 2 𝑎𝑥 2
(a ) a+b (b) + bx (c) + bx + C (d) b
2 2
π
12 2 1
9
What is the value of ∫ sin x dx
π
–
2
(𝑎 ) 0 (𝑏)1 (𝑐) − 1 (𝑑) 2
13 The projection of the vector ⃗⃗⃗⃗𝑎 = 2𝑖̂ − 𝑗̂ + 𝑘̂ on 𝑏⃗ = 𝑖̂ − 2𝑗̂ + 𝑘̂ is : 1
√5 5 5 √6
(a ) (b) (c) √6 (d)
2 √2 5
14 The value of (𝑖̂ × 𝑗̂) ∙ 𝑗̂ + (𝑗̂ × 𝑖̂) ∙ 𝑘̂ is 1
(a ) 2 (b) 0 (c) 1 (d) -1
15 ̂ ̂
The value of p for which the vectors 2𝑖̂ + 𝑝𝑗̂ + 𝑘 and -4𝑖̂ − 6𝑗̂ + 26𝑘 are perpendicular to 1
each other, is
−17 17
(a ) 3 (b) -3 (c) 3 (d) 3
16 The solution set of the inequality 3𝑥 + 4𝑦 < 4 is 1
(a ) An open half-plane not containing the origin
(b ) An open half-plane containing the origin
(c ) The whole 𝑥𝑦 plane not containing the line 3𝑥 + 4𝑦 = 4
(d ) A closed half-plane containing the origin
17 Objective function of an LPP is _____ 1
(a ) a constraint (b) a function which is to be optimized.
(c ) a relation between variables. (d) none of these.
18 If P(A ∩ B) = 70% and P(B) = 85%, then P(A/B) is equal to 1
14 17 7 1
(a ) 17 (b) 20 (c) 8 (d) 8
ASSERTION-REASON BASED QUESTIONS
(Question numbers 19 and 20 are Assertion-Reason based questions carrying 1 mark each. Two statements are
given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options
(a), (b), (c) and (d) as given below.
(a ) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b ) Both (A) and (R) are true but (R) is not the correct explanation of (A).
(c ) (A) is true but (R) is false.
(d ) (A) is false but (R) is true.
19 Assertion(A): All trigonometric functions have their inverses over their respective domains.
Reason(R): The inverse of tan-1x exists for some x ϵ R 1
20 Assertion(A): The area of parallelogram with diagonals 𝑎 and 𝑏⃗ is |𝑎 × 𝑏⃗ |.
1
Reason(R): If 𝑎 and 𝑏⃗ represent the adjacent sides of a triangle, then the area of a triangle,
