Class 12 PT I Question Paper 2025-26 Maths (Commerce)

CBSE CLASS 12
PT I Question Paper
Session 2025-26

MATHS
(COMMERCE)

Exam CBSE Class 12
Subject Maths (Commerce)
Session 2025-26
Document Type PT I Question Paper

Notes · Sample Papers · Previous Year Papers · Mock Tests

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se FIRST UNIT TEST a
Question Paper
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SESSION: 2025-2026

CLASS: XII MAXIMUM MARKS: 40
SUBJECT: MATHEMATICS TIME: 1 HOUR 30 MINUTES
General Instructions:

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a)� The question paper consists of 3 printed pages and 17 questions in all. All questions

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are compulsory.

b)� This question paper is divided into five Sections – A, B, C, D and E.

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c)� In Section A, Questions no. 1 to 5 are multiple choice questions (MCQs) and

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questions number 6 and 7 are Assertion-Reason based questions of 1 mark each.
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d)� In Section B, Questions no. 8 to 10 are very short answer (VSA) type questions,
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carrying 2 marks each.
e)� In Section C, Questions no. 11 to 13 are short answer (SA) type questions, carrying 3
marks each.
f)� In Section D, Questions no. 14 and 15 are long answer (LA) type questions carrying
5 marks each.
g)� In Section E, Questions no. 16 and 17 are case study-based question carrying 4
marks.
h)� There is no overall choice. However, an internal choice has been provided in 2
questions in Section B, 1 questions in Section C, 1 question in Section D and 1
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question in Section E.

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i)� Use of calculators is not allowed.

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achoice questions (MCQs) of 1 mark each)
Section – A

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(This section comprises multiple
𝑡 𝑡
Q.1. Let both 𝐴𝐵 and 𝐵 𝐴 be defined for matrices A and B. If order of A is n× 𝑚, 1
then order of B is:
(A) n×n (B) n×m
(C) m×m (D) m×n
Q.2. The following graph is a combination of:
1

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(A) y = sin−1 𝑥 and y = cos−1 𝑥 (B) y = cos 𝑥 and cos−1 𝑥

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(C) y = sin−1 𝑥 and y = sinx (D) y = cos−1 𝑥 and y = sin 𝑥

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Q.3. If the set A contains 5 elements and the set B contains 6 elements , then the 1
number of one-one and onto mappings from A to B is
A)720 B)120 C) 0 D)11
Q.4. −1 (𝑥 2 2) 𝑑𝑦 1
If tan + 𝑦 = 𝑎 , where a is a constant, then is:
𝑑𝑥
𝑥 𝑥
(A) (B) −
𝑦 𝑦
𝑎 𝑎
(C) (D)
𝑥 𝑦
Q.5. 3𝑥 − 2 0<𝑥≤1 1
If f(x) = { 2 } is continuous for 𝑥 ∈ (0,2), then a is equal
2𝑥 + 𝑎𝑥 1 < 𝑥 < 2
to:
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(A) −4 (B) −
2
(C) −2 (D) −1
Questions number 6 and 7 are Assertion and Reason based questions. Two
statements are given, one labelled Assertion (A) and the other labelled Reason
(R). Select the correct answer from the codes (A), (B), (C) and (D) as given
below.
(A)�Both Assertion (A) and Reason (R) are true and Reason (R) is the
correct explanation of the Assertion (A).
(B)�Both Assertion (A) and Reason (R) are true, but Reason (R) is not the
correct explanation of the Assertion (A).
(C)�Assertion (A) is true, but Reason (R) is false.
(D)�Assertion (A) is false, but Reason (R) is true.
Q.6. Assertion (A):- The function f: R→R defined by f(x) = x3 is a bijection. 1
Reason (R ):- Every polynomial function is a bijection.

Q.7. Assertion (A):Let A and B be two square matrices of order 3 such that 1
det(A) = 3 and det(B) = −4. Then the value of det (−6𝐴𝐵) = −2592.
Reason (R):If A = KB, where A and B are square matrices of order n, then
|𝐴| = 𝑘 𝑛 |𝐵| and |𝑃𝑄| = |𝑃||𝑄|.
Section – B
(This section comprises very short answer (VSA) type questions of 2 marks each)
Q.8. 𝑥 2
(a) Simplify sin−1 ( )
√(1+𝑥 2 )
OR
−1
(b)Find the domain of sin √𝑥 − 1
Q.9. Check the differentiability of f(𝑥) = 𝑥[𝑥] at 𝑥 = 2.5, where [𝑥] is the greatest 2
integer function.
Q.10 Find the derivative w.r.t. 𝑥 of 𝑓(𝑥) = 10logecosx 2
. OR
∞
(cos 𝑥)… 𝑑𝑦 𝑦 2 tan 𝑥
If 𝑦 = (cos 𝑥)(cos 𝑥) , then show that 𝑑𝑥 = 𝑦 log cos 𝑥−1
Section – C
(This section comprises short answer (SA) type questions of 3 marks each)
Q.11 Consider a relation R defined on N×N, where N is the set of all naturals, in the 3
. following way:
1 1 1 1
(a,b)R(c,d)⟹ + = + ∀ (a,b), (c,d) ∈ N×N. Show that R is an
𝑎 𝑑 𝑏 𝑐
Equivalence relation.
Q.12 0 − tan(𝛼⁄2) 3
. If�𝐴 = [ ]�and 𝐼 is the identity matrix of order 2, show that
tan(𝛼⁄2) 0
cos 𝛼 − sin 𝛼
𝐼 + 𝐴 = (𝐼 − 𝐴) [ ]�
sin 𝛼 cos 𝛼
OR�
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If 𝐴 is a symmetric matrix and 𝐵 is skew symmetric matrix such that 𝐴 + 𝐵 =

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2 3
[ ] then find 𝐴𝐵.
5 −1
Q.13 −1 −1 𝑑𝑦 𝑦 3
If 𝑥 = √𝑎 𝑠𝑖𝑛 𝑡 and 𝑦 = √𝑎𝑐𝑜𝑠 𝑡 then prove that = − .
. 𝑑𝑥 𝑥
Section – D
(This section comprises long answer type questions (LA) of 5 marks each)
Q.14 Find the product of the matrices 5
. 1 2 −3 −6 17 13
[2 3 2 ] [ 14 5 −8] and hence solve the system of linear

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3 −3 −4 −15 9 −1

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equations:

𝑥 + 2𝑦 − 3𝑧 = −4

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2𝑥 + 3𝑦 + 2𝑧 = 2

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3𝑥 − 3𝑦 − 4𝑦 = 11
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Q.15
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𝑑𝑦 1−𝑦 2
If √1 − 𝑥 2 + √1 − 𝑦 2 =𝑎(𝑥 − 𝑦), then prove that 𝑑𝑥
= √1−𝑥 2 .
OR
Differentiate 𝑥 𝑠𝑖𝑛𝑥 + 𝑠𝑖𝑛𝑥 𝑐𝑜𝑠𝑥 with respect to x
Section – E (This section comprises 2 case study-based question of 4 marks)
Q.16 Amit, Biraj and Chirag were given the task of creating a square matrix of order
. 2 . Below are the matrices A, B and C which are created by Amit, Biraj and
Chirag respectively.
1 2 4 0 2 0
A=[ ]������B=[ ]���������C=[ ]�

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−1 3 1 5 1 −2

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If a= 4 and b= −2

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(i)�Find the sum of the matrices A, B and C 1

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(ii)�Evaluate (AT)T .
(iii)�Find the matrix 𝐴𝐶 − 𝐵𝐶
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1
OR 2
(iii) Find the matrix of (𝑎 + 𝑏)𝐵.�
Q.17 Salini and Disha are playing Ludo at home. While rolling the dice, Salini’sister
. Raji observed and noted the possible outcomes of the throw every time belongs
to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible
outcomes.

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Read the above information and answer the following questions: 1
(i)� Find the number of relations on from A to B
(ii)� Calculate the number of possible functions from A to B. 1
(iii)� Let R= {(1,2),(2,2),(1,3),(3,4)(,3,1),(4,3),(5,5)}, then check whether
R is reflexive, symmetric or transitive . 2
OR
(iii)Let R:B →B be defined by R= {(x,y): y is divisible by x}.

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Check whether R is equivalence relation

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