Class 11 PT I Question Paper 2026-27 Maths (Commerce)

CBSE CLASS 11
PT I Question Paper
Session 2026-27

MATHS
(COMMERCE)

Exam CBSE Class 11
Subject Maths (Commerce)
Session 2026-27
Document Type PT I Question Paper

Notes · Sample Papers · Previous Year Papers · Mock Tests

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Question Paper

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SESSION: 2026-2027
CLASS: XI MAXIMUM MARKS: 40
SUBJECT: MATHEMATICS TIME: 1 HOUR 30 MINUTES
General Instructions:

1. This Question paper contains 17 questions in 2 pages. All questions are compulsory.
2. This Question paper is divided into five Sections - A, B, C, D and E.
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3. In Section A, Questions no. 01 to 04 are multiple choice questions (MCQs) with only one correct option

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and Questions no. 05 is Assertion-Reason based questions of 1 mark.
4. In Section B, Questions no. 6 to 11 are Very Short Answer (VSA)-type questions, carrying 2 marks each.
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5. In Section C, Questions no. 12 to 14 are Short Answer (SA)-type questions, carrying 3 marks each.
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6. In Section D, Questions no. 15 & 16 are Long Answer (LA)-type questions, carrying 5 marks each.
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7. In Section E, Questions no. 17 is Case study-based question, carrying 4 marks.
8. There is no overall choice. However, an internal choice has been provided in 2 question in Section B, 2
questions in Section C, 1 question in Section D and one subpart in the question of Section E.

SECTION –A
1. In set-builder method the null set is represented by 1
(a) {} (b) Φ (c) {x : x  x} (d) {x : x  x}
2. Let set 𝐴 = {𝑎, 𝑏} and 𝐵 = {𝑐, 𝑑}.Number of possible relation from the set 𝐴 to set 𝐵 will be 1
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(a) 16 (b) 4 (c) 32 (d) 2

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If tanA= and tanB= , then the value of A+B is
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3.

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2 3
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 
(a) (b)  (c) 0 (d)
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4. The value of 𝑡𝑎𝑛 is 1

(a)√3 (b) (c) (d) 1
√ √
5. Assertion (A):The domain of the real function f defined by 𝑓(𝑥) = √𝑥 − 1 is 𝑥 > 1 1
Reason(R) : The range of the function defined by 𝑦 = 𝑓(𝑥) is [0, ∞]

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(A) Assertion is true, Reason is true and Reason is a correct explanation for Assertion.

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(B) Assertion is true, Reason is true; Reason is not a correct explanation for Assertion.
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(C) Assertion is true, Reason is false.
(D) Assertion is false, Reason is true.
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SECTION –B

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If U={1,2,3,4,5,6,7,8,9},A={1,2,3,4},B={2,4,6,8}, C={3,4,5,6} find (i)(A  B)′ (ii) (B−C) ′ 2

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Two finite sets have m and n elements. The total number of subsets of the first set is 56 more
than the total number of subsets of the second set. Find the values of m and n.
2

Find the range of 𝑓(𝑥) = 2

OR

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Write down the domain and rannge of the above function.
9. Let 𝐴 and 𝐵 be two sets such tha hat 𝐴 × 𝐵 consists of 6 elements. If three elem
ments of 𝐴 × 𝐵 2
are (𝑎, 0), (𝑏, 1), (𝑐, 0), find 𝐴 × 𝐵
10. (
Prove that ( ) =
)
. 2
11. If the arcs of the same length inn two circles subtend angles of 65° and 110° at a their respective 2
centers, find the ratio of theirr ra
radii.
OR
Prove that : sec ( − 𝜃) sec( 𝜃 − ) + tan ( + 𝜃) tan( 𝜃 − ) = 1
SECTION –C
12. A market research group conduconducted a survey of 2000 consumers and reporteed that 1720
consumers liked product A andd 1450 cconsumers liked product B. What is the he least number 3
that must have liked both the produc
products?
13. If f = {(1,1),(2,3) ,(0,-1),(-1,-3)}
3)} be a linear function from z to z ,find f(x). 3
OR
Find the range of 𝑓(𝑥) = .

14. Prove that tan 3x tan 2x tan x=
= tan 3x- tan 2x - tan x 3
OR
If sin x= and cos y = here x and y lies in 2nd quadrant, find the value
, whe ue of sin (x+y).

SECTION –D
15. 2,3,4}, 𝐵 = {3,4,5}. Show that (𝐴 ∪ 𝐵)′ = 𝐴′ ∩ 𝐵 ′
Let 𝑈 = {1,2,3,4,5,6,8}, 𝐴 = {2 5
′ ′ ′
and (𝐴 ∩ 𝐵) = 𝐴 ∪ 𝐵
16. (a)If tan(𝛼 + 𝜃) = 𝑛 tan(𝛼 − 𝜃𝜃) ,show that (n+1)𝑠𝑖𝑛2𝜃 = (𝑛 − 1)𝑠𝑖𝑛2𝛼. 5
OR
(b)If 3𝑡𝑎𝑛𝐴 𝑡𝑎𝑛𝐵 = 1 , prove tthat 2cos (A+B) = cos (A-B).
SECTION –E
17. In a survey of 40 students, it waas found that 21 had taken Mathematics, 16 had
ha taken Physics 4(1+1+2)
and 15 taken Chemistry, 7 had ttaken Mathematics and Chemistry, 12 had take ken Mathematics
and Physics, 5 had taken Physiccs and Chemistry and 4 had taken all the threee subjects.

Based on the above information, n, aanswer the following questions:
(i) Find the number of students wwho had taken Mathematics only.
(ii) Find the number of studentss who had taken Physics and Chemistry but not Mathematics.
(iii)(a) Find the number of stude
dents who had taken at least one of the three suubjects.
OR
(b)Find the number of students w who had taken none of the subjects.

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