Class 11 PT II Question Paper 2025-26 Maths (Commerce)

CBSE CLASS 11
PT II Question Paper
Session 2025-26

MATHS
(COMMERCE)

Exam CBSE Class 11
Subject Maths (Commerce)
Session 2025-26
Document Type PT II Question Paper

Notes · Sample Papers · Previous Year Papers · Mock Tests

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SECOND UNIT TEST
SESSION: 2025-2026
CLASS: XI MAXIMUM MARKS: 40
SUBJECT: MATHEMATICS TIME: 1 HOUR 30 MINUTES
General Instructions:
1. The question paper consists of 2 printed pages and 17 questions in all and 5sections A, B, C, D and E

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2. Section - A comprises of 4 MCQs and 2 Assertion – Reason based questions of 1 mark each.

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3. Section - B comprises of 4 VSA type questions of 2 marks each.

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4. Section - C comprises of 4 SA type questions of 3 marks each.

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5. Section - D comprises of 2 LA type questions of 5 marks each.

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6. In Section E, Questions no.17 is Case study-based question, carrying 4 marks.
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7. There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2
questions in Section C, 01 question in Section D and in one subpart of question of Section E.
SECTION: A
This section comprises of multiple-choice questions (MCQs) (Q1.to Q4.) of 1 mark each.
Q.1 How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are 1
divisible by 10 and no digit is repeated?
(A) 24 (B) 48 (C) 120 (D) 720
Q.2 If the 5-th term of a GP is 2, then the product of first 9 terms is 1
(A) 64 (B)512 (C) 128 (D) 256
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Q.3 The minimum value of 4 + 4 is 1
(A) 2 (B) 4 (C) 1 (D) 0

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Q.4 In the parabola y2 = 4ax, the length of the chord passing through the vertex and inclined to 1
the axis at 450 is
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A) 4√2a (B) 2√2a C) √2a D) 4a
Assertion – Reason Based Questions
Direction: Question numbers 5 and 6 are Assertion (A) and Reason (R) based questions
carrying 1 mark each. Two statements are given, Assertion (A) and 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.

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Q.5 ASSERTION: The number of arrangements of the letters of the word LAUGH, if the 1

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vowels are adjacent is 12.
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REASON: The number of arrangements of n distinct items when r particular items come

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together is (n-r+1)! r!

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REASON: The equation of the circle passing through (1,0) and (0,1) and having the
a smallest possible radius is 𝑥 + 𝑦 − 𝑥 − 𝑦 = 0
SECTION: B
This section comprises of 4 very short answer (VSA) type questions of 2 marks each.
Q.7 Find the sum to n terms of the A.P., whose kth term is 5k+1. 2
OR
If a, b, c, and d are in G.P., then prove that a + b, b + c, and c + d are also in G.P.
Q.8 If there are 7 boys and 5 girls in a class, then in how many ways can they be seated in a 2
row such that no two girls sit together?

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Q.9 Using the letters of the word ‘EDUCATION’, how many words (with or without 2
meaning) using 6 letters can be made so that every word contains at least 4 vowels?
Q.10 Find the equation of a circle with origin as Centre and which circumscribes an equilateral 2
triangle whose median is of length 3𝑎.
OR
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find its focus
SECTION: C
This section comprises of 4 short answer (SA) type questions of 3 marks each.
Q.11 The ratio of A.M. and G.M. of two positive numbers a and b is 𝑚: 𝑛. Show that 𝑎: 𝑏 = 3
𝑚 + √𝑚 − 𝑛 : 𝑚 − √𝑚 − 𝑛
OR
If a and b are the roots of 𝑥 − 3𝑥 + 𝑝 = 0 and c, d are the roots of 𝑥 − 12𝑥 + 𝑞 = 0
where a, b, c, d form a G.P. Prove that (𝑞 + 𝑝)(𝑞 − 𝑝) = 17 ∶ 15
Q.12 Find the sum of the following series up to 𝑛 terms: 5 + 55 + 555 + ⋯ 3
Q.13 If 𝐶 ∶ 𝐶 = 1: 2 and 𝐶 ∶ 𝐶 = 2: 3, then find 𝑛 and 𝑟. 3
Q.14 Find the equation of an ellipse whose foci are (±4,0) and the eccentricity is . 3
OR
Find the equation of hyperbola whose foci are (0, ±12) and the length of latus rectum is
36.
SECTION: D
This section comprises of 2 long answer (LA) type questions of 5 marks each
A committee of 7 members has to be formed from 9 boys and 4 girls. In how many ways, 5
Q.15 can this be done when the committee consists of (i) exactly 3 girls? (ii) at least 3 girls?
(iii) at most 3 girls?
OR
In how many ways can the letters of the word PERMUTATIONS be arranged if
(i) words start with P and end with S.
(ii) vowels are all together.
(iii) there are always 4 letters between P and S.
Q.16 Find the length of transverse and conjugate axes, eccentricity, co-ordinates of vertices and 5
co-ordinates of foci and length of latus rectum of the hyperbola 25𝑥 − 36𝑦 = 225.
SECTION: E
This section comprises of 01 case-study of 4 marks each with subparts of marks 1, 1, 2 respectively.
Q.17 Rahul is paying with a long string, he 1+1+2
hangs the ends of the string at two points
on the wall. Now, it is in the form of
parabola with its vertical axis and is 10 m
high,5 m wide at its base as shown in the
following figure.

(i) Write down the standard equation of
the parabola in this case.

(ii) Determine one point through which
parabola passes.

(iii) (a) Find the particular equation of the parabola.
OR
(b) Find the width of the parabola at a height of 2 m from the vertex.

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