Session: 2025-26
Sample Paper
Class: 11
Subject: Mathematics
Time Allowed: 3Hrs
Maximum Marks: 80
General Instructions:
1. All questions are compulsory.
2. The question paper is divided into five Sections – A, B, C, D, and E.
3. Section A: Q.1 to Q.18 are MCQs; Q.19 & Q.20 are Assertion-Reason based (1 mark
each).
4. Section B: Q.21 to Q.25 are Very Short Answer type (2 marks each).
5. Section C: Q.26 to Q.31 are Short Answer type (3 marks each).
6. Section D: Q.32 to Q.35 are Long Answer type (5 marks each).
7. Section E: Q.36 to Q.38 are Case Study-based questions (4 marks each).
8. Use of calculators is not allowed.
Section A
1. Let A = {1,2,3}, B = {4,5}. The number of elements in A × B is:
a) 5
b) 6
c) 10
d) 8
2. If A = {x ∈ ℕ : x < 6}, then n(A) is:
a) 4
b) 5
d) 7
c) 6
(20x1=20)
3. The power set of a set with 3 elements has:
a) 6 elements
b) 9 elements
c) 8 elements
d) 3 elements
4. The intersection of sets A = {1, 2, 3}, B = {2, 3, 4} is:
a) {1, 2}
b) {2, 3}
c) {3, 4}
d) {1, 3}
5. Which of the following is a function?
a) {(1,2), (1,3)} b) {(1,2), (2,3)}
c) {(1,2), (3,2), (2,4), (4,4), (2,5)} d) {(1,1), (2,1), (1,2)}
6. If U = {1,2,3,4,5}, A = {2,4}, then A' is:
a) {2,4}
b) {1,3,5}
c) {1,2,3}
d) {3,4,5}
7. The number of subsets of a set with 4 elements is:
a) 8
b) 12
c) 16
d) 4
8. Domain of the function f(x) = √(x - 1) is:
a) x ≥ 1
b) x ≤ 1
c) All real numbers
d) x > 0
9. If f(x) = x², then f(-3) =
a) -9
b) 9
c) 0
d) 3
10. Which of the following sets is finite?
a) The set of all natural numbers b) The set of integers < 100
numbers between 0 and 1 d) The set of prime numbers
11. If A ⊆ B and B ⊆ A, then:
a) A = φ
b) B = φ
c) The set of real
c) A = B
d) A ∩ B = φ
12. A = {x: x is a letter in 'APPLE'}, number of elements in A is:
a) 5
b) 4
c) 3
d) 6
13. If f(x) = 3x + 1, then f(2) is:
a) 6
b) 7
d) 8
c) 5
14. The union of two disjoint sets A and B is:
a) A ∩ B
b) A ∪ B
c) A - B
d) B - A
15. A function is defined as:
a) Any set of ordered pairs b) A relation with unique image for every domain
element c) A
one-one relation only d) A reflexive relation
16. If A = {x ∈ ℤ : -2 < x < 3}, then A is:
a) {-1, 0, 1, 2}
b) {-2, -1, 0, 1, 2}
c) {-1, 0, 1}
d) {0, 1, 2, 3}
17. The set {x ∈ ℝ : x² = 4} is equal to:
a) {-2, 2}
b) {2}
c) {-2}
d) {0}
18. If a function maps elements from set A to set B, then A is called:
a) Domain
b) Co-domain
c) Range
d) Image
Assertion-Reason
Choose the correct option
(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): φ ⊆ A for any set A.
Reason (R): The empty set is a subset of every set.
20. Assertion (A): Every relation is a function.
Reason (R): A function must assign unique outputs to each input.
Section B
21. List all the subsets of A = {a, b}.
(5x2=10)
22. Let A = {1, 2, 3}, B = {4, 5}. Write all elements of A × B.
23. Find the number of elements in the power set of A = {1, 2, 3, 4}.
24. If f(x) = x² + 2, find f(1) and f(3).
25. If A = {1, 2, 3}, B = {a, b}, define a relation from A to B where second
element is fixed as
'a'.
Section C
26. Let A = {1, 2, 3} and B = {x, y}. Write all functions from A into B.
(6x3=18)
27. If A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}, define a relation R from A to B by R
= {(a,b): a + b = 7}.
28. Draw Venn diagram for sets A = {1,2,3}, B = {2,3,4}, U = {1,2,3,4,5}.
29. Show that intersection of two sets is a subset of each set.
30. If f(x) = x² – 3x + 2, find domain and range for x ∈ {1, 2, 3, 4}.
31. Prove: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
Section D
(4x5=20)
32. Define a function f: ℝ → ℝ by f(x) = 2x + 3. Show that it is one-one and onto.
33. Let A = {1, 2, 3}, define an equivalence relation on A × A.
34. Prove the following identities:
a) A ∪ A' = U
b) A ∩ A' = φ
35. If A = {x ∈ ℕ : x ≤ 4}, B = {x ∈ ℕ : 2 < x ≤ 6}, find:
a) A ∪ B
b) A ∩ B
c) A – B
d) B – A
Section E
36. A survey of 100 students found:
70 liked Maths, 60 liked Science, 40 liked both.
Find number of students who:
a) Liked only Maths
b) Only Science
c) Neither
(Use Venn diagram)
37. A function f is defined by f(x) = x² for x ∈ {1,2,3,4}. Represent f as:
a) A set of ordered pairs
(3x4=12)
b) Arrow diagram
c) Find range of f
38. In a school, student records are stored as sets.
A = {students who play football}
B = {students who play cricket}
If A = {Rahul, Sunil, Mohit}, B = {Sunil, Amit, Mohit}, find:
a) A ∪ B
b) A ∩ B
c) A – B
d) B – A
***End of the Paper***
