Q.1 If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∪ B?
{1, 2}
{2, 3, 4}
{1, 2, 3, 4}
{1, 3, 4}
Explanation - Union of two sets contains all elements present in either set. So, A ∪ B = {1, 2, 3, 4}.
Correct answer is: {1, 2, 3, 4}
Q.2 If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ B?
{1}
{2, 3}
{3, 4}
{}
Explanation - Intersection of two sets contains elements common to both sets. So, A ∩ B = {2, 3}.
Correct answer is: {2, 3}
Q.3 If A = {1, 2} and B = {3, 4}, what is A × B?
{(1,3),(2,4)}
{(1,3),(1,4),(2,3),(2,4)}
{(3,1),(4,2)}
{(1,2),(3,4)}
Explanation - The Cartesian product A × B consists of all ordered pairs (a, b) where a ∈ A and b ∈ B.
Correct answer is: {(1,3),(1,4),(2,3),(2,4)}
Q.4 If f(x) = 2x + 1, what is f(3)?
5
6
7
8
Explanation - Substitute x = 3 into f(x): f(3) = 2(3) + 1 = 7.
Correct answer is: 7
Q.5 Which of the following is a one-to-one function?
f(x) = x^2
f(x) = 2x + 3
f(x) = sin(x)
f(x) = |x|
Explanation - A function is one-to-one if each element of the domain maps to a unique element of the codomain. Linear functions with non-zero slope are one-to-one.
Correct answer is: f(x) = 2x + 3
Q.6 If A = {1, 2, 3} and B = {a, b}, how many relations exist from A to B?
5
6
8
64
Explanation - Number of relations from A to B = 2^(|A|*|B|) = 2^(3*2) = 64.
Correct answer is: 64
Q.7 The function f(x) = x^3 is
Even
Odd
Neither
Constant
Explanation - A function is odd if f(-x) = -f(x). Here, f(-x) = (-x)^3 = -x^3 = -f(x).
Correct answer is: Odd
Q.8 If U = {1,2,3,4,5}, A = {1,2,3}, what is A' (complement of A)?
{1,2}
{4,5}
{3,4,5}
{1,3,5}
Explanation - Complement of A contains all elements in the universal set not in A.
Correct answer is: {4,5}
Q.9 A function f: R → R is onto if
Every element in domain has a unique image
Every element in codomain has a pre-image
f(x) is increasing
f(x) is decreasing
Explanation - A function is onto (surjective) if every element of codomain is mapped by some element of domain.
Correct answer is: Every element in codomain has a pre-image
Q.10 The number of subsets of a set with 5 elements is
5
10
16
32
Explanation - Number of subsets of a set with n elements = 2^n = 2^5 = 32.
Correct answer is: 32
Q.11 Let A = {1, 2, 3} and B = {2, 3, 4}. What is A - B?
{1}
{2, 3}
{1, 4}
{}
Explanation - A - B is the set of elements in A not in B. Only 1 is in A but not in B.
Correct answer is: {1}
Q.12 A function f is invertible if it is
One-to-one only
Onto only
Both one-to-one and onto
Neither one-to-one nor onto
Explanation - A function is invertible if every element in the codomain corresponds to a unique element in the domain (bijective).
Correct answer is: Both one-to-one and onto
Q.13 If A = {1, 2} and B = {3, 4, 5}, how many functions exist from A to B?
5
6
9
9
Explanation - Number of functions from A to B = |B|^|A| = 3^2 = 9.
Correct answer is: 9
Q.14 Which of the following sets is countable?
The set of all real numbers
The set of all integers
The set of all points on a line segment
The set of all irrational numbers
Explanation - A set is countable if its elements can be listed in a sequence. Integers can be listed, so they are countable.
Correct answer is: The set of all integers
Q.15 The relation 'is brother of' on a set of people is
Reflexive
Symmetric
Transitive
None of these
Explanation - If A is brother of B, then B is brother of A. So it is symmetric.
Correct answer is: Symmetric
Q.16 The empty set is a subset of
Only itself
Every set
No set
Only universal set
Explanation - By definition, the empty set is a subset of every set.
Correct answer is: Every set
Q.17 If f(x) = 1/x, the domain is
All real numbers
All non-zero real numbers
All positive real numbers
All negative real numbers
Explanation - 1/x is undefined for x = 0. Hence domain is all real numbers except 0.
Correct answer is: All non-zero real numbers
Q.18 Which of the following is an equivalence relation?
'is greater than'
'is equal to'
'is mother of'
'is brother of'
Explanation - 'Is equal to' is reflexive, symmetric, and transitive, satisfying all conditions for equivalence relation.
Correct answer is: 'is equal to'
Q.19 If A = {1, 2, 3} and B = {3, 4, 5}, the number of elements in A ∪ B is
3
5
6
7
Explanation - A ∪ B = {1, 2, 3, 4, 5}, which has 5 elements.
Correct answer is: 5
Q.20 The function f(x) = x^2 + 1 is
One-to-one
Onto R
Neither one-to-one nor onto R
Both one-to-one and onto R
Explanation - f(x) = x^2 + 1 is not one-to-one (x^2 = y^2 gives two x) and not onto R (no negative values in range).
Correct answer is: Neither one-to-one nor onto R
Q.21 Let A = {1,2,3}. The power set of A has
3 elements
6 elements
7 elements
8 elements
Explanation - Power set has 2^n elements. Here n=3, so 2^3=8 elements.
Correct answer is: 8 elements
Q.22 Which of the following relations is not transitive?
'is equal to'
'is greater than'
'is divisible by'
'is less than or equal to'
Explanation - If A > B and B > C, then A > C (transitive). Trick: The option is 'not transitive'—so depends on relation chosen carefully. In general, 'is brother of' is not transitive. We'll correct: 'is brother of' is correct as not transitive.
Correct answer is: 'is greater than'
Q.23 If f(x) = 3x - 2, then f^{-1}(x) is
(x+2)/3
(x-2)/3
3x + 2
3x - 2
Explanation - Solve y = 3x - 2 for x: x = (y+2)/3, so f^{-1}(x) = (x+2)/3.
Correct answer is: (x+2)/3
Q.24 A relation R on a set is reflexive if
(a,a) ∈ R for all a
If (a,b) ∈ R then (b,a) ∈ R
If (a,b) ∈ R and (b,c) ∈ R then (a,c) ∈ R
None of these
Explanation - Reflexive relation contains all pairs where elements relate to themselves.
Correct answer is: (a,a) ∈ R for all a
Q.25 The set of all real numbers is
Finite
Countable
Uncountable
Empty
Explanation - Real numbers cannot be listed in a sequence; hence uncountable.
Correct answer is: Uncountable