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Finite and Infinite Sets — IISER Maths MCQs with Solutions
Free IISER Maths Finite and Infinite Sets MCQs with step-by-step solutions (13 questions). Part of Sets. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Finite and Infinite Sets · easy · theory
Which of the following is an infinite set?
A. $\{x \in \mathbb{N} : x < 100\}$
B. $\{x \in \mathbb{Z} : x^2 < 50\}$
C. $\{x \in \mathbb{R} : 0 < x < 1\}$ ✓ Correct
D. $\{x : x \text{ is a letter of the English alphabet}\}$
Solution: There are infinitely many real numbers between 0 and 1; the other three are finite.
Q2 — Finite and Infinite Sets · medium · theory
Which set is finite?
A. $\{x : x \text{ is a prime number}\}$
B. $\{x : x \text{ is a multiple of } 3\}$
C. $\{x \in \mathbb{R} : x^2 \le 100\}$
D. $\{x \in \mathbb{Z} : x^2 \le 100\}$ ✓ Correct
Solution: Integers with $x^2 \le 100$ run from $-10$ to $10$ (21 values) — finite; the others are infinite.
Q3 — Finite and Infinite Sets · medium · theory
The set of all lines passing through a fixed point in a plane is:
A. finite
B. infinite ✓ Correct
C. a singleton
D. empty
Solution: Infinitely many lines pass through any given point.
Q4 — Finite and Infinite Sets · medium · theory
Which of the following is a finite set?
A. The set of all circles in a plane
B. The set of points on a line segment
C. The set of natural numbers
D. $\{x \in \mathbb{N} : x \text{ is a factor of } 20\}$ ✓ Correct
Solution: Factors of 20 are 1, 2, 4, 5, 10, 20 — a finite set; the other three are infinite.
Q5 — Finite and Infinite Sets · medium · theory
The set $\{x \in \mathbb{N} : x \text{ is a factor of } 100\}$ is:
A. finite ✓ Correct
B. infinite
C. uncountable
D. empty
Solution: 100 has finitely many factors (1,2,4,5,10,20,25,50,100), so the set is finite.
Q6 — Finite and Infinite Sets · hard · theory
If $A$ is an infinite set, then its power set $P(A)$ is:
A. a singleton
B. infinite ✓ Correct
C. empty
D. finite
Solution: The power set of an infinite set is infinite (in fact of strictly greater cardinality).
Q7 — Finite and Infinite Sets · medium · theory
Which set is infinite?
A. $\{x \in \mathbb{Q} : 1 < x < 2\}$ ✓ Correct
B. $\{x \in \mathbb{Z} : 1 < x < 2\}$
C. $\{x : x \text{ is a vowel in English}\}$
D. $\{x \in \mathbb{N} : x \text{ divides } 12\}$
Solution: There are infinitely many rationals strictly between 1 and 2; the others are finite (in fact empty for the integer case).
Q8 — Finite and Infinite Sets · medium · theory
The set of all points on the circumference of a circle is:
A. a singleton
B. infinite ✓ Correct
C. finite
D. empty
Solution: A circle has infinitely many points on it.
Q9 — Finite and Infinite Sets · medium · numerical
The number of elements in the finite set $\{x \in \mathbb{Z} : -4 \le x \le 6\}$ is:
A. $9$
B. $12$
C. $11$ ✓ Correct
D. $10$
Solution: Integers from $-4$ to $6$ inclusive: $6-(-4)+1 = 11$.
Q10 — Finite and Infinite Sets · medium · theory
A set is called finite if:
A. it is a subset of $\mathbb{N}$
B. it is empty or its elements can be counted, the counting ending after a definite number ✓ Correct
C. it has at least one element
D. it contains only integers
Solution: A finite set is empty or has a definite number $n$ of elements after which counting stops.
Q11 — Finite and Infinite Sets · hard · theory
The set of rational numbers $\mathbb{Q}$ is:
A. finite
B. empty
C. uncountable
D. infinite (countably infinite) ✓ Correct
Solution: $\mathbb{Q}$ is infinite; moreover it is countably infinite (can be put in one-to-one correspondence with $\mathbb{N}$).
Q12 — Finite and Infinite Sets · hard · theory
Which of the following sets is finite?
A. $\{x \in \mathbb{Q} : 0 < x < 1\}$
B. $\{x \in \mathbb{Z} : x > 5\}$
C. $\{x \in \mathbb{R} : \sin x = 0\}$
D. $\{x \in \mathbb{N} : x^2 - 7x + 12 = 0\}$ ✓ Correct
Solution: $x^2-7x+12=0 \Rightarrow x=3,4$ — a finite (two-element) set; the others are infinite.
Q13 — Finite and Infinite Sets · hard · theory
If $A$ is finite with $n$ elements and $B$ is infinite, then $A \cup B$ is:
A. empty
B. infinite ✓ Correct
C. finite
D. of exactly $n$ elements
Solution: A union containing an infinite set is infinite.