Learn › JEE Main · Mathematics ›
Sets › Finite and Infinite Sets
Finite and Infinite Sets — JEE Main Mathematics MCQs with Solutions
Free JEE Main Mathematics Finite and Infinite Sets MCQs with step-by-step solutions (12 questions). Part of Sets. Practise online on Prepizo — no login needed.
▶ Practise Finite and Infinite Sets online (free)
Questions with solutions
Q1 — Finite and Infinite Sets · easy · theory
Which of the following is an infinite set?
A. $\{x \in \mathbb{R} : 0 < x < 1\}$ ✓ Correct
B. $\{x \in \mathbb{Z} : x^2 < 50\}$
C. $\{x \in \mathbb{N} : x < 100\}$
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. $\{x : x \text{ is a multiple of } 3\}$
B. $\{x \in \mathbb{R} : x^2 \le 100\}$
C. $\{x \in \mathbb{Z} : x^2 \le 100\}$ ✓ Correct
D. $\{x : x \text{ is a prime number}\}$
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. $\{x \in \mathbb{N} : x \text{ is a factor of } 20\}$ ✓ Correct
B. The set of points on a line segment
C. The set of natural numbers
D. The set of all circles in a plane
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. empty
B. finite ✓ Correct
C. uncountable
D. infinite
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. finite
B. a singleton
C. infinite ✓ Correct
D. empty
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. $\{x \in \mathbb{N} : x \text{ divides } 12\}$
C. $\{x : x \text{ is a vowel in English}\}$
D. $\{x \in \mathbb{Z} : 1 < x < 2\}$
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. finite
B. infinite ✓ Correct
C. empty
D. a singleton
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. $11$ ✓ Correct
B. $10$
C. $12$
D. $9$
Solution: Integers from $-4$ to $6$ inclusive: $6-(-4)+1 = 11$.
Q10 — Finite and Infinite Sets · hard · theory
Which of the following sets is infinite?
A. $\{x \in \mathbb{Z} : x^2 = 4\}$
B. $\{(x, y) \in \mathbb{Z}^2 : x^2 + y^2 = 1\}$
C. $\{(x, y) \in \mathbb{R}^2 : x + y = 1\}$ ✓ Correct
D. $\{x \in \mathbb{N} : x! < 100\}$
Solution: The line $x+y=1$ contains infinitely many real points; the others are finite (4, 2 and 4 elements respectively).
Q11 — Finite and Infinite Sets · hard · theory
Which of the following sets is finite?
A. $\{x \in \mathbb{Z} : x > 5\}$
B. $\{x \in \mathbb{R} : \sin x = 0\}$
C. $\{x \in \mathbb{Q} : 0 < x < 1\}$
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.
Q12 — Finite and Infinite Sets · medium · theory
The set of solutions of $\cos x = \tfrac12$ over all of $\mathbb{R}$ is:
A. finite with 2 elements
B. empty
C. infinite ✓ Correct
D. a singleton
Solution: Trigonometric equations with a valid value have infinitely many solutions (periodicity).