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Sets and their Representations — IISER Maths MCQs with Solutions
Free IISER Maths Sets and their Representations MCQs with step-by-step solutions (5 questions). Part of Sets. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Sets and their Representations · medium · numerical
How many elements are in $\{x \in \mathbb{N} : x \text{ is a factor of } 36 \text{ and } x \text{ is even}\}$?
A. $4$
B. $3$
C. $5$
D. $6$ ✓ Correct
Solution: Even divisors of 36 are 2, 4, 6, 12, 18, 36 — six elements.
Q2 — Sets and their Representations · medium · numerical
The number of elements in $\{(x, y) : x, y \in \mathbb{N},\ x + y = 6\}$ is:
A. $5$ ✓ Correct
B. $4$
C. $7$
D. $6$
Solution: Ordered pairs of naturals summing to 6: $(1,5),(2,4),(3,3),(4,2),(5,1)$ = 5.
Q3 — Sets and their Representations · hard · numerical
The number of elements in $\{x \in \mathbb{Z} : x^2 - 5|x| + 6 = 0\}$ is:
A. $2$
B. $4$ ✓ Correct
C. $3$
D. $1$
Solution: Let $t=|x|\ge0$: $t^2-5t+6=0 \Rightarrow t=2,3$, so $|x|=2$ or $3$, giving $x=\pm2,\pm3$: 4 values.
Q4 — Sets and their Representations · medium · numerical
The set $\{x \in \mathbb{N} : x \text{ and } 18 \text{ are coprime},\ x < 18\}$ has how many elements?
A. $8$
B. $6$ ✓ Correct
C. $5$
D. $9$
Solution: Numbers below 18 coprime to $18=2\cdot3^2$: 1,5,7,11,13,17 = 6 (this is $\varphi(18)=6$).
Q5 — Sets and their Representations · medium · theory
The set-builder form $\{x : x = 2^n,\ n \in \mathbb{W}\}$ (with $\mathbb{W}$ the whole numbers) in roster form begins:
A. $\{2, 4, 8, 16, \dots\}$
B. $\{1, 2, 4, 8, 16, \dots\}$ ✓ Correct
C. $\{1, 2, 3, 4, \dots\}$
D. $\{0, 2, 4, 8, \dots\}$
Solution: With $n=0,1,2,\dots$, $2^n = 1,2,4,8,16,\dots$