Venn Diagrams — IISER Maths MCQs with Solutions
Free IISER Maths Venn Diagrams MCQs with step-by-step solutions (15 questions). Part of Sets. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Venn Diagrams · easy · theory
In a Venn diagram, the universal set is usually represented by:
A. a circle
B. a rectangle ✓ Correct
C. a triangle
D. a point
Solution: By convention the universal set is drawn as a rectangle, with its subsets as circles inside.
Q2 — Venn Diagrams · medium · numerical
For two sets, $n(A) = 20$, $n(B) = 28$, and $n(A \cap B) = 8$. Then $n(A \cup B)$ is:
A. $36$
B. $56$
C. $48$
D. $40$ ✓ Correct
Solution: $n(A\cup B) = n(A) + n(B) - n(A\cap B) = 20 + 28 - 8 = 40$.
Q3 — Venn Diagrams · medium · numerical
In a group of $60$ people, $27$ like tea, $42$ like coffee, and each likes at least one. How many like both?
A. $9$ ✓ Correct
B. $15$
C. $12$
D. $18$
Solution: $n(T\cap C) = n(T) + n(C) - n(T\cup C) = 27 + 42 - 60 = 9$.
Q4 — Venn Diagrams · medium · numerical
In a class of $50$ students, $30$ play cricket, $20$ play football, and $10$ play both. How many play neither?
A. $20$
B. $5$
C. $0$
D. $10$ ✓ Correct
Solution: $n(C\cup F) = 30+20-10 = 40$; those playing neither $= 50 - 40 = 10$.
Q5 — Venn Diagrams · medium · numerical
If $n(A \cup B) = 50$, $n(A) = 28$, and $n(B) = 32$, then $n(A \cap B)$ is:
A. $14$
B. $10$ ✓ Correct
C. $6$
D. $18$
Solution: $n(A\cap B) = n(A)+n(B)-n(A\cup B) = 28+32-50 = 10$.
Q6 — Venn Diagrams · hard · numerical
In a survey of $100$ people, $72$ read newspaper $X$, $43$ read $Y$, and all read at least one. The number who read only $X$ is:
A. $57$ ✓ Correct
B. $29$
C. $43$
D. $15$
Solution: Both $= 72+43-100 = 15$; only $X = 72 - 15 = 57$.
Q7 — Venn Diagrams · medium · numerical
The shaded region "elements in $A$ but not in $B$" in a Venn diagram represents:
A. $A \cup B$
B. $A - B$ ✓ Correct
C. $A \cap B$
D. $B - A$
Solution: Elements in $A$ but outside $B$ form the difference $A - B$.
Q8 — Venn Diagrams · hard · numerical
In a town, $40\%$ read newspaper $A$, $30\%$ read $B$, and $10\%$ read both. The percentage reading neither is:
A. $50\%$
B. $60\%$
C. $40\%$ ✓ Correct
D. $20\%$
Solution: $A\cup B = 40+30-10 = 60\%$; neither $= 100 - 60 = 40\%$.
Q9 — Venn Diagrams · hard · numerical
For three sets, $n(A)=n(B)=n(C)=30$, each pairwise intersection $=10$, and $n(A\cap B\cap C)=5$. Then $n(A\cup B\cup C)$ is:
A. $70$
B. $75$
C. $60$
D. $65$ ✓ Correct
Solution: By inclusion-exclusion: $90 - (10+10+10) + 5 = 90 - 30 + 5 = 65$.
Q10 — Venn Diagrams · hard · numerical
In a group, $65\%$ like cricket and $40\%$ like tennis; $20\%$ like both (percent of whole group). What percent like at least one?
A. $85\%$ ✓ Correct
B. $80\%$
C. $45\%$
D. $105\%$
Solution: $n(C\cup T) = 65 + 40 - 20 = 85\%$.
Q11 — Venn Diagrams · hard · numerical
Among $600$ students, $300$ play cricket, $250$ hockey, $150$ football; $100$ cricket & hockey, $70$ hockey & football, $80$ cricket & football, and $50$ all three. How many play at least one?
A. $500$ ✓ Correct
B. $450$
C. $550$
D. $600$
Solution: Inclusion-exclusion: $(300+250+150) - (100+70+80) + 50 = 700 - 250 + 50 = 500$.
Q12 — Venn Diagrams · hard · numerical
For sets $A, B$ with $n(A - B) = 12$, $n(B - A) = 16$, and $n(A \cap B) = 8$, the value of $n(A \cup B)$ is:
A. $44$
B. $28$
C. $36$ ✓ Correct
D. $20$
Solution: $n(A\cup B) = n(A-B) + n(B-A) + n(A\cap B) = 12 + 16 + 8 = 36$.
Q13 — Venn Diagrams · medium · numerical
If $n(A \cap B) = 8$ and $n(A) = 20$, then $n(A - B)$ equals:
A. $12$ ✓ Correct
B. $8$
C. $28$
D. $20$
Solution: $n(A - B) = n(A) - n(A\cap B) = 20 - 8 = 12$.
Q14 — Venn Diagrams · hard · numerical
In a group of $400$ people, $250$ speak Hindi, $200$ speak English. If everyone speaks at least one language, the number speaking both is:
A. $150$
B. $450$
C. $50$ ✓ Correct
D. $100$
Solution: Both $= 250 + 200 - 400 = 50$.
Q15 — Venn Diagrams · hard · numerical
In a class of $100$, $55$ passed maths, $67$ passed physics. What is the minimum possible number who passed both?
A. $0$
B. $12$
C. $33$
D. $22$ ✓ Correct
Solution: Minimum both occurs when the union is largest ($=100$): $n(\cap) \ge 55+67-100 = 22$.