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Venn Diagrams — JEE Main Mathematics MCQs with Solutions
Free JEE Main Mathematics Venn Diagrams MCQs with step-by-step solutions (14 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 point
B. a rectangle ✓ Correct
C. a circle
D. a triangle
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. $40$ ✓ Correct
B. $36$
C. $48$
D. $56$
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. $12$
B. $18$
C. $9$ ✓ Correct
D. $15$
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. $0$
B. $20$
C. $5$
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. $6$
C. $18$
D. $10$ ✓ Correct
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. $29$
B. $15$
C. $57$ ✓ Correct
D. $43$
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. $A \cap B$
B. $B - A$
C. $A \cup B$
D. $A - B$ ✓ Correct
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. $40\%$ ✓ Correct
B. $50\%$
C. $60\%$
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. $65$ ✓ Correct
D. $60$
Solution: By inclusion-exclusion: $90 - (10+10+10) + 5 = 90 - 30 + 5 = 65$.
Q10 — Venn Diagrams · hard · numerical
In a class of $35$, each student takes Maths or Science. $17$ take Maths, $23$ take Science. The number taking exactly one subject is:
A. $30$ ✓ Correct
B. $25$
C. $35$
D. $5$
Solution: Both $=17+23-35 = 5$; exactly one $= 35 - 5 = 30$.
Q11 — Venn Diagrams · hard · numerical
Of $200$ students, $120$ know Hindi, $90$ know English, $50$ know both, and the rest know neither. The number knowing neither is:
A. $40$ ✓ Correct
B. $30$
C. $20$
D. $60$
Solution: Know at least one $= 120+90-50 = 160$; neither $= 200 - 160 = 40$.
Q12 — 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. $105\%$
B. $80\%$
C. $85\%$ ✓ Correct
D. $45\%$
Solution: $n(C\cup T) = 65 + 40 - 20 = 85\%$.
Q13 — 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. $100$
D. $50$ ✓ Correct
Solution: Both $= 250 + 200 - 400 = 50$.
Q14 — Venn Diagrams · hard · numerical
In a survey of $60$ students, $30$ like maths, $25$ like physics, $8$ like both. The number who like exactly one of the two subjects is:
A. $47$
B. $39$ ✓ Correct
C. $17$
D. $55$
Solution: Only maths $=30-8=22$, only physics $=25-8=17$; exactly one $=22+17=39$.