Sets and their representation; union, intersection and complement — practice questions

Question 1 · difficulty L2 · understanding

Let $$A=\{n \in[100,700] \cap \mathrm{N}: n$$ is neither a multiple of 3 nor a multiple of 4$$\}$$. Then the number of elements in $$A$$ is

• A. 300
• B. 310
• C. 290
• D. 280

Question 2 · difficulty L2 · understanding

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

• A. Q and R
• B. None of these
• C. P and R
• D. P and Q

Question 3 · difficulty L2 · understanding

If $A, B$ and $C$ are three sets such that $A \cap B=A \cap C$ and $A \cup B=A \cup C$, then :

• A. $A=C$
• B. $B=C$
• C. $A \cap B=\phi$
• D. $A=B$

Question 4 · difficulty L3 · understanding

Let $A = \{x : |x^2 - 10| \leq 6\}$ and $B = \{x : |x - 2| > 1\}$. Then

• A. $A \cup B = (-\infty, 1] \cup (2, \infty)$
• B. $B - A = (-\infty, -4) \cup (-2, 1) \cup (4, \infty)$
• C. $A - B = [2, 3)$
• D. $A \cap B = [-4, -2] \cup [3, 4]$

Question 5 · difficulty L3 · understanding

Let A = { ($\alpha, \beta$) $\in \mathbb{R} \times \mathbb{R}$ : |$\alpha$ - 1| $\leq 4$ and |$\beta$ - 5| $\leq 6$ } and B = { ($\alpha, \beta$) $\in \mathbb{R} \times \mathbb{R}$ : 16($\alpha$ - $2)^2$+ 9($\beta$ - $6)^2$ $\leq 144$ }. Then

• A. A $\subset$ B
• B. B $\subset$ A
• C. neither A $\subset$ B nor B $\subset$ A
• D. $A \cup B=\{(x, y):-4 \leqslant x \leqslant 4,-1 \leqslant y \leqslant 11\}$

Question 6 · difficulty L3 · understanding

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

• A. 10
• B. 15
• C. 21
• D. 9

Question 7 · difficulty L3 · understanding

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :

• A. {80, 83, 86, 89}
• B. {84, 86, 88, 90}
• C. {79, 81, 83, 85}
• D. {84, 87, 90, 93}

Question 8 · difficulty L4 · understanding

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and Mathematics; 40 studied both Mathematics and Physics and 10 studied none of these subjects. Let $$m$$ and $$n$$ respectively be the least and the most number of students who studied all the three subjects. Then $$\mathrm{m}+\mathrm{n}$$ is equal to ___________.