Venn Diagram

Q.

If $a=\frac{(3i+k)}{\sqrt{10}}\&b=\frac{(2i+3j-6k)}{7}$, then the value of $(2a-b).\left[\right(axb)\times (a+2b\left)\right]$is

1. $-3$

2. $5$

3. $3$

4. $-5$

Q. If relation $R$ is defined as $aRb$ if "$a$ is the father of $b".$ Then $R$ is

1. reflexive
2. symmetric
3. transitive
4. none of these

Q.

Let $\mathrm{f}\left(\mathrm{x}\right)=\left[\mathrm{x}\right]$, where $\left[\mathrm{x}\right]$ denotes the greatest integer less than or equal to $\mathrm{x}$. If $\mathrm{a}=\sqrt{{\left(2011\right)}^2+2012}$, then the value of $\mathrm{f}\left(\mathrm{a}\right)$ is equal to

1. $2010$

2. $2011$

3. $2012$

4. $2013$

Q. Out of $800$ boys in a school, $224$ played cricket, $240$ played hockey and $336$ played basketball of the total, $64$ played both basketball and hockey, $80$ played cricket and basketball, $40$ played cricket and hockey, $24$ played all the three games. The number of boys who did not play any game is

1. $128$
2. $216$
3. $240$
4. $160$

Q. A factory has $80$ workers and $3$ machines. Each worker knows to operate at least two machines. If there are $65$ persons who know to operate machine $\text{I}$, $60$ for machine $\text{II}$ and $55$ for machine $\text{III}$, what can be the minimum number of persons who know to operate all the three machines ?

1. $15$
2. $20$
3. $30$
4. $40$

Q.

In a class of 100 students, 12 students drink only milk and 5 students drink only coffee and 8 students drink only Tea. Other report says 30 students take both coffee and tea, 25 students take milk and tea and 20 students take only milk and coffee. 10 students drink all the three. Find the number of students who do not drink anything.

__

Q. Out of $60$ students in a class, anyone who has chosen to study maths elects to do physics as well. But no one does maths and chemistry, $16$ do physics and chemistry. All the students do at least one of the three subjects and the number of people who do exactly one of the three is more than the number who do more than one of the three. Then the range of cardinal number of students who could have done only chemistry is

1. $[0,40]$
2. $[0,44]$
3. $[2,28]$
4. $[2,38]$

Q. Let $n(A–B)=25+X,n(B–A)=2X$ and $n(A\cap B)=2X.$ If $n\left(A\right)=2\left(n\right(B\left)\right),$ then $X$ is

1. $4$
2. $5$
3. $6$
4. $7$

Q. Two newspapers $A$ and $B$ are published in a city. It is known that $25\%$ of the city population reads $A$ and $20\%$ reads $B$ while $8\%$ reads both $A$ and $B$. Further, $30\%$ of those who read $A$ but not $B$ look into advertisements and $40\%$ of those who read $B$ but not $A$ also look into advertisements, while $50\%$ of those who read both $A$ and $B$ look into advertisements. Then the percentage of the population who look into advertisements is :

1. $12.8$
2. $13$
3. $13.5$
4. $13.9$

Q. From the adjoining venn diagram, find $A\cap (B\cap C)$

1. $\{1,3,4,5\}$
2. $\{1,4,5,6\}$
3. $\{5,6\}$
4. $\left\{5\right\}$

Q. Let $A$ and $B$ be two sets containing $4$ and $7$ elements respectively. If the minimum and maximum number of elements in $A\cup B$ are $m$ and $n$ respectively, then $m+n$ is

1. $18$
2. $19$
3. $20$
4. $21$

Q. If $P=\{x\in N:\frac{14x}{x+1}-\left(\frac{9x-30}{x-4}\right)\le 0\},$
$Q=\{x\in Z:|x-1|\le 5\text{and}|x-1|\ge 2\}$
and $R=\{x\in R:{\log }_{6}x+\frac{2}{{\log }_{6}x}\}=3,$ then which of the following options is (are) CORRECT?

1. $n(P\cup Q\cup R)=10$
2. $n(P\cap Q\cap R)=1$
3. $n(P\cap Q^{\prime }\cap R^{\prime })=1$
4. $n(P\cap Q\cap R^{\prime })=1$

Q. The solution of the inequality $\frac{4x+4}{2}>-x$ is

1. $(\frac{2}{3},\infty )$
2. $(-\frac{2}{3},\infty )$
3. $(-\infty ,-\frac{2}{3})$
4. $(-\infty ,\frac{2}{3})$

Q.

Three sets $A,B$ and $C$ are such that $A=B\cap C$ and $B=C\cap A$, then

1. $A\subset B$

2. $A\supset B$

3. $A=B$

4. $A\subset B$

Q. Out of $800$ boys in a school, $224$ played cricket, $240$ played hockey and $336$ played basketball of the total, $64$ played both basketball and hockey, $80$ played cricket and basketball, $40$ played cricket and hockey, $24$ played all the three games. The number of boys who did not play any game is

1. $128$
2. $216$
3. $240$
4. $160$

Q.

Out of 200 students who are trying to improve their vocabulary, 120 students read newspaper H, 50 read newspaper T and 30 read both newspaper H and T. Find the number of students

i) who read H but not T

ii) who read T but not H

iii) who don't read any newspaper

Q.

Out of 200 students who are trying to improve their vocabulary, 120 students read newspaper H, 50 read newspaper T and 30 read both newspaper H and T. find the number of students

i) who read H but not T _____

ii) who read T but not H _____

iii) who don't read any newspaper _____

1. 30, 20, 60

2. 90, 20, 60

3. 90, 20, 30

4. 20, 30, 60

Q. Which of the following set is partition of the sample space we get while throwing a die?

1. $\left\{\right(1,2),(2,3),(3,4),(4,5),(5,6\left)\right\}$
2. $\left\{\right(1),(2),(3),(4),(5),(6\left)\right\}$
3. $\left\{\right(1,2),(3,4\left)\right\}$
4. $\left\{\right(1,2,3,4),(5,6\left)\right\}$

Q. In a group of $115$ people, each has at least one among passport and voter ID. If $65$ had passport and $30$ had both, how many had only voter ID but not passport?

1. $30$
2. $50$
3. $80$
4. $55$

Q. If $A,B$ and $C$ are three subsets of a non-empty set $X$, then $(A^{\prime }\cap B^{\prime }\cap C)\cup (B\cap C)\cup (A\cap C)$ is equal to

1. $A$
2. $B$
3. $C$
4. $X\cap (A\cup B\cup C)$

Q.

In a battle 70% of the combatants lost eye, 80% an ear, 75% an arm, 85% a leg, x% lost all of four body parts. The minimum value of x is

1. 10

2. 12

3. 15

4. 11

Q. From the adjoining figure, $A\cap B$ is

1. $\{8,5\}$
2. $\{8,5,0\}$
3. $\{1,5\}$
4. $\{0,1,2,3,5,8,9\}$