Intersection of Sets

Q.

Two finite sets $A$ and $B$ have $m$ and $n$ elements, respectively. If the total number of subsets of $A$ is$112$ more than the total number of subsets of $B$, then the value of $m$is

1. $7$

2. $9$

3. $10$

4. $12$

5. $13$

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.

If the sets $A$ and $B$ are defined as

$A=\left\{\right(x,y):y=\frac{1}{x},x\in R-\{0\left\}\right\}$

$B=\left\{\right(x,y):y=-x,x\in R\}$, then

1. $A\cap B=A$

2. $A\cap B=B$

3. $A\cap B=\varnothing$

4. None of these

Q.

If the set of factors of a whole number $n$, including $n$ itself but not $1$ is denoted by $F\left(n\right),$ and $F\left(16\right)\cap F\left(40\right)$ = $F\left(x\right)$ then $x$ is

1. 4

2. 8

3. 6

4. 10

Q. $A=\left\{\right(4^n-3n-1)|n\in N\},$ $B=\left\{9\right(n-1)|n\in N\},$ then $A\cap B$ is

1. $A$
2. $B$
3. $N$
4. $\varphi$

Q. If $A,B,C$ and $D$ be four sets such that $A=\{2,4,6,8,10,12\},B=\{3,6,9,12,15\}$, $C=\{1,4,7,10,13,16\}$ and $D=\{x:x\in N\}$, then the number of elements in $\left[\right(A\cup B)\cup C]\cap D$ is

Q. $M$ and $N$ are two sets such that $M=\{2,4,6,8,10,12\}$ and $N=\{1,3,5,7,9,11\}$ then what will be the $M\cap N$ ?

1. $\{1,2,3,4,5,6,7,8,9,10,11,12\}$
2. $\{2,4,6,8,10,12\}$
3. $\varphi$
4. None of the above

Q. If $A$ is the set of odd prime numbers and $B=\{x\in Z:-6<\frac{2x-5}{3}\le 7\text{and}-4\le \frac{x-7}{2}<4\},$ then the value of $n(A\cap B)$ is