Cardinality of Power Set of a Set

Q.

If a set A has n elements, then the total number of subsets of A is

1. n

2. 2n

3. n²

4. 2ⁿ

Q. Match the following sets with cardianality of their power set.

1. $16$
2. $1$
3. $2$

Q. Let $Z$ be the set of integers. If
$A=\{x\in Z:2^{(x+2)(x^2-5x+6)}=1\}$ and $B=\{x\in Z:-3<2x-1<9\}$, then the number of subsets of the set $A\times B$, is :

1. $2^{10}$
2. $2^{12}$
3. $2^{18}$
4. $2^{15}$

Q. Let $A$ and $B$ be two finite sets. The set $A$ has $480$ more subsets than $B.$ If $A\cap B$ has $2$ elements, then the number of elements in $A\cup B$ is

1. $14$
2. $12$
3. $13$
4. $10$

Q. Let set $R=\{P:B\subseteq P\subseteq A\}.$ If $A=\{1,2,3,4,5\}$ and $B=\{1,2\},$ then the number of elements in set $R$ is

1. $2$
2. $4$
3. $8$
4. $10$

Q. $A$ and $B$ are two finite sets, such that $A$ has $p$ elements and $B$ has $q$ elements. The number of elements in the power set of $A$ is $48$ more than number of elements in the power set of $B.$ Then select the correct statement about $p\&q.$

1. $p=4$
2. $p=6$
3. $q=6$
4. $q=4$

Q. For two finite disjoint sets $A$ and $B$, if the number of elements in power set of $A$ is $224$ more than the number of elements in power set of $B$, then the number of elements present in either of the sets is

1. $12$
2. $0$
3. $15$
4. $13$

Q.

A set S has 7 elements. How many subsets having at most 5 elements does it have?

1. 128

2. 125

3. 120

4. 116

Q. No of elements in the power set of set A are odd, them the no of elements in the set A are

1. 5
2. None of these
3. 1
4. 3

Q. If $A=\{1,2,\{3,4\left\}\right\}$, then the number of elements in $P\left(P\right(A\left)\right)$ is
(where $P\left(A\right)$ is the power set of $A$)