Cardinality of Power Set of a Set

Q. If the number of elements in the power set of set A are odd, them the number of elements in the set A are

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

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. $A$ 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. The number of elements in power set of $A=\{1,2,3,8,9,10\}$ is

1. $32$
2. $64$
3. $36$
4. $12$

Q. The number of elements in the power set of $A$, where $A=\{x:x\in W\text{and}{x}^3-1\le 7\}$

1. $3$
2. $16$
3. $8$
4. $64$

Q.

Match the following:

$$\begin{array}{cc}\text{Column A}& \text{Column B}\\ \text{1. {x: x}\in \text{R, -5 < x}\le \text{15 }}& \text{a. 1}\\ \text{2. A =}\varphi \text{, then the power set P(A) has}\underset{–}{}\text{elements}& b.8\\ \text{3. Universal set of Rational Numbers}\&\text{Irrational Numbers}& c.\text{Real Numbers}\\ \text{4. No. of elements in Power Set of A}=\{a,b,c\}& d.\text{Integers}\\ & e.(-5,15]\\ & f.[-5,15)\end{array}$$

1. 1 - b, 2 - a, 3 - c, 4 -e

2. 1 - b, 2 - c, 3 - a, 4 -e

3. 1 - e, 2 - a, 3 - c, 4 -b

4. 1 - e, 2 - a, 3 - b, 4 -c

Q. If $A=\{x:x$ is a prime number between $2$ and $16\},$ then number of subsets of $A$ with exactly two elements is

1. $5$
2. $10$
3. $15$
4. $20$

Q. If the number of elements in the power set of set A are odd, them the number of elements in the set A are

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

Q. For any empty set $X,$ the value of $n\left(P\right(P\left(P\right(P\left(P\right(X\left)\right)\left)\right)\left)\right)=$

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

Q. For any set $A$ such that $n\left(A\right)=m,$ match the following:

1. $2^m$
2. $2^m-1$
3. $1$

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

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

Q.

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

1. $n$

2. $n^2$

3. $2^n$

4. $2n$

Q.

In the matrix A = $\left[\begin{array}{cc}a& x^2\\ y^2& b\end{array}\right]$, write (iii) the elements $a_{21}$, $a_{12}$and $a_{22}$.

Q.

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

1. $n$

2. $n^2$

3. $2^n$

4. $2n$

Q.

Match the following:

$$\begin{array}{cc}\text{Column A}& \text{Column B}\\ \text{1. {x: x}\in \text{R, -5 < x}\le \text{15 }}& \text{a. 1}\\ \text{2. A =}\varphi \text{, then the power set P(A) has}\underset{–}{}\text{elements}& b.8\\ \text{3. Universal set of Rational Numbers}\&\text{Irrational Numbers}& c.\text{Real Numbers}\\ \text{4. No. of elements in Power Set of A}=\{a,b,c\}& d.\text{Integers}\\ & e.(-5,15]\\ & f.[-5,15)\end{array}$$

1. 1 - b, 2 - a, 3 - c, 4 -e

2. 1 - b, 2 - c, 3 - a, 4 -e

3. 1 - e, 2 - a, 3 - c, 4 -b

4. 1 - e, 2 - a, 3 - b, 4 -c