Cardinality of Sets

Q. If $A=\{x,x\in Z\text{and}\frac{x^2-4x+3}{x^2-8x+15}\le 0\}$, then $n\left(A\right)=$

Q. If $A=\left\{\right(a,b):a^2+b^2=25\text{and}a,b\in N\}$ then $n\left(A\right)=$

1. $1$
2. $2$
3. $4$
4. $12$

Q.

Find all possible factors of $440$ ?

Q. If $A=\{x:x$ is a letter of the word 'RAMANA'$\}$,
$B=\{x:x$ is a letter of the word 'MISSISSIPPI'$\}$,
$C=\{x:x$ is a letter of the word 'NOOKBOOK'$\}$,
Then relation between cardinality of sets $A,B$ and $C$ is

1. $n\left(A\right)=n\left(B\right)=n\left(C\right)$
2. $n\left(A\right)=2,n\left(B\right)=n\left(C\right)$
3. $n\left(A\right)+n\left(C\right)=n\left(B\right)$
4. $n\left(B\right)>n\left(A\right)>n\left(C\right)$

Q. If a set $Y$ is a singleton set, then $n\left(Y\right)=$

1. $0$
2. $1$
3. $\infty$

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 $A)$

Q. $A$ is set of letters of the word 'SARIKA', $B$ is set of letters of the word 'RAKASI', then $A$ and $B$ are

1. equivalent but not equal
2. equal but not equivalent
3. equal and equivalent
4. neither equal nor equivalent

Q. If $A=\{1,2,2,1,3,4,3,4\}$, then $n\left(A\right)=$

Q. If $A=\{x,x\in R\text{and}{x}^2-4x+1=0\}$, then $n\left(A\right)=$

Q. If $A=\{x:x$ is a letter in the word 'QUARANTINE'$\}$, then the cardinality of $A$ is

Q. If $A=\{x,x\in N\text{and}16-x^2\ge 0\}$, then cardinality of set $A$ is

Q. $A$ is set of letters of the word 'NARAYANA'
$B$ is the set of letters of the word 'ARANYA'.
Then which of the following option is incorrect ?

1. $A$ and $B$ are equivalent sets
2. $A$ and $B$ are equal sets
3. $n\left(A\right)=n\left(B\right)$
4. $n\left(A\right)>n\left(B\right)$