Intersection of Sets

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.

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.

If $x,y\mathrm{and}z$ are non-zero real numbers and $a=xi+2j,b=yj+3k\mathrm{and}c=xi+yj+zk$ are such that $a\times b=zi-3j+k$, then $[abc]$ is equal to:

1. $3$

2. $10$

3. $9$

4. $6$

Q. If $A=\left\{\right(x,y):x^2+y^2=25\}$ and $B=\left\{\right(x,y):x^2+9y^2=144\}$, then $A\cap B$ contains

1. One point
2. Three points
3. Two points
4. Four points

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. If $A=\{2,3,4,8,10\},$ $B=\{3,4,5,10,12\},$ $C=\{4,5,6,12,14\},$ then $(A\cup B)\cap (A\cup C)$ is

1. $\{2,3,4,5,8,10,12\}$
2. $\{2,4,8,10,12\}$
3. $\{3,8,10,12\}$
4. $\{2,8,10,\}$

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. Let $A,B,C$ are three sets such that

Then $A^C\cap B\cap C^C=$

1. $\left\{8\right\}$
2. $\left\{6\right\}$
3. $\{6,8\}$
4. $\{3,6,8\}$

Q. Let $Z$ be the set of all integers.
$A=\left\{\right(x,y)\in Z\times Z:(x-2{)}^2+y^2\le 4\}$,
$B=\left\{\right(x,y)\in Z\times Z:x^2+y^2\le 4\}$ and
$C=\left\{\right(x,y)\in Z\times Z:(x-2{)}^2+(y^2-2{)}^2\le 4\}$
If the total number of relations from $A\cap B$ to $A\cap C$ is $2^p$, then the value of $p$ is

1. $16$
2. $49$
3. $25$
4. $9$

Q. Given that $A=\{1,2,3\}$, $B=\{3,4\}$ and $C=\{4,5,6\}$, then $n(A\cup (B\cap C\left)\right)=$

1. $2$
2. $3$
3. $4$
4. $5$

Q. If $X=\{x:x=8^n-7n-1,n\in N\}$ and $Y=\{y:y=49n-49,n\in N\},$ then which of the following is (are) TRUE?

1. $X\subset Y$
2. $Y\subset X$
3. $X\cap Y=X$
4. $X\cap Y=Y$

Q. Two sets given as$A=\{2,6,5,7,8,3\}$and $B=\{6,3,5,8,7,2,1\},$ then tap the bubbles having elements in $A\cap B.\$$

1. $1$
2. $2$
3. $3$
4. $4$
5. $5$
6. $6$
7. $7$
8. $8$
9. $9$
10. $0$

Q. Let $A=\{0,1,2,3,4,5\}$, $B=\{2,4,6,8\}$, $C=\{2,3,5,7\}$, then the number of element(s) in $(A\cap B)\cap C$ is

Q. Let $A,B,C$ are three sets such that

Then $A^C\cap B\cap C^C=$

1. $\left\{8\right\}$
2. $\left\{6\right\}$
3. $\{6,8\}$
4. $\{3,6,8\}$

Q.

If A = { $(x,y)$: $x^2+y^2=25$ } And B = {(x, y): $x^2+9y^2=144$}, then $A\cap B$ contains

1. One point

2. Three points

3. Two points

4. Four points

Q. If $A$ and $B$ are two sets such that $A=\{x:x\in N,x\text{is a factor of 20}\}$ and $B=\{y:y\in N,y\text{is a factor of 30}\}$, then find the $A\cap B$

1. $\{1,2,4,5,10,20\}$
2. $\{1,5,10,20\}$
3. $\{1,2,5,15,20\}$
4. $\{1,2,5,10\}$

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. Let $A=\{x:x\text{is a prime factor of}240\}$ and $B=\{y:y\text{is the sum of any two prime factors of}240\}$. Then which of the following options is true?

1. $5\notin A\cap B$
2. $7\in A\cap B$
3. $8\in A\cap B$
4. $8\in A\cup B$

Q.

If sets A and B are defined as

A = $\left\{\right(x,y):y$ = $e^x,x\in R\}$

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

1. B $\subset$ A

2. A $\subset$ B

3. $A\cap B$ = $\varphi$

4. $A\cup B-A$