Intersection

Q. $ABCD$ is a square of length $a,a\in N,a>1.$ Let $L_1,L_2,L_3,\cdots$ be points on $BC$ such that $B{L}_1=L_1{L}_2=L_2{L}_3=\cdots =1$ and $M_1,M_2,M_3,\cdots$ are points on $CD$ such that $C{M}_1=M_1{M}_2=M_2{M}_3=\cdots =1.$ Then $\sum _{n=1}^{a-1}(A{L_n}^2+L_n{M_n}^2)$ is equal to

1. $\frac{1}{2}a(a-1)$
2. $\frac{1}{2}(a-1)(2a-1)(4a-1)$
3. $\frac{1}{2}a(a-1)(4a-1)$
4. $\frac{1}{2}(a-1{)}^2(2a-1)$

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.

How many elements would a period can maximum comprise of if there were ten periods in the periodic table?

Q.

If sets $A$ and $B$ are defined as
$A=\left\{\right(x,y)|y=\frac{1}{x},x\ne 0,x\in R\},$
$B=\left\{\right(x,y)|y=-x,x\in R\},$ then

1. $A\cap B=A$

2. $A\cup B=B$

3. $A\cap B=\varphi$

4. $A\cup B=A$

Q. If $\left|\frac{x+1}{x}\right|+|x+1|=\frac{(x+1{)}^2}{|x|},$ then $x\in$

1. $(0,\infty )\cup \{-1\}$
2. $(-\infty ,0)$
3. $(0,\infty )$
4. $(-\infty ,-1]\cup (0,\infty )$

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 the sets A and B are defined as
$A=\{x:x=2n,n\in N,n<100\}B=\{x:x=3n,n\in N,n<100\}$
then, the number of elements in $A\cap B$ is

1. 16
2. 198
3. 33
4. 59

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 $A$ and $B$ are two sets such that $(A-B)\cup B=A$, then

1. $B\subseteq A$
2. $A\subseteq B$
3. $A=B$
4. $A\cap B=A$

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. $\varphi$