Intersection

Q.

If two sets $A$and $B$ are having $99$ elements in common, then the number of elements common to each of the sets $A\times B$and $B\times A$ are

1. $2^{99}$

2. ${99}^2$

3. $100$

4. $18$

5. $9$

Q.

How many elements are there in period 4?

Q.

Empty relation on a set A is the subset of Cartesian product $A\times A$

1. True

2. False

Q. If $f\left(x\right)+2f\left(\frac{1}{x}\right)=3x,x\ne 0andS=xϵR:f\left(x\right)=f(-x)$; then S

1. is an empty set
2. contains exactly one element
3. contains exactly two elements
4. contains more than two elements

Q.

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

1. $A\cap B=A$

2. $A\cup B=A$

3. $A\cup B=B$

4. $A\cap B=\varphi$

Q.

In a factory 70% of the workers like oranges and 64% likes apples. What is the maximum Percentage of people who can like both?

__

Q. Let a function $f:R\to R$ be given by $f(x+y)=f\left(x\right)f\left(y\right)$ for all $x,y\in R$ and $f\left(x\right)\ne 0$ for any $x\in R$. If the function $f\left(x\right)$ is differentiable at $x=0$, show that $f^{\prime }\left(x\right)=f^{\prime }\left(0\right)f\left(x\right)\text{for all}x\in R$. Also, determine $f\left(x\right)$.

Q. Let $f\left(3\right)=4$ and $f^{\prime }\left(3\right)=5.$ Then , $\underset{x\to 3}{lim}\left[f\left(x\right)\right]$ where $[\cdot ]$ denotes the greatest integer function, is

1. $3$
2. $4$
3. does not exist
4. $5$

Q.

In a factory 70% of the workers like oranges and 64% likes apples. What is the maximum Percentage of people who can like both?

__

Q.

In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then, the percentage of the population traveling by car or bus is

1. 40 percent

2. 60 percent

3. 70 percent

4. 80 percent

Q. If $a\ne 0$ and $a-\frac{1}{a}=4$, then find $a^3-\frac{1}{a^3}$

1. $76$
2. $77$
3. $75$
4. $85$

Q. How do you solve $4x-3=-19$ ?

Q.

If $S_1=\left\{1,2,3,.....,20\right\},S_2=\left\{a,b,c,d\right\},S_3=\{b,d,e,f\};$

The number of elements of $\left(S_1*S_2\hspace{0.17em}\right)\cup \hspace{0.17em}\left(S_1*S_3\right)$ is

1. $100$

2. $120$

3. $140$

4. $40$

Q. The points $(3,5)$ and $(5,3)$ represent the same point.

1. True
2. False

Q. Define Relation $R$ in the set $A=1,2,3,4,5,6$ as $R=(x,y):y\text{is divisible by}x$

Q. The value of $x$ which satisfies $\frac{4x}{x^2+1}=\frac{4}{x+2}$ is:

1. $-\frac{1}{4}$
2. $\frac{1}{2}$
3. $0$
4. $2$

Q.

In a factory 70% of the workers like oranges and 64% likes apples. If x% like both oranges and apples, then the possible values of x are

1. $x\ge 34$

2. $x\le 64$

3. $34\le x\le 64$

4. $x\ge 44$