Law of Reciprocal

Q.

If $x_1,x_2,x_3,x_4$ are four positive real numbers such that $x_1+\frac{1}{x_2}=4,x_2+\frac{1}{x_3}=1,x_3+\frac{1}{x_4}=4$ and $x_4+\frac{1}{x_1}=1,$ then

1. $x_1=x_3$
   

2. $x_2=x_4$
   

3. $x_1{x}_2=1$
   

4. $x_3{x}_4=1$

Q. Which point lies in the third quadrant ?

1. P
2. Q
3. R
4. S

Q. If $xϵR$ and $m=\frac{x^2}{(x^4-2x^2+4)}$, then m lies in the interval

1. $[0,\frac{1}{4}]$
2. $[0,\frac{1}{3}]$
3. $[0,\frac{1}{2}]$
4. $[0,\frac{1}{5}]$

Q. The probability that $X=3$ equals

1. $\frac{25}{216}$
2. $\frac{25}{36}$
3. $\frac{125}{216}$
4. $\frac{5}{36}$

Q.

If the product of three positive real numbers is 1 and their sum is greater than sum of their reciprocals, then

1. exactly one of them exceeds 1

2. exactly one of them is less than 1

3. None of these

4. each of them equals 1

Q. Which point lies in the third quadrant ?

1. P
2. Q
3. R
4. S

Q. Relation making an unequal comparison between two numbers is called _____.

1. Equality
2. Inequality
3. Linear equation
4. None of the above

Q. Say True or False
If $a$=$3\sqrt{5}$ and $b$=$\sqrt{5}$
then does it satisfy the following commutative property $(a-b)=(b-a)$

1. True
2. False