Law of Reciprocal

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

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

Q.

The possible values of the expression $\frac{1}{x^2-2x+5}$

1. [4, $\infty$)

2. (4, $\infty$)

3. $(0,\frac{1}{4}]$

4. $(0,\frac{1}{4})$

Q.

The possible values of $\frac{1}{x^2+3}$ lie in the interval

1. 

2. 

3. 

4. 

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.

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. each of them equals 1

3. exactly one of them is less than 1

4. None of these

Q. Which of the following is/are true?

1. $\frac{1}{x}\ge 2\Rightarrow x\ge \frac{1}{2}$
2. $\frac{1}{x}>2\Rightarrow x<\frac{1}{2}$
3. $\frac{1}{x}>2\Rightarrow 0<x<\frac{1}{2}$
4. $\frac{1}{x}\ge 2\Rightarrow 0<x\le \frac{1}{2}$

Q. The solution set of $\frac{1}{x^2-9}\ge 0$ is

1. $(-3,3)$
2. $[-3,3]$
3. $(-\infty ,-3]\cup [3,\infty )$
4. $(-\infty ,-3)\cup (3,\infty )$

Q. If the inequality $\sqrt{\frac{-3}{x^2+2x+10}}\ge 0$ holds good, then $x\in$

1. $[0,\infty )$
2. $(-\infty ,0]$
3. $\varphi$
4. $[2,14]$

Q. If $x=\sqrt{7}-\sqrt{5}$ and $y=\sqrt{13}-\sqrt{11}$, then

1. $x>y$
2. $x<y$
3. $x=y$
4. None of these

Q. The interval(s) of $x$ which satisfies the inequality $\frac{1}{x+2}<\frac{1}{3x+7}$ is/are

1. $(-\frac{7}{3},-2)$
2. $(-2,\infty )$
3. $(-\frac{5}{2},-\frac{7}{3})$
4. $(-\infty ,-\frac{5}{2})$