# NDA MATHEMATICS

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## Question 1:

If $\frac{5 x}{x^{2}-4 x+1}=\frac{1}{3}$, where $x \neq 0$ then find the value of $x-\frac{1}{x}$.

## Question 2:

If $p^{2}+\frac{1}{p^{2}}=34$, then $\frac{2 p}{3 p^{2}-5 p+3}$ is equal to

## Question 3:

If $x^{4}+\frac{1}{x^{4}}=47$, then the value of $x+\frac{1}{x}$ is :

## Question 4:

If $x^{4}+\frac{1}{x^{4}}=727$, then find the value of $x^{3}-\frac{1}{x^{3}}$

## Question 5:

If $x=3+\sqrt{8}$, then find the value of $\sqrt{x}+\frac{1}{\sqrt{x}}$

## Question 6:

If $\frac{\mathrm{a}}{\mathrm{b}}=\frac{x+3}{x-3}$, then what is the value of $\frac{a^{2}+b^{2}}{a^{2}-b^{2}}$ ?

## Question 7:

If $n+\frac{2}{3} n+\frac{1}{2} n+\frac{1}{7} n=97$ then the value of $n$ is:

## Question 8:

If $a=\frac{1}{a-5}(a>0)$ then the value of $a-5+\frac{1}{a-5}$ is

## Question 9:

What is the value of the expression?

$\frac{(a-b)^{3}+(b-c)^{3}+(c-a)^{3}}{3(a-b)(b-c)(c-a)}=\text { ? }$

## Question 10:

If $a-\frac{1}{a}=7$, then $a^{2}+\frac{1}{a^{2}}=$ ?