Question 2 :
If $\sqrt { \sqrt { 2500 } +\sqrt { 961 }&#160; } =\left( x \right) ^2$, then $x$ equals<br/>

Question 3 :
If $a$^2$ + b$^2$ + c$^2$ = ab + bc + ca$, then the value of $a^3$ + b$^3$ + c$^3$ is&#160;

Question 7 :
Which of the following statements is CORRECT?<br>Statement I : If $\left(\dfrac{5}{4}\right)^5\times \left(\dfrac{5}{4}\right)^{11} = \left(\dfrac{5}{4}\right)^{8x}$; then $x=2$<br><br>Statement II : If $\left(\dfrac{2}{5}\right)^3\times \left(\dfrac{2}{5}\right)^{7} = \left(\dfrac{2}{5}\right)^{x-1}$; then $x=11$<br>

Question 11 :
The number of real solutions of the equation (5 + 2$\sqrt6)$ <br> $^{x^2 - 3}$ +(5 - 2$\sqrt6)$ <br> $^{x^2 - 3}$ = 10 is

Question 12 :
If $3^{n} = n^{6}$, find the value of $ n^{18} $

Question 13 :
Given: $x, y$ and $z$ are integers and&#160;$3^{x + 5} = 27^{y + 1}$, then&#160;$x$ is even.

Question 15 :
If&#160;$\displaystyle a^{m}=b^{m}$ and&#160;$(m &gt; 0)$, then which of the following options could be true:

Question 16 :
Let $f(x)=x^{100}$. If $f(x)$ is divided by $x^{2}+x,$ then the remainder is $r(x)$.Find the value of $r(5)$?<br>

Question 19 :
If $a , b , c$ and $d$ are natural numbers such that $a ^ { 3 } = b ^ { 6 } , c ^ { 3 } = d ^ { 4 } ,$ and $d - a = 61 ,$ then thesmallest value of $c - b$ is: