Question Text
Question 1 :
If $\displaystyle \dfrac{x^{2} + 1}{x} = 3\dfrac{1}{3}$ and $\displaystyle x > 1$; find the value of $\displaystyle x^{3} - \dfrac{1}{x^{3}}$
Question 4 :
Using the reals $a_n; \hspace {2mm} (n=1,2,...,5)$, if $l,m,n \in \{1,2,3,4,5\}$ $m < n$.
Question 9 :
If $3a = 4b = 6c$ and $a + b + c = 27 \displaystyle \sqrt{29}$, then $\displaystyle \sqrt{a^{2}+b^{2}+c^{2}}$ is 
Question 12 :
The value of$\displaystyle \left ( x-y \right )^{3}+\left ( x+y \right )^{3}+3\left ( x-y \right )^{2}\left ( x+y \right )+3\left ( x+y \right )^{2}\left ( x-y \right )$ is
Question 13 :
Two numbers are such that their sum multiplied by the sum of their squares is $5500$ and their difference multiplied by the difference of the squares is $352$. Then the numbers are ?<br/>
Question 14 :
Given the polynomial $a_{0}x^{n} + a_{1}x^{n - 1} + ... + a_{n - 1}x + a_{n}$, where $n$ is a positive integer or zero, and $a_{0}$ is a positive integer. The remaining $a's$ are integers or zero. Set$h = n + a_{0} + |a_{1}| + |a_{2}| + .... + |a_{n}|$. The number of polynomials with $h = 3$ is