Question Text
Question 1 :
State true or false:<br/>If $\displaystyle a + 2b + c = 0$; then <br/>$\displaystyle a^{3} + 8b^{3} + c^{3} = 6abc$<br/>
Question 2 :
If on division of a polynomial p (x) by a polynomial g (x), the quotient is zero, what is the relation between the degrees of p (x) and g (x) ?<br/>
Question 3 :
Without actually calculating the cubes, find the value of each of the following:$(28)^3+(-15)^3+(-13)^3$<br/>
Question 4 :
Find the value of 'a' if (x-2) is factor of $2x^3-6x^2+5x+a$.
Question 8 :
If $(x -2)$ is one factor of $x^2 +ax-6 = 0$ and  $ x^2 -9x + b= 0 $ then a + b = ____
Question 9 :
If $\displaystyle \dfrac{x^{2} + 1}{x} = 3\dfrac{1}{3}$ and $\displaystyle x > 1$; find the value of  $\displaystyle x - \dfrac{1}{x}$
Question 11 :
The remainder when $x^5 + Kx^2$ is divided by $ (x - 1) (x - 2) (x - 3)$ contains no term in $x^2$. Then the value of $K$ is 
Question 14 :
If $x - \dfrac{1}{x} = 5$, then $x^{3} - \dfrac{1}{x^{3}}$ equals<br/>
Question 18 :
$\displaystyle \frac{x^{-1}}{x^{-1} + y^{-1}} + \frac{x^{-1}}{x^{-1} - y^{-1}}$ is equal to
Question 19 :
Find the factor of the polynomial $P(x)= \left (12x^4+13x^3-35x^2-16x+20 \right )$ .<br/>