Question 1 :
State whether True or False.Divide: $12x^2 + 7xy -12y^2 $ by $ 3x + 4y $, then the answer is&#160;$x^4+2x^2+4$.<br/>

Question 3 :
If $a\ne 2$, which of the following is equal to $\cfrac { b\left( { a }^{ 2 }-4 \right) }{ ab-2b } $?

Question 5 :
State whether the following statement is true or false.After dividing $ (9x^{4}+3x^{3}y + 16x^{2}y^{2}) + 24xy^{3} + 32y^{4}$ by $ (3x^{2}+5xy + 4y^{2})$ we get<br/>$3x^{2}-4xy + 8y^{2}$

Question 6 :
State whether true or false:Divide: $4a^2 + 12ab + 91b^2 -25c^2 $ by $ 2a + 3b + 5c $, then the answer is&#160;$2a+3b+5c$.<br/>

Question 9 :
If $p$ and $q$ are the roots of the equation $ax^2 +bx +c =0$, then the value of $\dfrac {p}{q}+\dfrac {q}{p}$ is<br/>

Question 11 :
Simplify: $\displaystyle&#160;7\left( 4x+5 \right) \left( 2x+6 \right) \div \left( 4x+5 \right)&#160;$

Question 12 :
Let $ p $&#160;and $&#160;q $&#160;be real numbers such that $&#160;p \neq 0, p^{3} \neq q $&#160;and $&#160;p^{3} $&#160;$&#160;\neq-q . $&#160;If $&#160;\alpha $&#160;and $&#160;\beta $&#160;are non-zero complex numbers satisfying and $&#160;\alpha+\beta=-p $&#160;and $&#160;\alpha^{3}+\beta^{3}=q, $&#160;then a quadratic equation having $ \dfrac{\alpha}{\beta} $&#160;and $ \dfrac{\beta}{\alpha} $&#160;as its roots is

Question 13 :
Workout the following divisions<br/>$a(a + 1) (a + 2) (a + 3) \div a(a + 3)$

Question 14 :
Evaluate: $\displaystyle \frac { x\left( 8{ x }^{ 2 }-32 \right) &#160;}{ 8x\left( x-4 \right) &#160;}&#160;$

Question 15 :
Divide: $(6a^{5}+ 8a^{4}+ 8a^{3} +2a^{2}+26a +35)$ by $(2a^{2} + 3a +5)$<br/>Answer:&#160;$3a^{3} - 3a^{2} + a +7$

Question 16 :
$\left[2x\right]-2\left[x\right]=\lambda$ where $\left[.\right]$ represents greatest integer function and $\left\{.\right\}$ represents fractional part of a real number then&#160;

Question 17 :
If $\alpha$ and $\beta$ are the roots of $x^2 - ax + b^2 = 0$, then $\alpha^2 + \beta^2$ is equal to

Question 19 :
If $\alpha, \beta$ be the roots $x^2+px-q=0$ and $\gamma, \delta$ be the roots of $x^2+px+r=0$, then $\dfrac{(\alpha -\gamma)(\alpha -\delta)}{(\beta -\gamma )(\beta -\delta)}=$

Question 20 :
If the roots of $ax^2+bx+c=0, \neq 0,$ are p,q ($p \neq q $), then the roots of $cx^2-bx+a=0$ are.