Question 1 :
By Remainder Theorem find the remainder, when $ p(x)$ is divided by $g(x)$, where$p(x) = x^3-2x^2- 4x -1$ , &#160;$g(x) = x + 1$.<br/>

Question 4 :
Choose the correct answer from the alternatives given.<br/>If x - $\dfrac{1}{x}$ = 3 then find the value of $x^3 + \dfrac{1}{x^3}$.&#160;

Question 5 :
$f(x)=2x^3-5x^2+ax+a$Given that $(x+2)$ is a factor of $f(x)$, find the value of the constant $a$.

Question 6 :
Obtain all the zeros of $2x^4+5x^3-8x^2-17x-6$ if three of its zeros are $-1, -3, 2$.<br/>

Question 7 :
Using remainder theorem, find the remainder when $2x^3-3x^2+4x-5$ is divided by $x+3$.

Question 8 :
Factorise : ${ (ax+by) }^{ 2 }+{ (2bx-2ay) }^{ 2 }-6abxy$

Question 11 :
The equationd $x^{x^{x^{+}}} = 2$ is satisfied when $x$ is equal to

Question 12 :
Which of the following is the remainder when $z\left({5z}^{2}-80\right)$ is divided by $5z\left(z-4\right)$:

Question 13 :
Which of the following should be added to&#160;$\displaystyle 9x^{3}+6x^{2}+x+2$ so that the sum is divisible by $(3x + 1)$?

Question 14 :
The value of $x+y+z$ if ${x}^{2}+{y}^{2}+{z}^{2} = 18$ and $xy + yz + zx = 9$ is

Question 15 :
Assertion: Let $\displaystyle f\left ( x \right )=6x^{4}+5x^{3}-38x^{2}+5x+6 $ then all four roots of $\displaystyle f\left ( x \right )=0 $ are real & distinct out of which two are positive & two are negative. Reason: $\displaystyle f\left ( x \right ) $ has two changes in sign in given order as well as when $x$ is replaced by $-x$.