Question 1 :
If $p(x) = \dfrac{1 + x^2 + x^4 + ... + x^{2n - 2}}{1 + x + x^2 + ... + x^{n - 1}}$ is a polynomial in $x$, then $n$ can be
Question 3 :
$A=\left \{ x\in R: x\neq 0,-4\leq x\leq 4 \right \} f:A\rightarrow R$ is defined as $f(x)=\dfrac{\left | x \right |}{x}$ then the range of $f$ is <br>
Question 4 :
Evaluate $\displaystyle \left ( 4a + 3b \right )^{2} - \left ( 4a - 3b \right )^{2} + 48ab$
Question 5 :
If $X \in R,$ then sgn $\left( {{X^2} + 1} \right)$ is equal to
Question 6 :
We want to find a polynomial f(x) of degree n such that f(1) = $\sqrt2$ and f(3) =$\pi$. Which of the following is true?
Question 7 :
If $2\leq a < 3$, then the value of $\cos^{-1} \cos [a] + \text{cosec}^{-1} \text{cosec }[a] + \cot^{-1} \cot [a]$. where [.] denotes greater integer less then equal to $x$) is equal to:
Question 8 :
If $A=\left \{x:x^2-3x+2=0\right \}$ and $B=\left \{x:x^2+4x-5=0\right \}$ then the value of A-B is
Question 10 :
Find the values of $x$ for which the expression $\dfrac{3x+6}{3x(4x+8)(x-5)}$ is undefined.
Question 13 :
The relation $R$ defined on the set $A=\left\{ 1,2,3,4,5 \right\} $ by $R=\left\{ \left( a,b \right) :\left| { a }^{ 2 }-{ b }^{ 2 } \right| <16 \right\} $, is not given by
Question 14 :
The range of $f(x)=\cos { \cfrac { \pi \left[ x \right] }{ 2 } } $ is
Question 15 :
If f is even function and g is an odd function, then $f_og$ is ............function.
Question 18 :
Make n the subject of formula :<br/>$\displaystyle N=90\left ( 2-\frac{4}{n} \right )$ Find n, if $\displaystyle N =108$.<br/>
Question 19 :
If $|z|\geq 3$, then the least value of $\left |z + \dfrac {1}{4}\right |$ is
Question 20 :
If $f(x) = 3x + 5$ and $f(g(x)) = 6x - 4$, what is $g(x)$?
Question 21 :
Find the correct statement pertaining to the functions $\displaystyle f\left( x \right) ={ \left( x-3 \right) }^{ 2 }+2$ and $\displaystyle g\left( x \right) =\frac { 1 }{ 2 } x+1$ graphed above
Question 22 :
Let $F_n (\theta) = \displaystyle \sum_{k = 0}^n \frac{1}{4^K} \sin^4 (2^{k} \theta)$, then which of the following is true
Question 23 :
If $f(x) = \cos( \log x)$ then $f(x^2)f(y^2)-\dfrac{1}{2} \left [ f(x^2y^2)+f\left ( \dfrac{x^2}{y^2} \right) \right]=$
Question 24 :
Let $f(x)=2-|x-3|, 1 \le x \le 5$ and for rest of the values $f(x)$ can be obtained by using the relation $f(5x)=\alpha\, f(x)\forall\, x \in R$.<br>The value of $f(2007)$ taking $\alpha = 5$, is:
Question 25 :
Let $a, b, c,$ $\epsilon\ R$. If $f(x)=ax^2+bx+c$ is such that $a+b+c=3$ and $f(x+y)=f(x)+f(y)+xy, \forall \, x, y\,\epsilon\, R,$ the $\displaystyle \sum_{n=1}^{10}f(n)$ is equal to.
Question 27 :
Find $m$, if $\displaystyle v = 3, g = 10, h = 5$ and $\displaystyle E = 109$.<br/>
Question 28 :
In the problem below, $f(x)={x}^{2}$ and $g(x)=4x-2$<br/>Find the following function: $(f\circ g)(x)$
Question 29 :
<div>Given a function $f : A \rightarrow B$; where $A = \left \{1, 2, 3, 4, 5\right \}$ and $B = \left \{6, 7, 8\right \}$.<br/></div>The number of mappings of $g(x) : B\rightarrow A$ such that $g(i) \leq g(j)$ whenever $i < j$ is
Question 30 :
Find $r$, if $\displaystyle V = 22,\ R = 2,\ l = 4$ and $\displaystyle \pi =3\frac{1}{7}$.<br/>