Question 2 :
The number of different possible orders of matrices having 18 identical elements is

Question 3 :
If A =$\begin{bmatrix}1 & 2 \\ 3 & 4 \end{bmatrix}$, B =$\begin{bmatrix}2 & 3 \\ 4 & 5 \end{bmatrix}$, and 4A - 3B + C = 0, then C =

Question 4 :
Let $f: N\rightarrow R$ such that $f(x)=\dfrac{2x-1}{2}$ and $g: Q\rightarrow R$such that $g(x)=x+2$ be two function. Then $(gof)\left(\dfrac{3}{2}\right)$ is equal to

Question 5 :
The function $f:[0,\infty )\rightarrow R$ given by $f(x)=\cfrac { x }{ x+1 } $ is

Question 7 :
Consider the following statements:<br/>1. $\tan^{-1} 1+ \tan^{-1} (0.5) = \dfrac {\pi}2$<br/>2.&#160;$\sin^{-1}{\cfrac{1}{3} }+ \cos^{-1}{\cfrac{1}{3}} =\cfrac{\pi}{2}$<br/>Which of the above statements is/are correct ?&#160;

Question 8 :
What is $\tan ^{ -1 }{ \left( \dfrac { 1 }{ 2 } \right) } +\tan ^{ -1 }{ \left( \dfrac { 1 }{ 3 } \right) } $ equal to?

Question 10 :
$|f(x)|={\begin{bmatrix}{}<br/>\mathrm{s}\mathrm{i}\mathrm{n}x &amp; \mathrm{c}\mathrm{o}\mathrm{s}ecx &amp; \mathrm{t}\mathrm{a}\mathrm{n}x\\<br/>\mathrm{s}\mathrm{e}\mathrm{c}x &amp; x\mathrm{s}\mathrm{i}\mathrm{n}x &amp; x\mathrm{t}\mathrm{a}\mathrm{n}x\\<br/>x^{2}-1 &amp; \mathrm{c}\mathrm{o}\mathrm{s}x &amp; x^{2}+1<br/>\end{bmatrix}}$&#160;then . $.\displaystyle \int_{-a}^{a}|f(x)|d$&#160;equals&#160;<br/><br/><br/>

Question 11 :
If $f(x)=\begin{cases} \cfrac { x(1+a\cos { x } )-b\sin { x } }{ { x }^{ 3 } } ,\quad x\neq 0 \\ 1,\quad \quad \quad \quad x=0 \end{cases}$ then $f$ is continuous for values of $a$ and $b$ given by-

Question 12 :
$f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{\dfrac{{\cos 3x - cos4x}}{{{x^2}}}} &amp; {for\,x \ne 0}\\{\dfrac{7}{2}} &amp; {for\,x = 0}\end{array}} \right.$<br/><br/>at $x=0$ is&#160;<br/><br/>

Question 13 :
The values of $p$ and $q$ so that the function $ &#160;f(x)= &#160; &#160; &#160;\begin{cases} { \left| 1+\sin { x } &#160;\right| &#160;}^{ \tfrac { p }{ \sin { x } &#160;} &#160;}&amp;\cfrac { -\pi &#160;}{ 6 } &lt;x&lt;0 \\ q &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;&amp;x=0 \\ { e }^{ \tfrac { \sin { 2x } &#160;}{ \sin { 3x } &#160;} &#160;} &amp;0&lt;x&lt;\cfrac { \pi &#160;}{ 6 } &#160;\end{cases}$ is continuous at $x=0$ is

Question 15 :
If $\int \sin x d (\sec &#160;x) = f(x) - g(x) + c$, then

Question 17 :
Let $f$ be a function which is continuous and differentiable for all real $x$. If $f\left( 2 \right) = -4$ and $f^{ \prime }\left( x \right) \ge 6$ for all $x\in \left[ 2,4 \right] $, then

Question 18 :
Consider the following statements:<br/>1. $\dfrac {dy}{dx}$ at a point on the curve gives slope of the tangent at that point.<br/>2. If $a(t)$ denotes acceleration of a particle, then $\displaystyle \int a(t) dt + c$ give velocity of the particle.<br/>3. If $s(t)$ gives displacement of a particle at time $t$, then $\dfrac {ds}{dt}$ gives its acceleration at that instant.<br/>Which of the above statements is/ are correct?

Question 19 :
The motion of a particle along a straight line described by the function $x = (2t - 3)^{2}$, when is in metre and $t$ is in second. Then, the velocity of the particle at origin is

Question 20 :
A man is moving away from a tower 41.6 m high at a rate of 2 m/s. If the eye level of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of 30 m from the foot of the tower, is

Question 21 :
Let $S$ be the focus of $y^2 = 4x$ and a point $P$ is moving on the curve such that its abscissa is increasing at the rate of $4$ units/sec, then the rate of increase of projection of $SP$ on $x + y = 1$ when $P$ is at $(4, 4)$ is