Question 1 :
Solve:$\displaystyle \sin { \left( { \tan }^{ -1 }x \right) } ,\left| x \right| <1$ is equal to
Question 2 :
$\sin ^ { - 1 } 5 + \cos ^ { - 1 } 5 = \ldots \ldots$
Question 3 :
$\quad \sin ^{ -1 }{ x } +\sin ^{ -1 }{ \cfrac { 1 }{ x } } +\cos ^{ -1 }{ x } +\cos ^{ -1 }{ \cfrac { 1 }{ x } = } $
Question 4 :
Let $R$ be the relation over the set of all straight lines in a plane such that ${l}_{1}$ $R$ ${l}_{2}\Leftrightarrow {l}_{1}\bot {l}_{2}$. Then, $R$ is
Question 5 :
Let A={ 1, 2, 3, 4} and R= {( 2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is
Question 6 :
If $f: A \rightarrow B$is a bijective function and if n(A) = 5, then n(B) is equal to
Question 7 :
If A=$\displaystyle \begin{vmatrix} 0 & 1 \\ 2 & 4 \end{vmatrix} $, B=$\displaystyle \begin{vmatrix} -1 & 1 \\ 2 & 2 \end{vmatrix} $,<br>C=$\displaystyle \begin{vmatrix} 1 & 0 \\ 1 & 0 \end{vmatrix} $, then 2A+3B-C=<br>
Question 8 :
What is the order of the product $ \begin{bmatrix} x &  y & z \end{bmatrix} \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ ?
Question 9 :
A square matrix $\left[ { a }_{ ij } \right] $ such that ${ a }_{ ij }=0$ for $i\ne j$ and ${ a }_{ ij }=k$ where $k$ is a constant for $i=j$ is called:
Question 10 :
Find the values of x, if <br>$\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix}$= $\begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$
Question 11 :
If $A = \begin{bmatrix}1& \log_{b}a\\ \log_{a}b& 1\end{bmatrix}$ then $|A|$ is equal to<br>
Question 12 :
The value of the determinant$\begin{vmatrix} 5 & 1 \\ 3 & 2 \end{vmatrix}$
Question 13 :
If the displacement of a particle moving in straight line is given by $x=3t^2+2t+1$ at time $t$ then  the acceleration of the particle at time $t=3$ is
Question 14 :
What is the rate of change of the area of a circle with respect to its radius $r$ at $r = 6$ $cm$.
Question 15 :
The side of a square sheet is increasing at the rate of $4 cm$ per minute. The rate by which the area increasing when the side is $8 cm$ long is.
Question 16 :
The integer $'n'$ for which $\mathop {\lim }\limits_{x \to 0} \dfrac{{\cos 2x - 1}}{{{x^n}}}$ is a finite non-zero number is
Question 17 :
$f(x)=\left\{\begin{matrix} 2x-1& if &x>2 \\ k & if &x=2 \\  x^{2}-1& if & x<2\end{matrix}\right.$is continuous at $x= 2$ then $k =$
Question 18 :
The function $f\left( x \right)=\left[ x \right] ,$  at ${ x }=5$ is:<br/>
Question 19 :
What is the area of the region enclosed between the curve $y^2=2x$ and the straight line $y=x$ ?
Question 21 :
The area bounded by the curve $y = f\left( x \right)$, above the $x$-axis, between $x = a$ and $x = b$ is:
Question 24 :
The value of $\displaystyle\int \dfrac{\cos\ 2\ x}{\cos\ x}\ dx$ is equal to
Question 25 :
The order and degree of the differential equation $\sqrt { \dfrac { dy }{ dx } } -4\dfrac { dy }{ dx } -7x=0$ are
Question 26 :
The differential equation $1 + \dfrac{{dy}}{{dx}} - {\left( {\dfrac{{{d^2}y}}{{d{x^2}}}} \right)^{3/2}} = 0$ is of
Question 27 :
What is the solution of the differential equation $\sin \left (\dfrac {dy}{dx}\right ) - a = 0$?<br>where $c$ is an arbitrary constant.
Question 28 :
A straight line is inclined to the axes of $Y$ and $Z$ at angles $45^{\circ}$ and $60^{\circ}$ respectively. The inclination of the line with the $X$-axis is<br/>