Question 4 :
$\displaystyle \int_{}^{} {{{\tan }^{ - 1}}\sqrt {\dfrac{{1 - \cos 2x}}{{1 + \cos 2x}}} dx} $, where $0 < x < \dfrac{\pi }{2}$ is equal to
Question 6 :
The value of $\displaystyle\int { \cfrac { 1 }{ x+x\log { x } } } dx$
Question 8 :
If $\displaystyle \int { \cfrac { f(x) }{ \log { (\sin { x } ) } } } dx=\log { \left[ \log { \sin { x } } \right] } +c$, then $f(x)=$........
Question 9 :
$\displaystyle \int \dfrac{e^{5\log x} -e^{4\log x}}{e^{3\log x} - e^{2\log x}} dx =$ _______ $+ c$
Question 11 :
<p>The value of $\displaystyle\int {\dfrac{{\ln n\left( {1 - \left(<br/>{\dfrac{1}{x}} \right)} \right)dx}}{{x\left( {x - 1} \right)}}} $ is </p>
Question 12 :
The anti derivative of $\displaystyle \left (\sqrt x+\frac {1}{\sqrt x}\right )$ equals<br>
Question 13 :
$\displaystyle \int \frac{\sin x+\cos x}{\sqrt{\left ( 1+\sin 2x \right )}}$dx is
Question 14 :
Let $I=\displaystyle \int _{ \pi /4 }^{ \pi /3 }{ \cfrac { \sin { x } }{ x } } dx$. Then?
Question 16 :
A square matrix A has 9 elements. What is the possible order of A?
Question 17 :
Given that $\displaystyle M=\begin{bmatrix}3 &-2 \\-4 &0 \end{bmatrix}\:and\:N=\begin{bmatrix}-2 &2 \\5 &0 \end{bmatrix}$<span>, then $M+N$ is a </span>
Question 19 :
The order of the matrix $\displaystyle \begin{bmatrix}-1\\3 \\4 <br>\end{bmatrix}$ is :
Question 20 :
The inverse of $\begin{bmatrix} 1 & a & b \\ 0 & x & 0 \\ 0 & 0 & 1 \end{bmatrix}$ is $\begin{bmatrix} 1 & -a & -b \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ then $x=$
Question 21 :
The number of elements that a square matrix of order $n$ has below its leading diagonal is
Question 22 :
Let $A$ is a square matrix of order $n$ and $a$ being a scalar then $|aA|=$
Question 23 :
If a matrix $P$ has $8$ elements then how many different values the order of the matrix can take?
Question 24 :
The restriction on $ n, k$ and $p$ so that $PY + WY$ will be defined are:<br>
Question 25 :
The total number of matrices formed with the help of $6$ different numbers are
Question 26 :
The matrix $P=\begin{bmatrix} 0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0 \end{bmatrix}$ is a
Question 27 :
Let $A \begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{bmatrix} $. If $u_{1}$ and $ u_{2}$ are column matrix such that $ A{ u }_{ 1 } \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} $ and $ A{ u }_{ 2 } \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix} $ then $u_{1}+ u_{2}$ is equal to
Question 28 :
If $A$ and $B$ are non - zero square matrices of the same order such that $AB = 0$, then
Question 29 :
If two square matrices $A$ and $B$ are of same order and, $Tr(A) = 3, Tr(B) = 5$ then $Tr(A+B) =$
Question 30 :
If $A=\begin{bmatrix} 4 & 1 & 0 \\ 1 & -2 & 2 \end{bmatrix},B=\begin{bmatrix} 2 & 0 & -1 \\ 3 & 1 & 4 \end{bmatrix},C=\begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}$ and $(3B-2A)C+2X=0$ then $X=$