Question 1 :
If $A = \begin{bmatrix}1\end{bmatrix}$, then the order of the matrix is
Question 3 :
If $A=\begin{bmatrix}5 & 2\\ 7 & 4\end{bmatrix}$ is a $2\times 2$ matrix, then $a_{12}$=
Question 4 :
If the sum of the matrices $\begin{bmatrix} x \\ x \\ y \end{bmatrix},\begin{bmatrix} y \\ y \\ z \end{bmatrix}$ and $\begin{bmatrix} z \\ 0 \\ 0 \end{bmatrix}$ is the matrix $\begin{bmatrix} 10 \\ 5 \\ 5 \end{bmatrix}$, then what is the value of $y$?
Question 5 :
The matrix $A = \begin{bmatrix}0& 0 &4 \\ 0& 4 & 0\\ 4& 0 & 0\end{bmatrix}$ is a<br>
Question 6 :
<b>If $A={ \left[ { a }_{ ij } \right] }_{ 2\times 2 }$where ${ a }_{ 15 }=\begin{cases} i+j \\ { i }^{ 2 }-2j \end{cases}\begin{matrix} i\neq j \\ i=j \end{matrix}$ then ${ A }^{ -1 }=$</b>
Question 7 : <p>The rank of the matrix</p>$\left[ {\begin{array}{*{20}{c}}<br> 1&2&3 \\ <br> \lambda &2&4 \\ <br> 2&{ - 3}&1 <br>\end{array}} \right]$ is 3 if<br>
Question 8 :
If A=$\displaystyle \left [ a_{ij} \right ]_{2\times 2}$ such that $\displaystyle a_{ij}=i-j+3$ then find $A$
Question 9 :
If the order of a matrix is $\displaystyle 20\times 5$ then the number of elements in the matrix is _____
Question 10 :
If $\displaystyle \begin{bmatrix}2 &-1 \\2  &0 \end{bmatrix}+2A=\begin{bmatrix}-3 &5 \\4  &3 \end{bmatrix},$ then the matrix A equals
Question 11 :
If the number of elements in a matrix is $60$ then how many different order of matrix are possible 
Question 12 :
Out of the following matrices, choose that matrix which is a scalar matrix.
Question 13 :
If $A = \bigl(\begin{bmatrix}7 &2 \\ 1 & 3\end{bmatrix}\bigr)$ and $A + B = \bigl(\begin{bmatrix} -1& 0\\ 2 & -4\end{bmatrix}\bigr)$, then the matrix B =<br/>
Question 14 :
$\displaystyle \begin{vmatrix} 1 & a & {a}^{2}-bc \\ 1 & b & {b}^{2}-ca \\ 1 & c & {c}^{2}-ab \end{vmatrix}$=?
Question 15 :
If $A = \dfrac {1}{\pi} \begin{bmatrix}\sin^{-1}(\pi x) & \tan^{-1} \left (\dfrac {\pi}{\pi}\right )\\ \sin^{-1} \left (\dfrac {x}{\pi}\right ) &\cot^{-1} (\pi x)\end{bmatrix}, B =\dfrac {1}{\pi} \begin{bmatrix}-\cos^{-1}(\pi x) &\tan^{-1} \left (\dfrac {x}{\pi}\right ) \\ \sin^{-1} \left (\dfrac {x}{\pi}\right ) & -\tan^{-1} (\pi x)\end{bmatrix}$, then $A - B$ is equal to<br/>
Question 16 :
The relation $R$ on the set $Z$ of all integer numbers defined by $(x,y)\ \epsilon \ R\\Leftrightarrow x-y$ is divisible by $n$ is
Question 17 :
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 19 :
Let $T$ be the set of all triangles in the Euclidean plane, and let a relation $R$ on $T$ be defined as $aRb$, if $a$ is congruent to $b$ for all $a,b\in T$. Then, $R$ is
Question 20 :
Consider the following two binary relations on the set $A = \left \{a, b, c\right \} : R_{1} = \left \{(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\right \}$<br>and $R_{2} = \left \{(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)\right \}$ Then<br>
Question 21 :
If $f : A \rightarrow B $ defined as $f(x) = x^2+2x+\frac{1}{1+(x+1)^2}$ is onto function, then set B is equal to
Question 22 :
$f:(0,\infty )\rightarrow (0,\infty )$ defined by <br/>$f(x)=\begin{cases}2^{x} & x\in (0,1) \\5^{x} & x\in [1,\infty ) \end{cases}$ is
Question 24 :
Assertion: $ \displaystyle f:R \rightarrow R $ is a function defined by $ \displaystyle f(x)=\frac{5x-8}{3}$ then $ \displaystyle f^{-1}(x)=\frac{3x+8}{5}$
Reason: $f(x)$ is not a bijection.
Question 25 :
For any two real numbers $\theta$ $\phi $, we define $\theta R\phi $ if and only if $\sec ^{ 2 }{ \theta } -\tan ^{ 2 }{ \phi } =1$. The relation $R$ is
Question 26 :
Which of the following functions from $Z$ to itself are bijections?
Question 27 :
The function $f: [0, 3]$ $\rightarrow$ $[1, 29]$, defined by $f(x) = 2x^3-15x^2 + 36x+ 1$, is<br>
Question 29 :
Let $f:\{x, y , z\} \rightarrow \{1, 2, 3\}$ be a one-one mapping such that only one of the following three statements and remaining two are false : $f(x) \neq 2, f(y) =2, f(z) \neq 1$, then
Question 30 :
Let $f : R\rightarrow R$ is defined by $f(x)=\dfrac {|x|-1}{|x|+1}$ then $f$ is :
Question 31 :
Find the value of the following determinant:<br/>$\begin{vmatrix}3\sqrt{6} & -4\sqrt{2}\\ 5\sqrt{3} & 2\end{vmatrix}$
Question 32 :
If $\displaystyle{\left| {_2^{4\,}\,\,_1^1} \right|^2} = \left| {_1^3\,\,_x^2} \right| - \left| {_{ - 2}^x\,\,_1^3} \right|,$ then $x$=
Question 33 :
$D=\begin{vmatrix} 18 & 40 & 89 \\ 40 & 89 & 198 \\ 89 & 198 & 440 \end{vmatrix}=$
Question 34 :
If $A$ is a skew symmetric matrix, then $\left| A \right| $ is
Question 35 :
$\displaystyle \Delta = \begin{vmatrix}1 & \log_{x}y  & \log_{x}z \\ \log_{y}x & 1 & \log_{y}z \\ \log _{z}x  &\log _{z}y  & 1\end{vmatrix}$ is equal to <br/> <br/>
Question 36 :
A determinant of second order is made with the elements $0$ and $1.$ The number of determinants with non-negative values is:
Question 37 :
If A = $\begin{bmatrix}<br/>a & b\\ <br/> c& d<br/>\end{bmatrix}$ (where $b\neq c$) and satisfies the equation $A^{2}+kI=0$, then <br/>
Question 38 :
If $a, b, c> 1$, $\Delta =\begin{vmatrix}<br>\log _{a}\left ( abc \right ) & \log _{a}b & \log _{a}c\\ <br>\log _{b}\left ( abc \right ) & 1 & \log _{b}c\\ <br>\log _{c}\left ( abc \right ) & \log _{c}b & 1<br>\end{vmatrix}$ is<br>
Question 39 :
If $f(x)=\begin{vmatrix} 1 & x & x+1\\ 2x & x(x-1) & (x+1)x\\ 3x(x-1) & x(x-1)(x-2) & (x+1)x(x-1)\end{vmatrix}$ then $f(100)$ is equal to?
Question 40 :
The value of $\triangle$ = $<br>\left |<br>\begin{array}{111}<br>2 & a+r+2 & a+r \\<br>a+r+2 & 2(a+1)(r+1) & a(r+1)+r(a+1) \\<br>a+r & a(r+1)+r(a+1) & 2ar \\<br>\end {array}<br>\right |<br>$
Question 41 :
The least value of the product xyz for which the determinant $\begin{vmatrix} x & 1 & 1\\ 1 & y & 1\\ 1&1 & z\end{vmatrix}$ is non-negative, is :
Question 42 :
If [x] stands greatest integer $\leq x$ then the value of<br/>$\begin{vmatrix}<br/>\left [ e \right ] & \left [ \pi  \right ] & \left [ \pi ^{2}-6 \right ]\\ <br/>\left [ \pi  \right ] & \left [ \pi ^{2}-6 \right ] & \left [ e \right ]\\ <br/>\left [ \pi ^{2}-6 \right ] & \left [ e \right ] & \left [ \pi  \right ]<br/>\end{vmatrix}$ equals to=?<br/>
Question 43 :
Let n and r be two positive integers such that $n \geq r + 2$. Suppose $\Delta (n, r) =\begin{vmatrix}^nC_r & ^nC_{r + 1} & ^nC_{r + 2}\\ ^{n+1}C_r & ^{n + 1}C_{r + 1} & ^{n + 1}C_{r + 2}\\ ^{n + 2}C_r & ^{n + 2}C_{r + 1}& ^{n + 2} C_{r + 2}\end{vmatrix}$ Show that $\Delta(n, r) \displaystyle = \frac{^{n + 2} C_3}{^{n+ 2} C_3} \Delta (n - 2, r - 1)$ Hence or otherwise,
Question 44 :
If $\phi (\alpha ,\beta )=\begin{vmatrix} \cos { \alpha } & -\sin { \alpha } & 1 \\ \sin { \alpha } & \cos { \alpha } & 1 \\ \cos { (\alpha +\beta ) } & -\sin { (\alpha +\beta ) } & 1 \end{vmatrix}$, then <br>
Question 45 :
The number of positive integral solutions of the equation $\begin{vmatrix} y^3+1 & y^2z & y^2x\\ yz^2 & z^3+1 & z^2x\\ yx^2 & x^2z & x^3+1\end{vmatrix}=11$ is?
Question 50 : The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.<br/><table class="table table-bordered"><tbody><tr><td rowspan="2"> <b>Colour</b></td><td colspan="3"><b>   Number of cars manufactured</b></td></tr><tr><td><b> Vento</b></td><td><b> Creta</b></td><td><b>WagonR </b></td></tr><tr><td> Red</td><td> 65</td><td> 88</td><td> 93</td></tr><tr><td> White</td><td> 54</td><td> 42</td><td> 80</td></tr><tr><td> Black</td><td> 66</td><td> 52</td><td> 88</td></tr><tr><td> Sliver</td><td>37</td><td> 49</td><td> 74</td></tr></tbody></table>What was the total number of black cars manufactured?
Question 51 :
$\displaystyle z=10x+25y$ subject to$\displaystyle 0\le x\le 3$ and$\displaystyle 0\le y\le 3,x+y\le 5$ then the maximum value of z is<br>
Question 52 :
In order to obtain maximum profit, the quantity of normal and scientific calculators to be manufactured daily is:
Question 53 :
Given a system of inequation:$\displaystyle 2y-x\le 4$<br/>$\displaystyle -2x+y\ge -4$Find the value of $s$, which is the greatest possible sum of the $x$ and $y$ co-ordinates of the point which satisfies the following inequalities as graphed in the $xy$ plane.<br/>
Question 54 :
Linear programming model which involves funds allocation of limited investment is classified as
Question 55 :
In order for a linear programming problem to have a unique solution, the solution must exist
Question 56 :
The number of constraints allowed in a linear program is which of the following?
Question 57 :
In order to maximize the profit of the company, the optimal solution of which of the following equations is required?
Question 58 :
Find the output of the program given below if$ x = 48$<br/>and $y = 60$<br/>10  $ READ x, y$<br/>20  $Let x = x/3$<br/>30  $ Let y = x + y + 8$<br/>40  $ z = \dfrac y4$<br/>50  $PRINT z$<br/>60  $End$
Question 59 :
Conclude from the following:<br/>$n^2 > 10$, and n is a positive integer.A: $n^3$B: $50$
Question 60 :
If $x+y \leq 2, x\leq 0, y\leq 0$ the point at which maximum value of $3x+2y$ attained will be.<br/>
