Question 1 :
If A+$$\displaystyle \begin{vmatrix} 4 & 2 \\ 1 & 3 \end{vmatrix} $$=$$\displaystyle \begin{vmatrix} 6 & 9 \\ 1 & 4 \end{vmatrix} $$ then A=
Question 2 :
A square matrix $$(a_{ij})$$ in which $$a_{ij}=0$$ for $$i \neq j$$ and $$a_{ij}= k (constant)$$ for $$i=j$$ is a<br/>
Question 3 : <p>The possibility for the formation of rectangular matrices in the matrix algebra are</p>
Question 5 :
If P=$$\displaystyle  \begin{bmatrix} 4 & 3 &2   \end{bmatrix}  $$ and Q=$$\displaystyle  \begin{bmatrix} -1 & 2 &3   \end{bmatrix}  $$ then P-Q=
Question 6 :
If $$A=\displaystyle \left[ \begin{matrix} 1 &2 \\ 3& 4 \end{matrix} \right] $$, then which of the following is not an element of $$A$$?
Question 7 :
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 9 :
If $$A$$ and $$B$$ are square matrices such that $$AB = I$$ and $$BA = I$$, then $$B$$ is<br/>
Question 11 :
$$\mathrm{If}$$ $$\left|\begin{array}{lll}<br>1 & 0 & 0\\<br>2 & 3 & 4\\<br>5 & -6 & x<br>\end{array}\right|$$ $$= 45$$ $$\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}$$ $$\mathrm{x}=$$<br><br>
Question 12 :
$$A=\begin{bmatrix} 5 & 5a & a \\ 0 & a & 5a \\ 0 & 0 & 5 \end{bmatrix}$$ If $$\left| A^{ 2 } \right| =25$$ then $$|a|=$$
Question 13 :
Find the value of the following determinant:<br/>$$\begin{vmatrix}\displaystyle \frac{-4}{7} & \displaystyle \frac{-6}{35}\\ 5 & \displaystyle \frac{-2}{5}\end{vmatrix}$$
Question 14 :
The determinant $$\begin{vmatrix}a & b & a\alpha +b\\ b & c & b\alpha +c\\ a\alpha +b & b\alpha +c & 0\end{vmatrix}$$ is equal to zero, if.
Question 15 :
If $$\omega$$ is a non-real cube root of unity and n is not a multiple of 3, then $$\displaystyle \Delta =\left | \begin{matrix}<br>1 & \omega^{n} &\omega^{2n} \\ <br>\omega^{2n}&1 &\omega^{n} \\ <br>\omega^{n}&\omega^{2n} &1 <br>\end{matrix} \right |$$ is equal to<br>
Question 16 :
If $$\begin{vmatrix} 6i & -3i & 1\\ 4 & 3i & -1 \\ 20 & 3 & i\end{vmatrix}=x+iy$$, then<br>
Question 17 :
If $$\Delta_1=\begin{vmatrix} 1 & 0\\ a & b\end{vmatrix}$$ and $$\Delta_2=\begin{vmatrix} 1 & 0\\ c & d\end{vmatrix}$$ then $$\Delta_2 \Delta_1$$ is equal to<br>
Question 18 :
$$\begin{vmatrix} 2^3 & 3^3 & 3.2^2+3.2+1\\ 3^3 & 4^3 & 3.3^2+3.3+1\\ 4^3 & 5^3 & 3.4^2+3.4+1\end{vmatrix}$$ is equal to?
Question 19 :
If $$\begin{vmatrix} a & a & x\\ m & m & m\\ b & x & b\end{vmatrix}=0$$ then $$x=?$$
Question 20 :
Find the value of the following determinant:<br/>$$\begin{vmatrix}3\sqrt{6} & -4\sqrt{2}\\ 5\sqrt{3} & 2\end{vmatrix}$$
Question 21 :
If $$f(x) = \begin{cases}\dfrac{x^2-(a+2)x+a}{x-2} & x\ne 2\\ 2 & x = 2 \end{cases}$$ is continuous at $$x = 2$$, then the value of $$a$$ is
Question 22 :
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 23 :
$$f(x)=\left\{\begin{matrix} 2x-1& if &x>2 \\ k & if &x=2 \\  x^{2}-1& if & x<2\end{matrix}\right.$$is continuous at $$x= 2$$ then $$k =$$
Question 24 :
If $$f(x) = (1 + 2x)^{\frac{1}{x}}$$, for $$x \neq 0$$ is continuous at $$x = 0$$, then $$f(0) = $$_______.
Question 26 :
If $$f(x)=\displaystyle \frac{\sin x}{x},x\neq 0$$ is to be continuous at $${x}=0$$ then $$\mathrm{f}({0})=$$<br/>
Question 27 :
If $$f(x)=\displaystyle\frac{\log(1+ax)-log(1-bx)}{x}$$ for $$x\neq 0$$ and $$f(0)=k$$ and $$f(x)$$ is continuous at $$x=0$$, then $$k$$ is equal to:<br>
Question 28 :
The function $$f(x)=\dfrac{1-\sin x+\cos x}{1+\sin x+\cos x}$$ is not defined at $$x=\pi$$. The value of $$f(\pi)$$ so that $$f(x)$$ is continuous at $$x=\pi$$ is
Question 29 :
Following function is continous at the point $$x=2$$ <br/>          $$f\left( x \right) = \left\{ \begin{array}{l}1 + x,\,\,\,\,when\,\,x < 2\\5 - x,\,\,\,\,when\,\,x \ge 2\end{array} \right.$$
Question 30 :
If as continuous function 'f' satisfies the realation <br/>$$\int_{0}^{t}(f(x) \, - \, \sqrt{f^1(x)})dx \, = \, 0 \, and \, f(0) \, = \, {-1}$$<br/>the f(x) is equal to
Question 31 :
If $$f\left( x \right) =\dfrac { 3sinx-sin\left( 3x \right) }{ { 2x }^{ 3 } } ,x\neq 0,f\left( 0 \right) =2,$$ at $$x=0,f$$ is
Question 32 :
<br/>The function $$f(x)=\begin{cases}(1+x)^{\frac{5}{x}}& for \ {x}\neq 0,\\ e^{5} & for \  {x}=0\end{cases}$$ is ........ at $${x}=0$$<br/>
Question 33 :
The function $$f\left( x \right)=\left[ x \right] ,$$  at $${ x }=5$$ is:<br/>
Question 34 :
Function $$f(x) = \left\{\begin{matrix}(\log_{2}2x)^{\log_{x} 8};& x\neq 1\\(k - 1)^{3};& x = 1\end{matrix}\right.$$ is continuous at $$x = 1$$, then $$k =$$ _______.<br>
Question 35 :
If $$ f\left( x \right) =\begin{cases} 1 & x<0 \\ { x }^{ 2 } & x\ge 0 \end{cases}$$ then at $$x=0$$
