MCA Entrance Previous Year Question Bank

If $A$ is a $3\times 3$ matrix with $\det (A)=3$, then $\det (\text{adj }A)$ is:

A matrix $M_r$ is defined as $M_r=\left[\begin{array}{cc}r& r-1\\ r-1& r\end{array}\right],r\in N$, then the value of $\det (M_1)+\det (M_2)+\cdots +\det (M_{2015})$ is:

If $A=\left[\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right]$, where $a,b$ and $c$ are real positive numbers such that $abc=1$ and $A^{T}A=I$ then the equation that holds true among the following is:

$f(x)=\left|\begin{array}{ccc}x& 8& 8\\ 2& x& 8\\ 2& 2& x\end{array}\right|$ has local maximum at?

Let $\omega \ne 1$ be a cube root of unity and $i=\sqrt{-1}$. The value of the determinant $\left|\begin{array}{ccc}1& 1+i+{\omega }^2& {\omega }^2\\ 1-i& -1& {\omega }^2-1\\ -i& -i+\omega -1& -{\omega }^3\end{array}\right|$ is:

The derivatives of $(x^3+e^x+3^x+cotx)$ with respect to x is

If $x,y,z$ are distinct real numbers and $\left|\begin{array}{ccc}x& x^2& 2+x^3\\ y& y^2& 2+y^3\\ z& z^2& 2+z^3\end{array}\right|=0$, then xyz =