MCA Entrance Previous Year Question Bank

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:

If $A$ and $B$ are two square matrices such that $B=-A^{-1}BA$, then $(A+B{)}^2$ will be equal to:

Consider the matrix $A=\left[\begin{array}{ccc}1& -2& 2\\ 0& 2& 0\\ 1& 1& 3\end{array}\right]$. Then $A^3-9A$ is:

The matrix A has x rows and $(x+5)$ columns and the matrix B has y rows and $(11-y)$ columns. If both the matrices AB and BA exits, then the value of x and y are

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

Find a matrix X such that $2A+B+X=0$, where

$A=\left[\begin{array}{cc}-1& 2\\ 3& 4\end{array}\right]$ and $B=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]$

If $A=\left[\begin{array}{cc}0& 5\\ 0& 0\end{array}\right]$ and $f(x)=1+x+x^2+\dots +x^{16}$, then $f(A)=$

If A is an invertible skew-symmetric matrix, then $A^{-}1$ is a:

If $F(\theta )=\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0\\ \sin \theta & \cos \theta & 0\\ 0& 0& 1\end{array}\right]$, then $F(\theta )F(\alpha )=$

If A and B are square matrices such that $B=-A^{-1}BA$, then $(A+B{)}^2$ is