MCA Entrance Previous Year Question Bank

The value of $X^4+9X^3+35X^2-X+4$ for $X=-5+2\sqrt{-4}$ is:

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:

If $\omega$ is a cube root of unity, then find the value of the determinant $\left|\begin{array}{ccc}1+\omega & {\omega }^2& -\omega \\ 1+{\omega }^2& \omega & -{\omega }^2\\ {\omega }^2+\omega & \omega & -{\omega }^2\end{array}\right|$ is:

The solution of the equation $\frac{dy}{dx}=e^{x+y}+x^2{e}^y$ is

Let $\alpha ,\beta$ be the roots of the equation ${\mathrm{x}}^2-$px+r=0 and $\frac{\alpha }{2},\beta$ be the roots of the equation $x^2-$qx+r= 0$. Then the value of r is

In a survey where 100 students reported which subjects they like, 32 students in total liked Mathematics, 38 students liked Business and 30 students liked Literature. Moreover 7 students liked both Mathematics and Literature, 10 students liked both Mathematics and Business, 8 students liked both Business and Literature, 5 students liked all three subjects. Then the number of people who liked exactly one subject is

A particle P starts from the point $z_0=1+2i$, where $i=\sqrt{-1}$. It moves first horizontally away from the origin by 5 units and then vertically away from origin by 3 units to reach a point $z_1$. From $z_1$ the particle moves $\sqrt{2}$ units in the direction of the vector $i+j$ to reach $z_2$, and then it moves through an angle $\frac{\pi }{2}$ in an anti-clock-wise direction on a circle with center at origin, to reach a point $z_3$. The point $z_3$ is given by:

If $x_k=\cos \left(\frac{2\pi k}{n}\right)+i\sin \left(\frac{2\pi k}{n}\right)$, then ${\sum }_{k=1}^n(x_k)=?$