MCA Entrance Previous Year Question Bank

If $a$, $b$, $c$ are in A.P., then $\tan \frac{A}{2}\cdot \tan \frac{C}{2}=$

If $x+y=1$ and $x^3+y^3=4$, then $x^5+y^5=$

The ages of students in a group are in A.P. If the youngest is $5$ years old, and the oldest is $15$ years old, then the average age of the group is:

$T_n$ represents the no. of triangles formed from a polygon having $n$ vertices. If $T_{n+1}-T_n=21$, then $n$ is equal to:

The number of roots of the equation $x^3+x^2+3+2\sin x=0$, $x\in [-\pi ,\pi ]$ is:

If the $m^{\text{th}}$ term of an H.P. is $n$ and its $n^{\text{th}}$ term is $m$, then find its $(m+n{)}^{\text{th}}$ term?

If $a=1+{\log }_x(yz)$, $b=1+{\log }_y(xz)$, $c=1+{\log }_z(xy)$, then $ab+bc+ca$ is equal to:

The equation of line passing through $(-2,3)$ and perpendicular to $2x-3y+6=0$ is given by:

The velocity of a boat relative to water is $3\hat{i}+4\hat{j}$ and that of water relative to earth is $\hat{i}-3\hat{j}$. What is the magnitude and direction of boat w.r.t earth?

A particle is acted upon by constant forces $4\hat{i}+\hat{j}-3\hat{k}$ and $3\hat{i}+\hat{j}-\hat{k}$ which displace it from a point $\hat{i}+2\hat{j}+3\hat{k}$ to the point $5\hat{i}+4\hat{j}+\hat{k}$. The work done in standard units by the forces is given by: