MCA Entrance Previous Year Question Bank

A line through (4, 2) meets the coordinate axes at P and Q. Then the locus of the circumference of ΔOPQ is

Through any point (x, y) of a curve which passed through the origin, lines are drawn parallel to the coordinate axes. The curve given that divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of

In a triangle $ABC$, $\angle A=90^{\circ }$ and $D$ is mid-point of $AC$. The value of $B{C}^2-B{D}^2$ is equal to

If sin θ = 3 sin (θ + 2α), then the value of tan (θ + α) + 2 tan α is

The value of $\cot \left({\mathrm{cosec}}^{-1}\frac{5}{3}+{\tan }^{-1}\frac{2}{3}\right)$ is

A bird is flying in a straight line with velocity vector 10î + 6ĵ + k̂, measured in km/hr. If starting point is (1, 2, 3), how much time does it to take to reach a point in space that is 13 meter high from the ground?

Forces $4\hat{i}-3\hat{j}+7\hat{k}$ and $-2\hat{i}+2\hat{j}-8\hat{k}$ are acting on a particle and displaced it from the point (5, 7, 1) to (2, 5, -6), then the work done by the force is

The vector $\vec{a}=\alpha \hat{i}+2\hat{j}+\beta \hat{k}$ lies in the plane of the vector $\vec{b}=\hat{i}+\hat{j}$ and $\vec{c}=\hat{j}+\hat{k}$ and bisects the angle between $\vec{b}$ and $\vec{c}$. Then, which one of the following gives possible values of $\alpha$ and $\beta$?

If $\vec{a}$, $\vec{b}$ and $\vec{c}$ are unit vectors, then $|\vec{a}-\vec{b}{|}^2+|\vec{b}-\vec{c}{|}^2+|\vec{c}-\vec{a}{|}^2$ does not exceed

$f(x)=x+|x|$ is continuous for