MCA Entrance Previous Year Question Bank

Solution of the equation ${\tan }^{-1}\sqrt{x^2+x}+{\sin }^{-1}\sqrt{x^2+x+1}=\frac{\pi }{2}$ are

If $a_1,a_2,\dots ,a_n$ are in arithmetic progression with common difference $d$, then the sum $\sin d(\csc a_1\csc a_2+\csc a_2\csc a_3+\cdots +\csc a_{n-1}\csc a_n)$ is equal to:

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse observed from the ships are $30^{\circ }$ and $45^{\circ }$ respectively. If the lighthouse is $100\text{ m}$ high, the distance between the two ships is:

An airplane, when $4000$ m high from the ground, passes vertically above another airplane at an instant when the angles of elevation of the two airplanes from the same point on the ground are $60^{\circ }$ and $30^{\circ }$, respectively. Find the vertical distance between the two airplanes.

The angles of depression of the top and bottom of an $8$ m tall building from the top of a multi-storied building are $30^{\circ }$ and $45^{\circ }$, respectively. Find the height of the multi-storied building and the distance between the two buildings.

A tower subtends an angle of $30^{\circ }$ at a point on the same level as the foot of the tower. At a second point $h$ meters above the first, the depression of the foot of the tower is $60^{\circ }$. What is the horizontal distance of the tower from the point?