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The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object,the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is

If $x^2 y - x^3 \frac{dy}{dx} = y^4 \cos x$, then $x^3 y^{-3}$ is equal to

The area (in square units) of the triangle formed by the lines $x=0$,$y=0$ and $3x+4y=12$ is:

Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that each makes a complete circle in the same time $t$. The ratio of the angular speeds of the first to the second car is

Which of the following is the composition of glass?