Compound $X$ is the anhydride of sulphuric acid. The number of $\sigma$-bonds and the number of $\pi$-bonds present in $X$ are,respectively:

The angles of a triangle are in the ratio $3: 5: 10$. Then the ratio of the smallest side to the greatest side is:

If $\tan A$ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0$,then $\sin^2(A+B)$ is equal to

$y+x^2=\frac{dy}{dx}$ has the solution

In Young's double slit experiment,the two slits act as coherent sources of equal amplitude $A$ and wavelength $\lambda$. In another experiment with the same setup,the two slits are sources of equal amplitude $A$ and wavelength $\lambda$,but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case to that in the second case is:

From a point on the level ground,the angle of elevation of the top of a pole is $30^{\circ}$. On moving $20 \ m$ nearer to the pole,the angle of elevation becomes $45^{\circ}$. The height of the pole (in metres) is: