The tension $T$ in the string shown in the figure 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

How many litres of oxygen (at $STP$) are required for complete combustion of $39 \text{ g}$ of liquid benzene? (Atomic weights: $C=12, O=16, H=1$)

The hydride ion $H^-$ is a stronger base than the hydroxide ion $OH^-$. If sodium hydride $(NaH)$ is dissolved in water,which of the following reactions will occur?

When a sound wave of wavelength $\lambda$ is propagating in a medium,the maximum velocity of the particle is equal to the wave velocity. The amplitude of the wave is:

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is