Data Entry - Physics

If $\tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\frac{\pi}{2}$,then $1-xy-yz-zx$ is equal to

In a meter bridge,a $30 \Omega$ resistance is connected in the left gap and a pair of resistances $P$ and $Q$ in the right gap. Measured from the left,the balance point is $37.5 \text{ cm}$ when $P$ and $Q$ are in series,and $71.4 \text{ cm}$ when they are in parallel. The values of $P$ and $Q$ (in $\Omega$) are:

The number of molecules of $CO_2$ liberated by the complete combustion of $0.1 \text{ mol}$ of graphite in air is:

Which of the following figures represents the variation of particle momentum $p$ and the associated de-Broglie wavelength $\lambda$?

If $x = \sin t$ and $y = \sin pt$,then the value of $(1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} + p^2y$ is equal to