The radius of which of the following orbits is the same as that of the $1^{st}$ orbit of $H$ atom?

$A$ motor of power $P_0$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe $n$ times,the power of the motor is increased to $P_1$. The ratio of $P_1$ to $P_0$ is

The figure shows the variation of the gravitational acceleration $a_g$ of four planets with the radial distance $r$ from the centre of the planet for $r \geq$ radius of the planet. Plots $1$ and $2$ coincide for $r \geq R_2$,and plots $3$ and $4$ coincide for $r \geq R_4$. The sequence of the planets in the descending order of their densities is:

In a slide caliper, \((m+1)\) number of vernier divisions is equal to \(m\) number of smallest main scale divisions. If \(d\) unit is the magnitude of the smallest main scale division, then the magnitude of the vernicr constant is

$A$ plane $\pi$ makes intercepts $3$ and $4$ respectively on $Z$-axis and $X$-axis. If $\pi$ is parallel to $Y$-axis,then its equation is:

If the sum of the roots of the equation $x^2 + px + q = 0$ is three times their difference,then which of the following is true?