$A$ body of mass $m$ falls from a height $R$ above the surface of the earth,where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$)

Two resistances of $400 \ \Omega$ and $800 \ \Omega$ are connected in series with a $6 \ V$ battery of negligible internal resistance. $A$ voltmeter of resistance $10,000 \ \Omega$ is used to measure the potential difference across the $400 \ \Omega$ resistor. The error in the measurement of the potential difference in volts is approximately:

The solution of $\frac{dy}{dx} = \frac{y^2}{xy - x^2}$ is

Let $f(x) = x^3 + bx^2 + cx + d$ where $0 < b^2 < c$. Then $f(x)$:

$A$ photon of energy $8\, eV$ is incident on a metal surface of threshold frequency $1.6 \times 10^{15}\, Hz$. The maximum kinetic energy of the emitted photoelectrons is ............. $eV$ $(h = 6.6 \times 10^{-34}\, Js)$.

$\int_0^{2 \pi} \sin^6 x \cos^5 x \, dx$ is equal to