$A$ neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is

When a non-volatile solute is added to a solvent,the vapor pressure decreases by $10 \ mm$. The mole fraction of the solute is $0.2$. If the vapor pressure decreases by $20 \ mm$,what will be the mole fraction of the solvent?

In an experiment,four quantities $a, b, c$ and $d$ are measured with percentage errors of $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $P$ is calculated as $P = \frac{a^3 b^2}{cd}$. The percentage error in the measurement of $P$ is .......... $\%$

$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $\frac{g}{8}$,then the ratio of masses $m_2 : m_1$ is:

In an experiment with $15$ observations of $x$,the results $\sum x^2 = 2830$ and $\sum x = 170$ are obtained. If one observation $20$ is found to be incorrect and is replaced by the correct observation $30$,what is the correct variance?

$A$ particle executes simple harmonic motion between $x = -A$ and $x = +A$. It starts from $x = 0$ and moves in the $+x$ direction. The time taken for it to move from $x = 0$ to $x = \frac{A}{2}$ is $T_1$,and the time taken to move from $x = \frac{A}{2}$ to $x = \frac{A}{\sqrt{2}}$ is $T_2$. Then: