The vectors $\overrightarrow{AB} = 3\hat{i} + 4\hat{k}$ and $\overrightarrow{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a triangle $ABC$. The length of the median through $A$ is

The surface of water in a water tank of cross-sectional area $750 \, cm^2$ on the top of a house is $h \, m$ above the tap level. The speed of water coming out through the tap of cross-sectional area $500 \, mm^2$ is $30 \, cm/s$. At that instant,$\frac{dh}{dt}$ is $x \times 10^{-3} \, m/s$. The value of $x$ will be $.............$.

Two point charges $-10 \mu C$ and $+5 \mu C$ are situated on the $X$-axis at $x=0$ and $x=\sqrt{2} \ m$. The point along the $X$-axis where the electric field becomes zero is:

Two identical containers $A$ and $B$ with frictionless pistons contain an ideal gas at the same temperature and the same volume $V$. The mass of the gas in $A$ is $m_A$ and in $B$ is $m_B$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2V$. The changes in pressure in $A$ and $B$ are found to be $\Delta P$ and $1.5\Delta P$ respectively. Then:

The equivalent weight of $H_3PO_4$ in the following reaction is:
$H_3PO_4 + Ca(OH)_2 \to CaHPO_4 + 2H_2O$

Assertion : $HClO_4$ is a stronger acid than $HClO_3$.
Reason : Oxidation state of $Cl$ in $HClO_4$ is $+7$ and in $HClO_3$,it is $+5$.