$A$ coil of $50$ turns and $4$ cm radius carries $2$ $A$ current. The magnetic field at its centre is ...... mT.

The position vectors of $P$ and $Q$ are respectively $\overrightarrow{a}$ and $\overrightarrow{b}$. If $R$ is a point such that $\overrightarrow{PR}=5 \overrightarrow{PQ}$,then the position vector of $R$ is

If $5x - 12y + 10 = 0$ and $12y - 5x + 16 = 0$ are two tangents to a circle,then the radius of the circle is

If a unit vector is represented by $0.5\hat{i} - 0.8\hat{j} + c\hat{k}$,then the value of $c$ is:

If Avogadro number $N_A$ is changed from $6.022 \times 10^{23} \ mol^{-1}$ to $6.022 \times 10^{20} \ mol^{-1}$,this would change:

Molar volume $( V_m )$ of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_m$ as the variable. The ratio $($in $mol dm ^{-3} )$ of the coefficient of $V_m^2$ to the coefficient of $V_m$ for a gas having van der Waals constants $a=6.0 dm ^6 atm \ mol ^{-2}$ and $b=0.060 dm ^3 mol^{-1}$ at $300 K$ and $300 atm$ is $....$ .
Use: Universal gas constant $(R)=0.082 dm ^3 atm \ mol { }^{-1} K^{-1}$