Resistance of a decimolar solution between two electrodes $0.02 \ m$ apart and $0.0004 \ m^2$ in area was found to be $50 \ \Omega$. Specific conductance $(k)$ is : ........... $S \ m^{-1}$

$A$ die is thrown four times. The probability of getting a perfect square in at least one throw is

If $A = \begin{bmatrix} -2 & 2 \\ -3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then $(B^{-1} A^{-1})^{-1}$ is equal to

The acute angle between the line $\vec{r}=(\hat{i}+2\hat{j}+\hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k})$ and the plane $\vec{r} \cdot(2\hat{i}+\hat{j}+\hat{k})=5$ is

$A$ vector $n$ of magnitude $8$ units is inclined to $x$-axis at $45^\circ$,$y$-axis at $60^\circ$ and an acute angle with $z$-axis. If a plane passes through a point $(\sqrt{2}, -1, 1)$ and is normal to $n$,then its equation in vector form is

The density of a mixture of $He$ and $O_2$ gases at $27 \, ^oC$ and $760 \, torr$ is found to be $0.543 \, g \, dm^{-3}$. What is the mass percentage of helium in the mixture?