The ratio of $C_p$ and $C_v$ of a gas $'X'$ is $1.4$. The number of atoms of the gas $'X'$ present in $11.2 \ L$ of it at $NTP$ will be:

Assertion $(A)$: White tin is an example of a tetragonal system.
Reasoning $(R)$: For a tetragonal system,$a=b=c$ and $\alpha=\beta=\gamma \neq 90^{\circ}$. The correct answer is

Let $\overline{a}=2 \hat{i}+\hat{j}-2 \hat{k}$ and $\overline{b}=\hat{i}+\hat{j}$. Let $\overline{c}$ be a vector such that $|\overline{c}-\overline{a}|=3$,$|(\overline{a} \times \overline{b}) \times \overline{c}|=3$,and the angle between $\overline{c}$ and $\overline{a} \times \overline{b}$ is $30^{\circ}$. Then $\overline{a} \cdot \overline{c}$ is equal to

If $\Delta = a^2 - (b - c)^2$ is the area of the $\triangle ABC$,then $\tan A$ is equal to

The value of $k$ such that the line $\frac{x - 4}{1} = \frac{y - 2}{1} = \frac{z - k}{2}$ lies in the plane $2x - 4y + z = 7$ is: