If $\vec{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\vec b = \frac{1}{7}(2 \hat{i} + 3 \hat{j} - 6 \hat{k})$,then the value of $(2\vec a - \vec b) \cdot [(\vec a \times \vec b) \times (\vec a + 2\vec b)]$ is

If $x^3 + y^3 - 3axy = 0$,then $\frac{dy}{dx}$ equals

Sodium and copper have work functions $2.3 \ eV$ and $4.5 \ eV$ respectively. The ratio of the threshold wavelength of sodium to that of copper is nearest to:

Assertion $(A)$ At $300 \ K$,kinetic energy of $16 \ g$ of methane is equal to the kinetic energy of $32 \ g$ of oxygen.
Reason $(R)$ At constant temperature,kinetic energy of one mole of all gases is equal.

In the triangle with vertices at $A(6, 3), B(-6, 3)$ and $C(-6, -3)$,the median through $A$ meets $BC$ at $P$,the line $AC$ meets the $x$-axis at $Q$,while $R$ and $S$ respectively denote the orthocentre and centroid of the triangle. Then the correct matching of the coordinates of points in List-$I$ to List-$II$ is

List-$I$	List-$II$
$(i) P$	$(A) (0, 0)$
$(ii) Q$	$(B) (6, 0)$
$(iii) R$	$(C) (-2, 1)$
$(iv) S$	$(D) (-6, 0)$
	$(E) (-6, -3)$
	$(F) (-6, 3)$

$(i) (ii) (iii) (iv)$

For the reaction $SnO_{2(s)} + 2H_{2(g)} \rightleftharpoons 2H_2O_{(g)} + Sn_{(l)}$,calculate $K_p$ at $900 \, K$,where the equilibrium steam-hydrogen mixture was $45 \% \, H_2$ by volume.