If the plane $7x + 11y + 13z = 3003$ meets the coordinate axes at $A, B, C$,then the centroid of the $\triangle ABC$ is

$A$ magnet freely suspended in a vibration magnetometer makes $40$ oscillations per minute at place $A$ and $20$ oscillations per minute at a place $B$. If the horizontal component of earth's magnetic field at $A$ is $36 \times 10^{-6} ~T$,then its value at $B$ is

The point in the eye of mammals from which optic nerves and blood vessels leave the eyeball is:

$NH_3 + O_2 \xrightarrow[\Delta]{Pt} A + H_2O;$
$A + O_2 \to B$
$B + O_2 + H_2O \to C$
$A, B$ and $C$ are:

Match the List-$I$ with List-$II$:

List-$I$ (Isothermal process for ideal gas system)	List-$II$ (Work done)
$(A)$ Reversible expansion	$(I)$ $w = 0$
$(B)$ Free expansion	$(II)$ $w = -nRT \ln \frac{V_f}{V_i}$
$(C)$ Irreversible expansion	$(III)$ $w = -p_{ex}(V_f - V_i)$
$(D)$ Irreversible compression	$(IV)$ $w = -p_{ex}(V_i - V_f)$

Choose the correct answer from the options given below:

$\mathop {\lim}\limits_{x \to 0} \frac{{\sin \left( {\pi {{\cos }^2}x} \right)}}{{{x^2}}} = $