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

We have two spheres,one of which is hollow and the other solid. They have identical masses and moments of inertia about their respective diameters. The ratio of their radii is given by

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

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

$A$ reaction,$3 X_{(g)} \rightarrow 2 Y_{(g)} + Z_{(g)}$,takes place in a closed vessel. What is the rate of formation of $Y$ (in $mol \ L^{-1} \ s^{-1}$) if the rate of disappearance of $X$ is $7.2 \times 10^{-3} \ mol \ L^{-1} \ s^{-1}$?

$\lim _{x \rightarrow \infty}\left(\frac{x+5}{x+2}\right)^{x+3}$ equals

Data Entry - Physics