If $\cos A = \frac{3}{4}$,then $32 \sin \left(\frac{A}{2}\right) \sin \left(\frac{5A}{2}\right) = $

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

If $A$ is any set,then:

$A$ car starts from rest and moves with uniform acceleration $a$ on a straight road from time $t = 0$ to $t = T$. After that,a constant deceleration brings it to rest. In this process,the average speed of the car is

The oxidation state and covalency of $Al$ in $[AlCl(H_2O)_5]^{2+}$ are respectively

At $550 \ K$,the $K_c$ for the following reaction is $10^4 \ L \ mol^{-1}$: $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$. At equilibrium,it was observed that $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$. What is the value of $[Z]$ (in $mol \ L^{-1}$) at equilibrium?