Two friends $A$ and $B$ are $30 \, km$ apart and they start simultaneously on motorcycles to meet each other. The speed of $A$ is $3$ times that of $B$. The distance between them decreases at the rate of $2 \, km$ per minute. Ten minutes after they start,$A$'s vehicle breaks down and $A$ stops and waits for $B$ to arrive. After how much time (in minutes) since $A$ started riding,does $B$ meet $A$?

In a simple harmonic oscillator,at the mean position

Which has the maximum number of molecules among the following?

Consider the reaction:
$Cl_{2(aq)} + H_2S_{(aq)} \to S_{(s)} + 2H^{+}_{(aq)} + 2Cl^{-}_{(aq)}$
The rate equation for this reaction is $\text{rate} = k[Cl_2][H_2S]$. Which of these mechanisms is/are consistent with this rate equation?
$A.$ $Cl_2 + H_2S \to H^{+} + Cl^{-} + Cl^{+} + HS^{-}$ (slow)
$Cl^{+} + HS^{-} \to H^{+} + Cl^{-} + S$ (fast)
$B.$ $H_2S \rightleftharpoons H^{+} + HS^{-}$ (fast equilibrium)
$Cl_2 + HS^{-} \to 2Cl^{-} + H^{+} + S$ (slow)

Match the following columns and select the correct option:

Column-$I$	Column-$II$
$(a)$ Floating ribs	$(i)$ Located between $2^{nd}$ and $7^{th}$ ribs
$(b)$ Acromion process	$(ii)$ Head of humerus
$(c)$ Scapula	$(iii)$ Clavicle articulation
$(d)$ Glenoid cavity	$(iv)$ Do not connect with the sternum

$(a)\quad(b)\quad(c)\quad(d)$

If $f(x) = \sin^6 x + \cos^6 x$ for $x \in R$,then $f(x)$ lies in the interval