Two particles which are initially at rest,move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of the centre of mass of the system will be

An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency is doubled. The temperature of the source is $.........^{\circ}C$.

Identify $A$ and $B$ in the following reaction:
$A \xrightarrow[\Delta]{aq. NaOH} C_2H_5OH \xleftarrow{AgOH} B$

Assertion : In humans,the gamete contributed by the male determines whether the child produced will be male or female.
Reason : Sex in humans is a polygenic trait depending upon a cumulative effect of some genes on $X-$ chromosome and some on $Y-$ chromosome.

The condition that $f(x)=a x^3+b x^2+c x+d$ has no extreme value, is

The major product of the following reaction is