The process requiring absorption of energy is

$A$ particle is projected vertically upwards from a point $A$ on the ground. It takes $t_1$ time to reach a point $B$ but it still continues to move up. If it takes further $t_2$ time to reach the ground from point $B$,then the height of point $B$ from the ground is:

Calculate the heat of combustion (in $kJ$) of methane from the following data:
$(I)$ $C_{(graphite)} + 2H_{2(g)} \rightarrow CH_{4(g)} \quad \Delta H = -74.8 \ kJ$
$(II)$ $C_{(graphite)} + O_{2(g)} \rightarrow CO_{2(g)} \quad \Delta H = -393.5 \ kJ$
$(III)$ $H_{2(g)} + 1/2 O_{2(g)} \rightarrow H_2O_{(l)} \quad \Delta H = -286.2 \ kJ$

An inductor $L$,a resistance $R$ and two identical bulbs $B_1$ and $B_2$ are connected to a battery through a switch $S$ as shown in the figure. The resistance of the coil having inductance $L$ is also $R$. Which of the following statements gives the correct description of the happenings when the switch $S$ is closed?

Acetone on addition to methyl magnesium bromide forms a complex,which on decomposition with acid gives $X$ and $Mg(OH)Br$. Which one of the following is $X$?

The area (in sq units) of the region bounded by $x=-1, x=2, y=x^2+1$ and $y=2x-2$ is