One litre of oxygen at a pressure of $1 ~atm$ and two litres of nitrogen at a pressure of $0.5 ~atm$ are introduced into a vessel of volume $1 ~L$. If there is no change in temperature,the final pressure of the mixture of gas (in $atm$) is

The given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths $A, B, C$. Let $Q, W$,and $\Delta U$ represent the heat supplied to the gas,work done by the gas,and the change in internal energy of the gas,respectively. Which of the following conditions is true?

The velocity of a particle at time $t$ is given by the relation $v = 6t - \frac{t^2}{6}$. The distance traveled in $3$ seconds is,if $s = 0$ at $t = 0$.

What are $\underline{A}, \underline{B}, \underline{C}$ in the following reactions?
$(I)$ $(CH_3 CO_2)_2 Ca \xrightarrow{\Delta} \underline{A}$
$(II)$ $CH_3 CO_2 H \xrightarrow[Red\ P]{HI} \underline{B}$
$(III)$ $2 CH_3 CO_2 H \xrightarrow{P_4 O_{10}} \underline{C}$
$\underline{A} \quad \underline{B} \quad \underline{C}$

Which of the following is a group of blue-green algae that acts as a biofertilizer?

Two identical balls $A$ and $B$ are released from the positions shown in the figure. They collide elastically on the horizontal portion $MN$. The ratio of the heights attained by $A$ and $B$ after the collision will be: (neglect friction)