The volume of one mole of the gas is changed from $V$ to $2 V$ at constant pressure $p$. If $\gamma$ is the ratio of specific heats of the gas, what is the change in internal energy of the gas?

An object of mass $2m$ is projected with a speed of $100 \ m/s$ at an angle $\theta = \sin^{-1}(3/5)$ to the horizontal. At the highest point,the object breaks into two pieces of same mass $m$ and the first one comes to rest. The distance between the point of projection and the point of landing of the bigger piece (in metre) is (Given,$g = 10 \ m/s^2$)

Charges are placed on the vertices of a square as shown. Let $\overrightarrow{E}$ be the electric field and $V$ be the electric potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively,then:

When a certain circuit consisting of a constant $emf$ $E$,an inductance $L$,and a resistance $R$ is closed,the current in it increases with time according to curve $1$. After one parameter ($E$,$L$,or $R$) is changed,the increase in current follows curve $2$,when the circuit is closed a second time. Which parameter was changed and in what direction?

The major product of the following reaction is

If the number of $5$-element subsets of the set $A = \{a_1, a_2, \ldots, a_{20}\}$ of $20$ distinct elements is $k$ times the number of $5$-element subsets containing $a_4$,then $k$ is