$A$ mass $m$ moving horizontally (along the $x-$ axis) with velocity $v$ collides and sticks to a mass of $3m$ moving vertically upward (along the $y-$ axis) with velocity $2v$. The final velocity of the combination is

The $pK_a$ values of four carboxylic acids are $4.76, 4.19, 0.23$,and $3.41$ respectively. The $pK_a$ value of the strongest carboxylic acid among them is

$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as $a_c = k^2rt^2$. The power delivered to the particle by the forces acting on it is

Two full turns of the circular scale of a screw gauge cover a distance of $1\,mm$ on the main scale. The total number of divisions on the circular scale is $50$. Further,it is found that the screw gauge has a zero error of $+0.03\,mm$. While measuring the diameter of a thin wire,a student notes the main scale reading of $3\,mm$ and the number of the circular scale division in line with the main scale is $35$. The diameter of the wire is .......... $mm$.

During the depression in freezing point experiment,an equilibrium is established between the molecules of

Who proposed the theory that "Cells arise only from the pre-existing cells"?