$A$ light and a heavy body have equal kinetic energy. Which one has a greater momentum?

If $y$ is a function of $x$ and $\log(x+y) = 2xy$,then the value of $y'(0)$ is

Let $P(3, 2, 6)$ be a point in space and $Q$ be a point on the line $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(-3\hat{i} + \hat{j} + 5\hat{k})$. Then the value of $\mu$ for which the vector $\vec{PQ}$ is parallel to the plane $x - 4y + 3z = 1$ is:

According to the Neo-Darwinian theory,which of the following is responsible for the origin of new species?

$A$ particle is tied to a $20\,cm$ long string. It performs circular motion in a vertical plane. What is the angular velocity of the string when the tension in the string at the top is zero? (Take $g = 9.8\,m/s^2$)

$A$ and $C$ are concentric conducting spherical shells of radii $a$ and $c$ respectively. $A$ is surrounded by a concentric dielectric layer of inner radius $a$,outer radius $b$,and dielectric constant $k$. If sphere $A$ is given a charge $Q$,the potential at the outer surface of the dielectric (at radius $b$) is: