If $\sin A + \sin B = \sqrt{3}(\cos B - \cos A)$,then $\sin 3A + \sin 3B$ is equal to:

$A$ 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:

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered $1$ to $6$) and let $E_k = \{(a, b) \in S : ab = k\}$ for $k \geq 1$. If $p_k = P(E_k)$ for $k \geq 1$, then which of the following is correct?

Which one of the following is a slime mould?

What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ into a circular orbit at an altitude of $2R$?

Which plot is the adsorption isobar for chemisorption?