The solution of $\tan y \frac{dy}{dx} = \sin(x+y) + \sin(x-y)$ is

$M_p$ denotes the mass of a proton and $M_n$ denotes the mass of a neutron. $A$ given nucleus,of binding energy $B$,contains $Z$ protons and $N$ neutrons. The mass $M(N, Z)$ of the nucleus is given by ($c$ is the velocity of light):

Suppose $X$ follows a binomial distribution with parameters $n$ and $p$, where $0 < p < 1$. If $\frac{P(X=r)}{P(X=n-r)}$ is independent of $n$ for every $r$, then $p$ is equal to

The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively $\rho_1$ and $\rho_2$. The ratio of the accelerations due to gravity at their surfaces is

If the angle between the circles $x^2+y^2-2x-4y+c=0$ and $x^2+y^2-4x-2y+4=0$ is $60^{\circ}$,then $c$ is equal to

Assertion $(A)$: $A$ catalyst increases the rate of a reaction.
Reason $(R)$: In the presence of a catalyst,the activation energy of the reaction increases.
The correct answer is