$\lim _{x \rightarrow 0} \frac{(1-e^x) \sin x}{x^2+x^3}$ is equal to

The energy liberated on complete fission of $1\, kg$ of $_{92}U^{235}$ is (Assume $200\, MeV$ energy is liberated on fission of $1$ nucleus).

Every planet revolves around the sun in an elliptical orbit. Consider the following statements:
$A.$ The gravitational force acting on a planet is inversely proportional to the square of the distance from the sun.
$B.$ The gravitational force acting on a planet is inversely proportional to the product of the masses of the planet and the sun.
$C.$ The centripetal force acting on the planet is directed away from the sun.
$D.$ The square of the time period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of the elliptical orbit.
Choose the correct statements from the options given above:

If $|x| < \frac{1}{2}$,then the coefficient of $x^r$ in the expansion of $\frac{1+2x}{(1-2x)^2}$ is

The solution set of $(5 + 4\cos \theta )(2\cos \theta + 1) = 0$ in the interval $[0, 2\pi ]$ is

If $\triangle ABC$ is right-angled at $A$,then $r_2+r_3$ is equal to