Cyclic photophosphorylation results in the formation of:

Which of the following theories provides the latest explanation for the closure of stomata?

If the circle $x^2+y^2+6x-2y+k=0$ bisects the circumference of the circle $x^2+y^2+2x-6y-15=0$,then $k$ is equal to

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$a$. Sodium laurylsulphate	$i$. Toilet soap
$b$. Cetyltrimethyl ammonium chloride	$ii$. Non-ionic detergent
$c$. Sodium stearate	$iii$. Anionic detergent
$d$. Polyethyleneglycyl stearate	$iv$. Cationic detergent

Choose the correct answer from the options given below:

The plank in the figure moves a distance $100\,mm$ to the right while the centre of mass of the sphere of radius $150\,mm$ moves a distance $75\,mm$ to the left. The angular displacement of the sphere (in radian) is (there is no slipping anywhere):-

If $\int(1-\cos x) \operatorname{cosec}^2 x \, dx = f(x) + c$, then $f(x)$ is equal to