The period of $f(x)=\cos \left(\frac{x}{3}\right)+\sin \left(\frac{x}{2}\right)$ is (in $\pi$)

In a $\triangle ABC$,the expression $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$ is equal to:

$A$ $x : 1$ molar mixture of $He$ and $CH_4$ is contained in a vessel at $20 \ bar$ pressure. Due to a hole in the vessel,the gas mixture leaks out. If the composition of the mixture effusing out initially is $8 : 1$,then the value of $x$ will be

Select the two correct statements out of the four $(i-iv)$ given below about the lac operon.
$i.$ Glucose or galactose may bind with the repressor and inactivate it.
$ii.$ In the absence of lactose,the repressor binds with the operator region.
$iii.$ The $z$-gene codes for permease.
$iv.$ This was elucidated by Francois Jacob and Jacques Monod.

$A$ particle of mass $5 \times 10^{-5} \ kg$ is placed at the lowest point of a smooth parabola $x^2 = 40y$ (where $x$ and $y$ are in $m$). If it is displaced slightly such that it is constrained to move along the parabola,the angular frequency of oscillation (in $rad/s$) will be approximately:

The chemical entities present in the thermosphere of the atmosphere are: