If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

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.

The binding energy per nucleon versus mass number curve for nuclei is shown in the figure. $W, X, Y$ and $Z$ are four nuclei indicated on the curve. The process that would release energy is:

If $\int e^x(1+x) \cdot \sec ^2(x e^x) \, dx = f(x) + \text{constant}$, then $f(x)$ is equal to

Which characteristics are included in the Kingdom $Monera$?

Choose the incorrect statements with respect to chordates
$(A)$ Presence of mid ventral, solid and double nerve cord.
$(B)$ Presence of open circulatory system.
$(C)$ Presence of ventral heart.
$(D)$ Presence of paired pharyngeal gills slits.
$(E)$ Triploblastic acoelomate animals.