$A$ nucleus with $Z = 92$ emits the following in a sequence: $\alpha, \alpha, \beta^-, \beta^-, \alpha, \alpha, \alpha, \alpha, \beta^-, \beta^-, \alpha, \beta^-, \beta^-, \alpha$. The $Z$ of the resulting nucleus is

In a photosystem,the antennae complex includes all pigments except:

Assertion $(A)$: Propagation of light through an optical fibre is due to total internal reflection taking place at the core-clad interface.
Reason $(R)$: Refractive index of the material of the core of the optical fibre is greater than that of air.

Two opposite and equal charges $4 \times 10^{-8} \, C$ are placed $2 \times 10^{-2} \, cm$ apart,forming a dipole. If this dipole is placed in an external electric field of $4 \times 10^8 \, N/C$,what are the values of the maximum torque and the work done in rotating it through $180^o$?

$\cos 36^{\circ} - \cos 72^{\circ}$ is equal to

If $ax^2+6xy+by^2-10x+10y-6=0$ represents a pair of perpendicular lines,then the value of $|a|$ equals