$A$ parallel beam of monochromatic light falls normally on a single narrow slit. The angular width of the central maximum in the resulting diffraction pattern

If $(1+x+x^2+x^3)^5 = \sum_{k=0}^{15} a_k x^k$,then $\sum_{k=0}^7 a_{2k}$ is equal to

The number of octahedral and tetrahedral holes respectively present in a hexagonal close packed $(hcp)$ crystal of '$X$' atoms are

If the number average molecular weight and weight average molecular weight of a polymer are $40000$ and $60000$ respectively,the polydispersity index of the polymer will be

Identify $B$ in the following reaction:
$H_4SiO_4$ $\xrightarrow[1000^{\circ}C]{-2H_2O} A$ $\xrightarrow[\Delta]{\text{Carbon}} B + CO$

Assertion $A$: An astronaut inside a massive spaceship orbiting around the Earth will experience a finite but small gravitational force.
Reason $R$: The centripetal force necessary to keep the spaceship in orbit around the Earth is provided by the gravitational force between the Earth and the spaceship.