Which of the following is the smallest size grain that can be seen using a normal microscope using visible light $(400 \ nm < \lambda < 700 \ nm)$ (in $nm$)?

Resolving power of a telescope increases when

The average distance between the earth and moon is $38.6 \times 10^4 \ km$. The minimum separation between the two points on the surface of the moon that can be resolved by a telescope whose objective lens has a diameter of $5 \ m$ with $\lambda = 6000 \ \mathring{A}$ is ...... $m$.

With the help of a telescope that has an objective of diameter $200 \,cm$, it is proved that light of wavelengths of the order of $6400 \text{ Å}$ coming from a star can be easily resolved. Then, the limit of resolution is

$A$ telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength $500 \text{ nm}$, at a resolution of $5 \times 10^{-7} \text{ radian}$. The value of $R$ is . . . . . . $\text{cm}$.

Assertion : $A$ famous painting was painted by not using brush strokes in the usual manner,but rather a myriad of small colour dots. In this painting the colour you see at any given place on the painting changes as you move away.
Reason : The angular separation of adjacent dots changes with the distance from the painting.