Examine Assertion A

Assertion A says: Number of photons increases with increase in frequency of light.

The energy of one photon is $E = h\nu$ where $h$ is Planck's constant and $\nu$ is frequency.

For a given amount of radiant energy $U$, the number of photons is $N = \frac{U}{h\nu}$

So, if frequency $\nu$ increases while total energy remains fixed, the number of photons decreases, not increases.

Hence, Assertion A is incorrect.

Examine Reason R

Reason R says: Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation.

From Einstein’s photoelectric equation, $K_{\max} = h\nu - \phi$ where $\phi$ is the work function.

Clearly, as $\nu$ increases, $K_{\max}$ increases linearly (provided $\nu$ is above threshold frequency).

Hence, Reason R is correct.

Check the relation between A and R

Since Assertion A is false and Reason R is true, the correct option is: $\boxed{\text{A: A is not correct but R is correct}}$

Compare with stored correct answer

Stored correct answer: A

My derived answer: A

So, they agree.