1. Magnetic flux through the rotating coil

For a coil of $N$ turns and area $A$ rotating in a uniform magnetic field $B$ with angular speed $\omega$,

$\Phi = N B A \cos(\omega t)$

where $\Phi$ is the total flux linked with the coil.

2. Induced emf using Faraday's law

By Faraday's law,

$e = -\frac{d\Phi}{dt}$

So,

$e = -\frac{d}{dt}(N B A \cos \omega t)$

$e = N B A \omega \sin(\omega t)$

3. Maximum value of emf

The induced emf is sinusoidal, and its maximum value is

$e_{\max} = N B A \omega$

4. Role of resistance $R$

The resistance of the coil does not affect the maximum emf generated. It affects the current if the circuit is closed, but not the induced emf itself.

5. Match with options

• A: $NABR\omega$ — incorrect, contains $R$
• B: $NAB$ — incorrect, missing $\omega$
• C: $NABR$ — incorrect, contains $R$
• D: $NAB\omega$ — correct

Therefore, the correct answer is:

$\boxed{D}$