1. Use Faraday’s law

   The induced emf in a coil is produced when the magnetic flux through the coil changes: $\mathcal{E} = -\frac{d\Phi_B}{dt}$ where magnetic flux is $\Phi_B = BA\cos\theta$ for a coil in a uniform magnetic field.

   So emf is induced if any of the following changes with time:

   • magnetic field $B$
   • area $A$
   • angle $\theta$

2. Check each statement

   A. Moving the coil with uniform speed inside uniform magnetic field

   If the coil moves as a whole in a uniform magnetic field, then $B$, $A$, and $\theta$ remain unchanged. Hence flux does not change. $\frac{d\Phi_B}{dt}=0$ So no induced emf.

   Therefore, A is false.

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   B. Moving the coil with non-uniform speed inside uniform magnetic field

   Even if the speed is non-uniform, as long as the coil moves bodily inside a uniform magnetic field without changing area or orientation, the flux remains constant.

   So again, $\frac{d\Phi_B}{dt}=0$ Hence no induced emf.

   Therefore, B is false.

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   C. Rotating the coil inside the uniform magnetic field

   On rotating the coil, the angle $\theta$ between the field and the area vector changes with time. Therefore flux changes: $\Phi_B = BA\cos\theta(t)$ Hence induced emf is produced.

   Therefore, C is true.

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   D. Changing the area of the coil inside the uniform magnetic field

   If the area $A$ changes with time, then flux changes: $\Phi_B = B A(t) \cos\theta$ Hence induced emf is produced.

   Therefore, D is true.

3. Conclusion

   The correct statements are: $C \text{ and } D$

4. Match with options

   • Option A: A and C only — incorrect
   • Option B: C and D only — correct
   • Option C: B and D only — incorrect
   • Option D: B and C only — incorrect

Therefore, the correct answer is Option B.