Consider the following statements:

Statement-I: Giant stars live much longer than dwarf stars.
Statement-II: Compared to dwarf stars, giant stars have a greater rate of nuclear reactions.

Which one of the following is correct in respect of the above statements?

The correct option is: Statement-I is incorrect, but Statement-II is correct.

Let us analyze each statement to understand why this option is correct:

Analysis of Statement-I:
Statement-I claims that "Giant stars live much longer than dwarf stars." This is scientifically incorrect.
The lifespan of a star is determined by its mass and the rate at which it consumes its nuclear fuel. Although giant and massive stars have significantly more hydrogen fuel than dwarf stars, they also experience much greater gravitational forces. To counteract this intense gravity and remain stable, their cores must maintain extremely high temperatures and pressures. Consequently, they consume their fuel at an exponentially faster rate than smaller dwarf stars.
Because of this rapid fuel consumption, giant stars have much shorter lifespans (typically millions of years) compared to dwarf stars (which can burn steadily for tens of billions to even trillions of years). Thus, Statement-I is incorrect.

Analysis of Statement-II:
Statement-II claims that "Compared to dwarf stars, giant stars have a greater rate of nuclear reactions." This is scientifically correct.
As mentioned above, giant stars possess much higher core temperatures and densities due to their immense mass. Since the rate of thermonuclear fusion reactions is highly sensitive to temperature and pressure, the fusion reactions inside giant stars occur at a vastly higher rate than in dwarf stars. Therefore, Statement-II is correct.

Conclusion:
Since Statement-I is incorrect and Statement-II is correct, the chosen option is the accurate description.