If the speed of rotation of the armature of a generator is increased,…

The correct answer is Option (2) → Maximum emf and frequency both increase

In an ac generator a coil of \( N \) turns and area \( A \) rotates with angular speed \( \omega \) in a field \( B \). The induced emf is

    \( \displaystyle \varepsilon = N B A \omega \sin \omega t \)

So the maximum emf is \( \varepsilon_0 = N B A \omega \), and the frequency of the emf is the frequency of rotation, \( \nu = \omega / 2\pi \).

Both are proportional to \( \omega \). A faster rotation therefore increases the maximum emf and the frequency together.

Option (2) Maximum emf and frequency both increase — Correct. Both \( \varepsilon_0 = NBA\omega \) and \( \nu = \omega/2\pi \) increase with \( \omega \).

NCERT (2026-27):
AC Generator – “… Thus, the instantaneous value of the emf is

    \( \displaystyle \varepsilon = NBA\omega \sin \omega t \qquad (6.19) \)

where NBAω is the maximum value of the emf, which occurs when sin ωt = ±1. … Since ω = 2πν, Eq (6.20) can be written as

    \( \displaystyle \varepsilon = \varepsilon_0 \sin 2\pi \nu t \qquad (6.21) \)

where ν is the frequency of revolution of the generator’s coil.”