A $$12.5 \mathrm{~eV}$$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

The amplitude of $$15 \sin (1000 \pi \mathrm{t})$$ is modulated by $$10 \sin (4 \pi \mathrm{t})$$ signal. The amplitude modulated signal contains frequencies of

A. $$500 \mathrm{~Hz}$$

B. $$2 \mathrm{~Hz}$$

C. $$250 \mathrm{~Hz}$$

D. $$498 \mathrm{~Hz}$$

E. $$502 \mathrm{~Hz}$$

Choose the correct answer from the options given below:

Given below are two statements:

Statement I : When the frequency of an a.c source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases.

Statement II : In a series LCR circuit, the value of power factor at resonance is one.

In the light of given statements, choose the most appropriate answer from the options given below.

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____________ KJ. [The coefficient of friction between tyre of bus and road is 0.04.]