A body is projected from the ground at an angle of 45$$^\circ$$ with the horizontal. Its velocity after 2s is 20 ms^$$-$$1. The maximum height reached by the body during its motion is __________ m. (use g = 10 ms^$$-$$2)

An antenna is placed in a dielectric medium of dielectric constant 6.25. If the maximum size of that antenna is 5.0 mm, it can radiate a signal of minimum frequency of __________ GHz.

(Given $$\mu$$_r = 1 for dielectric medium)

A potentiometer wire of length 10 m and resistance 20 $$\Omega$$ is connected in series with a 25 V battery and an external resistance 30 $$\Omega$$. A cell of emf E in secondary circuit is balanced by 250 cm long potentiometer wire. The value of E (in volt) is $${x \over {10}}$$. The value of x is __________.

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $$y = (10\cos \pi x\sin {{2\pi t} \over T})$$ cm

The amplitude of the particle at $$x = {4 \over 3}$$ cm will be ___________ cm.