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.

In the given circuit, the value of current I_L will be ____________ mA. (When R_L = 1k$$\Omega$$)

A sample contains 10^$$-$$2 kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is $${x \over {100}}$$. The value of x is ___________.