A carrier wave V_c(t) = 160 sin(2$$\pi$$ $$\times$$ 10⁶t) volts is made to vary between V_max = 200 V and V_min = 120 V by a message
signal V_m(t) = A_m sin(2$$\pi$$ $$\times$$ 10³t) volts. The peak voltage A_m of the modulating signal is ___________.

An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m, if the focal length of the eyepiece is equal to __________ cm.

The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m/s. Then the speed of car is ___________ km/h.

A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it makes time 't₁'. When it rolls down the plane, it takes time t₂. The value of $${{{t_2}} \over {{t_1}}}$$ is $$\sqrt {{3 \over x}} $$. The value of x will be _______________.