In the given figure, there is a circuit of potentiometer of length AB = 10 m. The resistance per unit length is 0.1 $$\Omega$$ per cm. Across AB, a battery of emf E and internal resistance 'r' is connected. The maximum value of emf measured by this potentiometer is :

In amplitude modulation, the message signal

V_m(t) = 10 sin (2$$\pi$$ $$\times$$ 10⁵t) volts and

Carrier signal

V_C(t) = 20 sin(2$$\pi$$ $$\times$$ 10⁷ t) volts

The modulated signal now contains the message signal with lower side band and upper side band frequency, therefore the bandwidth of modulated signal is $$\alpha$$ kHz. The value of $$\alpha$$ is :

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4^th second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap ? (Take g = 9.8 m/s²)

The minimum and maximum distances of a planet revolving around the sun are x₁ and x₂. If the minimum speed of the planet on its trajectory is v₀ then its maximum speed will be :