A satellite is revolving in a circular orbit at a height h form the earth surface, such that h < < R where R is the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is :

An amplitude modulated signal is given by V(t) = 10[1 + 0.3cos(2.2 $$ \times $$ 10⁴ t)] sin(5.5 $$ \times $$ 10⁵ t). Here t is in seconds. The sideband frequencies (in kHz) are, [Given $$\pi $$ = 22/7]

An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be :

If the de Broglie wavelength of an electron is equal to the 10^–3 times the wavelength of a photon of frequency 6 $$ \times $$ 10¹⁴ Hz, then the speed of electron is equal to : (Speed of light = 3 $$ \times $$ 10⁸ m/s, Planck's constant = 6.63 $$ \times $$ 10^–34 J.s, Mass of electron = 9.1 $$ \times $$ 10^–31 kg)