A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths '$$\lambda $$_x' and '$$\lambda $$_y' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-

A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances x₁ and x₂ (x₁ > x₂) from the lens. The ratio of x₁ and x₂ is :-

Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600nm. coming from a distant object, the limit of resolution of the telescope is close to :-

A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely ? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K)