Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of 20 ms^–1 with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the sound coming from car B, what is the natural frequency of the sound source in car B ?
(speed of sound in air = 340 ms^–1) :-

A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by :-

Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are '$$\theta $$₂' and '$$\theta $$₁' respectively, ($$\theta $$₂ > $$\theta $$₁). The temperature at the interface is :-

A He⁺ ion is in its first excited state. Its ionization energy is :-