Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K. If the efficiencies of the two energies A and B are represented by $${\eta _A}$$ and $${\eta _B},$$ respectively, then what is the value of $${{{\eta _B}} \over {{\eta _A}}}$$ ?

When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes $${{5r} \over 4}.$$ Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) :

The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms^-1 is :
[k_B =1.4 $$ \times $$ 10^-23 J/K; m_He = 7 $$ \times $$ 10 ^-27 kg ]

Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures.
x(t) = A sin (at + $$\delta $$)
y(t) = B sin (bt)

Identify the correct match below.