If a circle C, whose radius is 3, touches externally the circle,
$${x^2} + {y^2} + 2x - 4y - 4 = 0$$ at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :

If the area of the region bounded by the curves, $$y = {x^2},y = {1 \over x}$$ and the lines y = 0 and x= t (t >1) is 1 sq. unit, then t is equal to :

A heating element has a resistance of 100 $$\Omega $$ at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is 500^oC more than room temperature. what is the temperature coefficient of resistance of the heating element ?

Both the nucleus and the atom of some element arein their respective first excited states. They get de-excted by emitting photons of wavelengths ^{$$\lambda $$}N, ^{$$\lambda $$}A respectively. The ratio $${{{}^\lambda N} \over {{}^\lambda A}}$$is closest to :