The locus of the point of intersection of the lines, $$\sqrt 2 x - y + 4\sqrt 2 k = 0$$ and $$\sqrt 2 k\,x + k\,y - 4\sqrt 2 = 0$$ (k is any non-zero real parameter), is :

A galvanometer with its coil resistance 25 $$\Omega $$ requires a current of 1 mA for its full deflection. In order to construct an ammeter to read upto a current of 2 A, the approximate value of the shunt resistance should be :

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 :

The de-Broglie wavelength ($$\lambda $$_B) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state ($$\lambda $$_G) by :