The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line.

The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is :

Charge is distributed within a sphere of radius R with a volume charge density $$\rho \left( r \right) = {A \over {{r^2}}}{e^{ - {{2r} \over s}}},$$ where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :

In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed '$$\upsilon $$' more than that of car B. Both the cars start from rest and travel with constant acceleration a₁ and a₂ respectively. Then '$$\upsilon $$' is equal to :

The magnetic field associated with a light wave is given, at the origin, by B = B₀ [sin(3.14 $$ \times $$ 10⁷)ct + sin(6.28 $$ \times $$ 10⁷)ct]. If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons ?
(Take c = 3 $$ \times $$ 10⁸ ms^$$-$$1, h = 6.6 $$ \times $$ 10^$$-$$34J-s)