A parallel plate capacitor with square plates is filled with four dielecytrics of dielectrics constants K₁, K₂, K₃, K₄ arranged as shown in the figure. The effective dielectric constant K will be :

The position co-ordinates of a particle moving in a 3-D coordinate system is given by
x = a cos$$\omega $$t
y = a sin$$\omega $$t and
z = a$$\omega $$t

The speed of the particle is :

In the given circuit the the internal resistance of the 18 V cell is negligible. If R₁ = 400 $$\Omega $$, R₃ = 100 $$\Omega $$ and R₄ = 500 $$\Omega $$ and the reading of an ideal voltmeter across R₄ is 5V, then the value of R₂ will be :

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 :