Physics

Two capacitors of capacitances C and 2C are charged to potential differences V and 2 V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:

An electrical power line, having a total resistance of 2Ω, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately:

Activities of three radioactive substances A, B and C are represented by the curves A, B and C in the figure. Then their half lives T₁(A): T₁(B): T₁(C) are in the ratio:

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to [ g is the acceleration due to gravity]:

Assume that the displacement (s) of air is proportional to the pressure difference (Ap) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air ( ρ ) and the frequency (f). If Ap ~ 10 Pa, v ~ 300 m/s, p ~ π11g/m³ and f ~ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1)

A square loop of side 2a, and carrying current I, is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z axis and passing through the point (0, b, 0), (b >> a). The magnitude of the torque on the loop about z - axis is given by:

Number of molecules in a volume of 4 cm³ of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is 4 * 10⁻¹⁴erg, g = 980 cm/s², density of mercury = 13.6 g/cm³ )

A galvanometer of resistance G is converted into a voltmeter of range 0 - 1V by connecting a resistance R? in series with it. The additional resistance that should be connected in series with R? to increase the range of the voltmeter to 0 – 2V will b

A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height h (see figure), then: (assume the remaining portion to be spherical)

For a concave lens of focal length f, the relation between object and image distances u and is v, respectively, from its pole can best be represented by ( u = v is the reference line): (Ray Optics)