A mass (M) is split into two parts (m) and (M–m). Which are then separated by a certain distance. What ratio m M will maximise the gravitational force between the parts ?A mass (M) is split into two parts (m) and (M–m). Which are then separated by a certain distance. What ratio m/ M will maximise the gravitational force between the parts ?

Two stationary particles of masses M1 and M2 are at a distance 'd' apart. A third particle lying on the line joining the particles, experiences no resultant gravitational forces. What is the distance of this particle from M1 ?

Departure from reason, focus on nature and the supernatural are all features of the literature of what period?

From a group of 8 boys and 5 girls a committee of 5 is to be formed. Find the probability that the committee contains 3 boys and 2 girls?

Find the differential equation of the family of all circles which pass through the origin and whose centre lie on y–axis?

A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, what is the probability of

- no success ?
- 6 successes ?
- at least 6 successes ?
- at most 6 successes ?

A problem in statistics is given to three students A, B and C. Their chances of solving the problem are 1/3, 1/4 and 1/5 respectively. If all of them try independently, what is the probability that?

- (i) problem is not solved ?
- (ii) problem is solved ?
- (iii) exactly two students solve the problems

A pair of dice is thrown. If sum of the numbers is an even number, what is the probability that it is a perfect square ?

How many half-lives should eclapse for a 1^{st} order reaction A → products so that the reaction is atleast 95% completed?

a) 4

b) 5

c) 6

d) 7

The rate of a certain reaction depends on concentration according to the equation :

What will be the order of reaction, when concentration (C) :

a) very-very high

b) very-very low

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A wire has resistance of 24 is bent in the following shape. The effective resistance between A and B is?

An electrical cable of copper has just one wire of radius 9 mm. Its resistance is 5 ohm. This single copper wire of the cable is replaced by 6 different well insulated copper wires each of radius 3 mm. The total resistance of the cable will now be equal to?

A short bar magnet with its north pole facing north forms a neutral point at P in the horizonatal plane. If the magnet is rotated by 90° in the horizontal plane, the net magnetic induction at P is (Horizontal component of earth's magnetic field = BH )

An equation of the plane passing through the points (3, 2, –1), (3, 4, 2) and (7, 0, 6) is 5x + 3y – 2z = l, where l is

The maximum peak to peak voltage of an AM wire is 24 mV and the minimum peak to peak voltage is 8 mV. The modulation factor is?

A drunken man takes a step forward with probability 0.4 and backwards with probability 0.6. Find the probability that at the end of eleven steps, he is one step away from the starting point?

A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is?

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats g. It is moving with speed v and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by:

A particle performs S.H.M. of amplitude A along a straight line. At two positions of the particle, the ratio of speeds is 1/2 and that of potential energy is 1/2 also. Then one position of them (distance from mean position) nearest to the extreme is :

If the frequency of a wave is increased by 25 %, then the change in its wavelength will be: (medium not changed)

A chain of uniform mass density is hanging as shown in figure.The total mass is M and the length is l.When chain is completely fall from the table then what will be the speed of chain?

A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor?

On moving a charge of 20 coulomb by 2 cm, 2 J of work is done, then the potential difference between the points is?

A particle of mass 10 gm is placed in a potential field given by

The frequency of oscillation in cycle/sec is ?

A particle is projected from ground with an initial velocity 20 m/sec making an angle 60° with horizontal. If R1 and R2 are radius of curvatures of the particle at point of projection and highest point respectively,find the value of R1/R2?

The average kinetic energy associated with one mole of gas is?

Why the HgO decomposes into its constituent elements on heating ?

Name of one chloride which is soluble in hot water as well as in excess of HCl.

If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to?

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would?

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency w. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is?

A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is?

A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere.

The time period of a satellite of earth is 5 hour. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become

The escape velocity of a body depends upon mass as?

A round uniform body of radius R, mass M and moment of inertia I rolls down (without slipping) an inclined plane making an angle q with the horizontal. Then its acceleration is

Angular momentum of the particle rotating with a central force is constant due to

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)?

The moment of inertia of a uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the center is?

A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?

Two protons of equal kinetic energies enter a region of uniform magnetic field. The

first proton enters normal to the field direction while the second enters at 30 degree to the field direction. Name the trajectories followed by them.

Describe briefly three factors which justify the need for modulation of audio frequency signals over long distances in communication?

The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45° with the vertical, the escape velocity will be

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will?