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A particle of mass 4 m which is at rest explodes into three fragments, two of the fragments each of mass m are found to move each with a speed v making an angle 90 with each other. The total energy relased in this explosion is -

A slow moving electron collides elastically with a hydrogen atom at rest. The initial and final motions are along the same straight line. What fraction of electron's kinetic energy is transferred to the hydrogen atom? The mass of hydrogen atom is 1850 times the mass of electron?

If the circles x^{2} + y^{2} + 2ax + cy + a = 0 and x^{2} + y^{2} – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x+by – a = 0 passes through P and Q for

If a vertex of a triangle is (1, 1) and the midpoints of two sides through this vertex are (–1, 2) and (3, 2), then what will be the centroid of the triangle.

If non zero numbers a, b, c are in H.P., then the straight line always passes through a fixed point. That point is

The line parallel to thexaxis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx – 2ay – 3a = 0, where (a, b) (0, 0) is

Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of midpoint of PQ is

The mass of a rocket is 500 kg and the relative velocity of the gases ejecting from it is 250 m/s with respect to the rocket. The rate of burning of the fuel in order to give the rocket an initial acceleration 20 m/s2 in the vertically upward direction (g = 10 m/s2), will be

A 20 g bullet pierces through a plate of mass m1 = 1 kg and then comes to rest inside a second plate of mass m2 = 2.98 kg. It is found that the two plates, initially at rest, now move with equal velocities. The percentage loss in the initial velocity of bullet when it is between m1 and m2. (Neglect any loss of material of the bodies, due to action of bullet.) will be

If the straight lines x = 1 + s, y = –3 z = 1 + and x = t/2, y = 1 + t, z = 2 – t, with parameters s and t respectively, are coplanar, then equals

A bullet of mass 10g travelling horizontally with a velocity of 300 m/s strikes a block of wood of mass 290 g which rests on a rough horizontal floor. After impact the block and the bullet move together and come to rest when the block has travelled a distance of 15 m. The coefficient of friction between the block and the floor will be - (Duration of impact is very short)

From a tower of height H, a particle is thrown vertically upwards with a speed U. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is :

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement :

A block is suspended by an ideal spring constant K. If the block is pulled down by constant force F and if maximum displacement of block from it’s initial position of rest is z, then

Centre of mass - Centre of mass - A circular disc of radius 20cm is cut from one edge of larger disc of radius 50cm the shift in centre of mass

Let a relation be defined on a set of functions defined on R R such that R = {(f, g)|f – g is an even function} then, relation R is?

The number of solutions of sin

The electron of hydrogen atom was excited from ground state to a higher orbit. During de-excitation of the electron, photons of six different wavelengths were emitted. If each photon forms a spectral line, how many spectral line will be visible to naked eye?

a fluid containercontaining a liquid of density p is accelerating a towards east if angle if inclination alpha of free surface is 37 deg then value of a will be

fluid - A drop of liquid of diameter 2.8 mm beaks up into 125 identical drops. The change in energy is nearly (S.T. of liquid = 75 × 10-3 N/m)

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is?

Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is?

A college offers 6 courses in the morning and 4 in the evening. The possible number of choices with the student if he wants to study one course in the morning and one in the evening is?

A college offers 6 courses in the morning and 4 in the evening. The number of ways a student can select exactly one course, either in the morning or in the evening?

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 ?

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