A small ball thrown with an initial velocity μ directed at an angle θ = 37° above the horizontal collides inelastically (e = 1/4) with a vertical massive wall moving with a uniform horizontal velocity u/5 towards ball. After collision with the wall, the ball returns to the point from where it was thrown. Neglect friction between ball and wall. The time t from beginning of motion of the ball till the moment of its impact with the wall is (tan37° = 3/4)

A cube of side l and mass M is placed on rough horizontal surface and the friction is sufficient so that it will not move, if a constant force F = Mg is applied horizontally l/4 above the surface. Then the torque due to normal force about center of the cube is equal to

A particle of charge q and mass m is projected with a velocity v₀ towards a circular region having uniform magnetic field B perpendicular and into the plane of paper from point P as shown in the figure. R is the radius and O is the centre of the circular region. If the line OP makes an angle θ with the direction of v₀ then the value of v₀ so that particle passes through O is

A ray of light from a liquid ( μ = √3 ) is incident on a system of two right angled prism of refractive indices √3 and √2 as shown. The ray suffers zero deviation when emerges into air from CD. The angle of incidence i is

The formula of the following chain silicate (pyroxene) can be represented as

 is a first order reaction. If A is strong mono protic acid and B is strong diprotic acid and reaction kinetic is studied by using a standard solution of NaOH required toneutralise reaction mixture at different instants of time. When initially we had taken sameconcentration of A in each case.Now it was observer that volume required after 971 sec was double that required initially, then thehalf life of reaction is:

Reduction potentials of some ions are given below. Arrange them in decreasing order of oxidizing power.

Area of the region bounded by the curve y=1/x + 1 , the tangent at P (2, 3/2) and the line x = 1 is