A particle of mass \(20\,g\) is released with an initial velocity \(5\,m/s\) along the curve from the point \(A,\) as shown in the figure. The point \(A\) is at height \(h\) from point \(B.\) The particle slides along the frictionless surface. When the particle reaches point \(B,\) its angular momentum about \(O\) will be ......... \(kg - m^2/s\). [Take \(g = 10\,m/s^2\) ]

You are asked to design a shaving mirror assuming that a person keeps it \(10\,cm\) from his face and views the magnified image of the face at the closest comfortable distance of \(25\,cm.\) The radius of curvature of the mirror would then be.....\(cm\)

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed: \(A.\) By changing the magnitude of the magnetic field within the coil. \(B.\) By changing the area of coil within the magnetic field. \(C.\) By changing the angle between the direction of magnetic field and the plane of the coil. \(D.\) By reversing the magnetic field direction abruptly without changing its magnitude. Choose the most appropriate answer from the options given below

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of \(\lambda\). An alpha particle having certain kinetic energy has the same de-Brogle wavelength \(\lambda\). The ratio of kinetic energy of proton and that of alpha particle is:

A Carnot engine take \(5000 \,k\,cal\) of heat from a reservoir at \(727\,^{\circ}C\) and gives heat to a \(\operatorname{sink}\) at \(127\,^{\circ}C\). The work done by the engine is \(.......... \times 10^{6}\,J\)

A uniform sphere of mass \(500\; g\) rolls without slipping on a plane horizontal surface with its centre moving at a speed of \(5.00\; \mathrm{cm} / \mathrm{s}\). Its kinetic energy is

A system of two blocks of masses \(m =2 \; kg\) and \(M=8 \; kg\) is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is \(0.5\). The maximum horizontal force \(F\) that can be applied to the block of mass \(M\) so that the blocks move together will be \(\dots \; N\)

A plano convex lens of refractive index \({\mu _1}\) and focal length \(f_1\) is kept in contact with another plano concave lens of refractive index \({\mu _2}\) and focal length \(f_2\). If the radius of curvature of their spherical faces is \(R\) each and \(f_1 = 2f_2\), then \({\mu _1}\) and \({\mu _2}\) are related as

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are :- \(A.\) Real \(B.\) Erect \(C.\) Smaller in size then object \(D.\) Laterally inverted Choose the most appropriate answer from the options given below :

Regarding self-inductance:
A. The self-inductance of the coil depends on its geometry.
B. Self-inductance does not depend on the permeability of the medium.
C. Self-induced e.m.f. opposes any change in the current in a circuit.
D. Self-inductance is electromagnetic analogue of mass in mechanics.
E. Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:

The surface of water in a water tank of cross section area \(750\,cm ^2\) on the top of a house is \(h m\). above the tap level. The speed of water coming out through the tap of cross section area \(500\,mm ^2\) is \(30\,cm / s\). At that instant, \(\frac{d h}{d t}\) is \(x \times 10^{-3} m / s\). The value of \(x\) will be \(.............\).