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 :

A triangular shaped wire carrying \(10 A\) current is placed in a uniform magnetic field of \(0.5\,T\), as shown in figure. The magnetic force on segment \(CD\) is \(....N\) \((\) Given \(BC = CD = BD =5\,cm )\).

Let \(\eta_{1}\) is the efficiency of an engine at \(T _{1}=447^{\circ}\,C\) and \(T _{2}=147^{\circ}\,C\) while \(\eta_{2}\) is the efficiency at \(T _{1}=947^{\circ}\,C\) and \(T _{2}=47^{\circ}\,C\). The ratio \(\frac{\eta_{1}}{\eta_{2}}\) will be.

From the given data, the amount of energy required to break the nucleus of aluminium \({ }_{13}^{27} {Al}\) is \(....\,x \times 10^{-3} {J}\) Mass of neutron \(=1.00866 \,{u}\) Mass of proton \(=1.00726 \,{u}\) Mass of aluminium nucleus \(=27.18846\, {u}\) (Assume \(1\,u\) corresponds to \(x\,J\) of energy) (Round off to the nearest integer)

A ring is hung on a nail. It can oscillate, without slipping or sliding \((i)\) in its plane with a time period \(T_{1}\) and, \((ii)\) back and forth in a direction perpendicular to its plane, with a period \(T _{2}\). the ratio \(\frac{ T _{1}}{ T _{2}}\) will be 

A car moving with a speed of \(54\) km/h takes a turn of radius \(20\) m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take \(g=10\) m/s\(^2\))

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 volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of \(7 \times 10^6 \mathrm{~Pa}\), would be ____ \(\mathrm{mm}^3\).
(Given bulk modulus of copper \(=1.4 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\) )

An infinitely long straight wire carrying current \(I,\) one side opened rectangular loop and a conductor \(C\) with a sliding connector are located in the same plane, as shown in the figure. The connector has length \(l\) and resistance \(R\). It slides to the right with a velocity \(V.\) The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation \(r,\) between the connector and the straight wire is

A gas balloon is going up with a constant velocity of \(10\) m/s. When this balloon reached a height of \(75\) m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ________ m. (Take \(g=10\) m/s\(^2\))

\(B _{ X }\) and \(B _{ Y }\) are the magnetic field at the centre of two coils of two coils \(X\) and \(Y\) respectively, each carrying equal current. If coil \(X\) has \(200\) turns and \(20 cm\) radius and coil \(Y\) has \(400\) turns and \(20 cm\) radius, the ratio of \(B _{ X }\) and \(B _{ Y }\) is

A big drop is formed by coalescing \(1000\) small identical drops of water. If \(E_1\) be the total surface energy of \(1000\) small drops of water and \(E_2\) be the surface energy of single big drop of water, the \(E_1\) : \(\mathrm{E}_2\) is \(\mathrm{x}: 1\) where \(x\) = _____.

Two ions having same mass have charges in the ratio \(1: 2\). They are projected normally in a uniform magnetic field with their speeds in the ratio \(2: 3\). The ratio of the radii of their circular trajectories is -