A hydraulic automobile lift is designed to lift vehicles of mass \(5000\,kg\). The area of cross section of the cylinder carrying the load is \(250\,cm ^2\). The maximum pressure the smaller piston would have to bear is [Assume \(g=10\,m / s ^2\)]

A coil is placed in a magnetic field \(\overrightarrow{{B}}\) as shown below: A current is induced in the coil because \(\overrightarrow{{B}}\) is:

A telescope has an objective lens of focal length \(150\,\,cm\) and an eyepiece of focal length \(5 \,\,cm.\) If a \(50\,\,m\) tall tower at a distance of \(1\,\,km\) is observed through this telescope in normal setting, the angle formed by the image of the tower is \(\theta \), then \(\theta \) is close to.....\(^o\)

A rectangular coil (Dimension \(5\,cm\times 2\,cm\) ) with \(100\,turns,\) carrying a current of \(3\,A\) in the clock-wise direction, is kept centered at the origin and in the \(X-Z\) plane. A magnetic field of \(1\,T\) is applied along \(X-\) axis. If the coil is tilted through \(45^o\) about \(Z-\) axis, then the torque on the coil is.....\(Nm\)

For a body executing \(S.H.M. :\) \((a)\) Potential energy is always equal to its \(K.E.\) \((b)\) Average potential and kinetic energy over any given time interval are always equal. \((c)\) Sum of the kinetic and potential energy at any point of time is constant. \((d)\) Average \(K.E.\) in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below:

Interference pattern is observed at \('P'\) due to superimposition of two rays coming out from a source \('S'\) as shown in the figure. The value of \('I'\) for which maxima is obtained at \('P'\) is: ( \(R\) is perfect reflecting surface)

Let \(l, r, c\) and \(v\) represent inductance, resistance, capacitance and voltage, respectively. The dimension of \(\frac {l}{rcv}\) in \(SI\,units\) will be

Given below are two statements Statement \(I:\) The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination. Statement \(II\) : The resistivity of the material is independent of temperature. In the light of the above statements, choose the correct answer from the options given below

The sum of two forces \(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) is \(\overrightarrow{\mathrm{R}}\) such that \(|\overrightarrow{\mathrm{R}}|=|\overrightarrow{\mathrm{P}}| .\) The angle \(\theta\) (in degrees) that the resultant of \(2 \overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) will make with \(\overrightarrow{\mathrm{Q}}\) is

Match List - I with List - II.

List - I	List - II
(A) Permeability of free space	(I) \(\left[\mathrm{M} \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)
(B) Magnetic field	(II) \(\left[\mathrm{M} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]\)
(C) Magnetic moment	(III) \(\left[\mathrm{M} \mathrm{~L} \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]\)
(D) Torsional constant	(IV) \(\left[\mathrm{L}^2 \mathrm{~A}\right]\)

Choose\(\text{ }\)the\(\text{ }\)correct\(\text{ }\)answer\(\text{ }\)from\(\text{ }\)the\(\text{ }\)options\(\text{ }\)given\(\text{ }\)below\(\text{ }\):

The current in a conductor is expressed as \(I=3 t^2+4 t^3\), where \(I\) is in Ampere and \(t\) is in second. The amount of electric charge that flows through a section of the conductor during \(t=1\) s to \(t=2 \mathrm{~s}\) is _______ \(\mathrm{C}\).

The \(Q\)-value of a nuclear reaction and kinetic energy of the projectile particle, \(K _{ p }\) are related as