The magnetic field inside a 200 turns solenoid of radius 10 cm is \(2.9 \times 10^{-4} \mathrm{Tesla}\). If the solenoid carries a current of 0.29 A , then the length of the solenoid is ________ \(\pi \mathrm{cm}\).

A force \(\overrightarrow{ F }=(2+3 x) \hat{ i }\) acts on a particle in the \(x\) direction where \(F\) is in newton and \(x\) is in meter. The work done by this force during a displacement from \(x =0\) to \(x =4\,m\), is .......\(J\).

In the experiment of calibration of voltmeter, a standard cell of \(e.m.f\,\,1.1\,volt\) is balanced against \(440\,cm\) of potential wire. The potential difference across the ends of resistance is found to balance against \(220\,cm\) of the wire. The corresponding reading of voltmeter is \(0.5\,volt.\) The error in the reading of volmeter will be .................. \(volt\)

Given below are two statements : Statement \(I\) : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. Statement \(II\) : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube. In the light of the above statements, choose the correct answer from the options given below :

Imagine that the electron in a hydrogen atom is replaced by a muon \((\mu) .\) The mass of muon particle is \(207\) times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be ............. \(eV\)

Two plane mirrors \({M}_{1}\) and \({M}_{2}\) are at right angle to each other shown. A point source \('P'\) is placed at \('a'\) and \('2a'\) meter away from \({M}_{1}\) and \({M}_{2}\) respectively. The longest distance between the images thus formed is : (Take \(\sqrt{5}=2.3\) )

The work functions of Aluminium and Gold are \(4.1\,eV\) and \(5.1\,eV\) respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is \(.......\)

A person of \(80\, kg\) mass is standing on the rim of a circular platform of mass \(200\, kg\) rotating about its axis as \(5\) revolutions per minute \((rpm).\) The person now starts moving towards the centre of the platform. What will be the rotational speed (in \(rpm\) ) of the platform when the person reaches its centre \(......rpm\)

Given below are two statements Statement \(-I\) : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive. Statement \(-II\) : An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero. Choose the correct answer from the options given below 

Two circular coils \(P\) and \(Q\)of \(100\) turns each have same radius of \(\pi \mathrm{cm}\). The currents in \(\mathrm{P}\) and \(\mathrm{R}\) are \(1 \mathrm{~A}\) and \(2 \mathrm{~A}\) respectively. \(\mathrm{P}\) and \(\mathrm{Q}\) are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is \(\sqrt{\mathrm{x}} \mathrm{mT}\), where \(\mathrm{x}=\) _______. \(\left[\text { Use } \mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]\)

The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as \(R_1\) has the colour code (Orange, Red, Brown). The resistors \(R_2\) and \(R_4\) are \(80\, \Omega \) and \(40\,\Omega \), respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as \(R_3\) would be

A uniform rod \(A B\) of mass \(2 \mathrm{~kg}\) and Length \(30 \mathrm{~cm}\) at rest on a smooth horizontal surface. An impulse of force \(0.2\  \mathrm{Ns}\) is applied to end \(B.\) The time taken by the rod to turn through at right angles will be \(\frac{\pi}{\mathrm{x}}\ \mathrm{s}\), where  X = _______.