The reading in the ideal voltmeter \((V)\) shown in the given circuit diagram is _______.

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure What is the value of current at \(t = 4\,s\) ? ............... \(\mu  A\)

Position of an ant ( \(\mathrm{S}\) in metres) moving in \(\mathrm{Y}-\mathrm{Z}\) plane is given by \(S=2 t^2 \hat{j}+5 \hat{k}\) (where \(t\) is in second). The magnitude and direction of velocity of the ant at \(t=1 \mathrm{~s}\) will be :

A \(1 \mathrm{~kg}\) mass is suspended from the ceiling by a rope of length \(4 \mathrm{~m}\). A horizontal force ' \(F\) ' is applied at the mid point of the rope so that the rope makes an angle of \(45^{\circ}\) with respect to the vertical axis as shown in figure. The magnitude of \(F\) is _______.

In the circuit shown in the figure, the ratio of the quality factor and the band width is \(.............\) s.

An object is kept at rest at a distance of 3 R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :
(Assume \(\mathrm{M}=\) mass of earth, \(\mathrm{G}=\) Universal gravitational constant)

As shown in figure, a \(70\,kg\) garden roller is pushed with a force of \(\overrightarrow{ F }=200\,N\) at an angle of \(30^{\circ}\) with horizontal. The normal reaction on the roller is \(.......\,N\) \(\left(\right.\) Given \(\left.g =10\,m s ^{-2}\right)\)

An ideal battery of \(4\, V\) and resistance \(R\) are connected in series in the primary circuit of a potentiometer of length \(1\, m\) and resistance \(5\,\Omega \) . The value of \(R\), to give a difference of \(5\, mV\) across \(10\, cm\) of potentiometer wire, is: ................ \(\Omega\)

During an adiabatic compression, \(830\, J\) of work is done on \(2\, moles\) of a diatomic ideal gas to reduce its volume by \(50\%\). The change in its temperahture is nearly..... \(K\) \((R\, = 8.3\, J\,K^{-1}\, mol^{-1} )\)

The least count of the main scale of a vernier callipers is \(1\, mm\). Its vernier scale is divided into \(10\) divisions and coincide with \(9\) divisions of the main scale. When jaws are touching each other, the \(7\) th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between \(3.1\, cm\) and \(3.2\, cm\) and \(4^{th}\) \(VSD\) coincides with a main scale division.The length of the cylinder is \(.....cm\) (\(VSD\) is vernier scale division)

Two carnot engines \(A\) and \(B\) operate in series such that engine \(A\) absorbs heat at \(T_{1}\) and rejects heat to a sink at temperature \(T\). Engine \(B\) absorbs half of the heat rejected by engine \(A\) and rejects heat to the sink at \({T}_{3}\). When workdone in both the cases is equal, the value of \({T}\) is 

A satellite of mass \(\frac{M}{2}\) is revolving around earth in a circular orbit at a height of \(\frac{R}{3}\) from earth surface. The angular momentum of the satellite is \(M \sqrt{\frac{G M R}{x}}\). The value of \(x\) is ______ , where \(M\) and \(R\) are the mass and radius of earth, respectively. ( G is the gravitational constant)

A monochromatic light of frequency \(5 \times 10^{14} \mathrm{~Hz}\) travelling through air, is incident on a medium of refractive index ' 2 '. Wavelength of the refracted light will be :