A guitar string of length \(90\,cm\) vibrates with a fundamental frequency of \(120\,Hz.\) The length of the string producing a fundamental frequency of \(180\,Hz\) will be \(...........cm\).

Monochromatic light of frequency \(6 \times 10^{14} \mathrm{~Hz}\) is produced by a laser. The power emitted is \(2 \times 10^{-3} \mathrm{~W}\). How many photons per second on an average, are emitted by the source? (Given \(\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}\) )

In a screw gauge, \(5\) complete rotations of the screw cause it to move a linear distance of \(0.25\, cm\). There are \(100\) circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of \(4\) main scale divisions and \(30\) circular scale divisions . Assuming negligible zero error, the thickness of the wire is

A transverse wave on a string is described by \(y = 3\sin(36t + 0.018x + \pi/4)\), where \(x, y\) are in cm and \(t\) in seconds. The least distance between the two successive crests in the wave is _____ cm. (Nearest integer)
(\(\pi = 3.14\))

\(c_P\) and \(c_V\) are specific heats at constant pressure and constant volume respectively. It is observed that \(c_P - c_V = a\) for hydrogen gas \(c_P - c_V = b\) for nitrogen gas The correct relation between \(a\) and \(b\) is

In a reflecting telescope, a secondary mirror is used to:

A series \(LR\) circuit is connected to an ac source of frequency \(\omega \) and the inductive reactance is equal to \(2R\). A capacitance of capacitive reactance equal to \(R\) is added in series with \(L\) and \(R\). The ratio of the new power factor to the old one is

Starting with the same initial conditions, an ideal gas expands from volume \(V_{1}\) to \(V_{2}\) in three different ways. The work done by the gas is \(W_{1}\) if the process is purely isothermal. \(W _{2}\). if the process is purely adiabatic and \(W _{3}\) if the process is purely isobaric. Then, choose the coned option

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
\(E_y=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} t\right) V / m\)
(where \(x, t\) and other values have S.I. units). The dielectric constant of the medium is __________ .
(speed of light in free space is \(3 \times 10^8 m / s\) )

A radioactive nucleus can decay by two different processes. Half-life for the first process is \(3.0\, hours\) while it is \(4.5\, hours\) for the second process. The effective half- life of the nucleus will be \(.........\,hours.\)

A velocity selector consists of electric field \(\overrightarrow{ E }= E \hat{ k }\) and magnetic field \(\overrightarrow{ B }= B \hat{ j }\) with \(B =12 mT\). The value \(E\) required for an electron of energy \(728 eV\) moving along the positive \(x\)-axis to pass undeflected is: (Given, , ass of electron \(=9.1 \times 10^{-31} kg\) )

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If \(r_{d}\) and \(r_{p}\) are the radii of their circular paths respectively, then the ratio \(\frac{r_{d}}{r_{p}}\) will be \(\sqrt{ x }: 1\) where \(x\) is ..........