The activity of a radioactive material is \(6.4 \times 10^{-4}\) curie. Its half life is \(5\; days\). The activity will become \(5 \times 10^{-6}\) curie after \(.......day\)

\(1\) mole of rigid diatomic gas performs a work of \(Q / 5\) when heat \(Q\) is supplied to it. The molar heat capacity of the gas during this transformation is \(\frac{ x R }{8},\) The value of \(x\) is \(\ldots \ldots \ldots .\) \([ K =\) universal gas constant \(]\)

For designing a voltmeter of range \(50\,V\) and an ammeter of range \(10\,mA\) using a galvanometer which has a coil of resistance \(54\,\Omega\) showing a full scale deflection for \(1\,mA\) as in figure. \((A)\) for voltmeter \(R \approx 50\,k\Omega\) \((B)\) for ammeter \(r \approx 0.2\,\Omega\) \((C)\) for ammeter \(r \approx 6\,\Omega\) \((D)\) for voltmeter \(R \approx 5\,k \Omega\) \((E)\) for voltmeter \(R \approx 500 \Omega\) Choose the correct answer from the options given below

The electric current through a wire varies with time as \(I=I_0+\beta t\). where \(I_0=20 \mathrm{~A}\) and \(\beta=3 \mathrm{~A} / \mathrm{s}\). The amount of electric charge crossed through a section of the wire in \(20 \mathrm{~s}\) is :

The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by \({E}=20 \cos \left(2 \times 10^{10} {t}-200 {x}\right) \,{V} / {m} .\) The dielectric constant of the medium is equal to : (Take \(\mu_{{r}}=1\) )

A particle of mass \(9.1 \times 10^{-31}\, {kg}\) travels in a medium with a speed of \(10^{6}\, {m} / {s}\) and a photon of a radiation of linear momentum \(10^{-27} \,{kg}\, {m} / {s}\) travels in vacuum. The wavelength of photon is \(....\) times the wavelength of the particle.

The exit surface of a prism with refractive index \(n\) is coated with a material having refractive index \(\frac{ n }{2}\). When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle is _________

Eight equal drops of water are falling through air with a steady speed of \(10\,cm / s\). If the drops coalesce, the new velocity is \(.........\,cm/s\)