In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength . If wavelength of red light is \(6600\,\mathop A\limits^o\) , then wavelength of first maximum will be.....\(\mathop A\limits^o \)

A thin uniform rod of length \(2\,m\). cross sectional area ' \(A\) ' and density ' \(d\) ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity \(\omega\). If value of \(\omega\) in terms of its rotational kinetic energy \(E\) is \(\sqrt{\frac{\alpha E}{ Ad }}\) then the value of \(\alpha\) is \(...........\)

The root mean square speed of molecules of a given mass of a gas at \(27^{\circ} C\) and \(1\) atmosphere pressure is \(200\, ms ^{-1}\). The root mean square speed of molecules of the gas at \(127^{\circ} C\) and \(2\) atmosphere pressure is \(\frac{ x }{\sqrt{3}}\, ms ^{-1} .\) The value of \(x\) will be ......\(ms ^{-1} .\)

A metal exposed to light of wavelength \(800\,nm\) and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength \(500\, nm\) is used. The work function of the metal is \(...eV\) (Take \(hc =1230 \,eV - nm\) ).

A network of four resistances is connected to \(9\,V\) battery, as shown in figure. The magnitude of voltage difference between the points \(A\) and \(B\) is .......... \(V.\)

If one mole of an ideal gas at \(\left( P _{1}, V _{1}\right)\) is allowed to expand reversibly and isothermally (\(A\) to \(B\) ) its pressure is reduced to one-half of the original pressure (see \(figure\)). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value \(( B \rightarrow C ) .\) Then it is restored to its initial state by a reversible adiabatic compression (\(C\) to \(A\)). The net workdone by the gas is equal to  ...... .

A parallel plate capacitor was made with two rectangular plates, each with a length of \(l=3 \mathrm{~cm}\) and breath of \(\mathrm{b}=1 \mathrm{~cm}\). The distance between the plates is \(3 \mu \mathrm{~m}\). Out of the following, which are the ways to increase the capacitance by a factor of 10 ?
A. \(l=30 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
B. \(l=3 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=30 \mu \mathrm{~m}\)
C. \(l=6 \mathrm{~cm}, \mathrm{~b}=5 \mathrm{~cm}, \mathrm{~d}=3 \mu \mathrm{~m}\)
D. \(l=1 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=10 \mu \mathrm{~m}\)
E. \(l=5 \mathrm{~cm}, \mathrm{~b}=2 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
Choose the correct answer from the options given below:

The temperature of a gas is \(-78^{\circ} \mathrm{C}\) and the average translational kinetic energy of its molecules is \(\mathrm{K}\). The temperature at which the average translational kinetic energy of the molecules of the same gas becomes \(2 \mathrm{~K}\) is _______.

Figure shows elliptical path \(abcd\) of a planet around the sun \(S\) such that the area of triangle \(csa\) is \(\frac {1}{4}\) the area of the ellipse. (See figure) With \(db\)  as the semimajor axis, and  \(ca\) as the semiminor axis. If \(t_1\)  is the time taken for planet to go over path \(abc\) and \(t_2\) for path taken over \(cda\) then

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 _________