Two streams of photons, possessing energies to five and ten times the work function of metal are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectron emitted, in the two cases respectively, will be.

Read the following statements: \((A)\) Volume of the nucleus is directly proportional to the mass number. \((B)\) Volume of the nucleus is independent of mass number. \((C)\) Density of the nucleus is directly proportional to the mass number. \((D)\) Density of the nucleus is directly proportional to the cube root of the mass number. \((E)\) Density of the nucleus is independent of the mass number. Choose the correct option from the following options.

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm , at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :

A butterfly is flying with a velocity \(4 \sqrt{2} \,{m} / {s}\) in North-East direction. Wind is slowly blowing at \(1\) \({m} / {s}\) from North to South. The resultant displacement of the butterfly in \(3\, seconds\) is \(....\,{m}.\)

If the electric potential at any point \((x, y, z) \,m\) in space is given by \(V =3 x ^{2}\) volt. The electric field at the point \((1,0,3) \,m\) will be ............

A parallel plate capacitor has plate of length \('l',\) width \('w'\) and separation of plates is \('d'.\) It is connected to a battery of emf \(V\). A dielectric slab of the same thickness '\(d\)' and of dielectric constant \(k =4\) is being inserted between the plates of the capacitor. At what length of the slab inside plates, will be energy stored in the capacitor be two times the initial energy stored\(?\)

A particle executes simple harmonic motion between \(x =- A\) and \(x =+ A\). If time taken by particle to go from \(x=0\) to \(\frac{A}{2}\) is \(2 s\); then time taken by particle in going from \(x =\frac{ A }{2}\) to \(A\) is \(.........\,s\)

Visible light of wavelength \(6000 \times 10^{-8}\; \mathrm{cm}\) falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at \(60^{\circ}\) from the central maximum. If the first minimum is produced at \(\theta_{1},\) then \(\theta_{1}\) is close to.....\(^o\)

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength \(980\,\mathop A\limits^o \). The radius of the atom in the excited state, in  terms of Bohr radius \(a_0,\) will be \((hc\,=\,12500\,eV-\mathop A\limits^o)\)

Two coils have mutual inductance \(0.002 \ \mathrm{H}\). The current changes in the first coil according to the relation \(\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}\), where \(\mathrm{i}_0=5 \mathrm{~A}\) and \(\omega=50 \pi\) \(\mathrm{rad} / \mathrm{s}\). The maximum value of \(\mathrm{emf}\) in the second coil is \(\frac{\pi}{\alpha} \mathrm{V}\). The value of \(\alpha\) is_______.

A regular hexagon is formed by six wires each of resistance \(r \Omega\) and the corners are joined to centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be

A uniform thin bar of mass \(6 \,kg\) and length \(2.4\, meter\) is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is ...... \(\times \,10^{-1} \,kg m ^{2}\)