When a metallic surface is illuminated with radiation of wavelength \(\lambda\) , the stopping potential is \(V.\) If the same surface is illuminated with radiation of wavelength \(2\lambda\), the stopping potential is \(\frac{V}{4}\). The threshold wavelength for the metallic surface is 

A uniform rod of length \(200 \,\mathrm{~cm}\) and mass \(500 \,\mathrm{~g}\) is balanced on a wedge placed at \(40\,cm\) mark. A mass of \(2\, \mathrm{~kg}\) is suspended from the rod at \(20\, \mathrm{~cm}\) and another unknown mass \('m'\) is suspended from the rod at \(160\, \mathrm{~cm}\) mark as shown in the figure. Find the value of \('m'\) such that the rod is in equilibrium. \(\left(\mathrm{g}=10 \,\mathrm{~m} / \mathrm{s}^{2}\right)\)

The magnetic field on the axis of a circular loop of radius \(100\,cm\) carrying current \(I=\sqrt{2}\,A\), at point \(1\,m\) away from the centre of the loop is given by

A rope is wound around a hollow cylinder of mass \(3\, kg\) and radius \(40\, cm.\) ........ \(rad/sec^2\) is the angular acceleration of the cylinder if the rope is pulled with a force of \(30\, N\,?\)

What happens to the mass number and atomic number of an element when it emits \(\gamma\)-radiation?

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): The potential ( \(V\) ) at any axial point, at \(2 \mathrm{~m}\) distance ( \(r\) ) from the centre of the dipole of dipole moment vector \(\vec{P}\) of magnitude, \(4 \times 10^{-6} \mathrm{C} \mathrm{m}\), is \(\pm 9 \times 10^3 \mathrm{~V}\). (Take \(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{Sl}\) units) Reason \(R\): \(V= \pm \frac{2 P}{4 \pi \epsilon_0 r^2}\), where \(r\) is the distance of any axial point, situated at \(2 \mathrm{~m}\) from the centre of the dipole. In the light of the above statements, choose the correct answer from the options given below:

Two charged spherical conductors of radius \(R_{1}\) and \(\mathrm{R}_{2}\) are connected by a wire. Then the ratio of surface charge densities of the spheres \(\left(\sigma_{1} / \sigma_{2}\right)\) is :

The reagents with which glucose does not react to give the corresponding tests/products are \(A\). Tollen's reagent  \(B\). Schiff's reagent \(C\). \(\mathrm{HCN}\) \(D\). \(\mathrm{NH}_2 \mathrm{OH}\) \(E\). \(\mathrm{NaHSO}_3\) Choose the correct options from the given below:

Identify the correct statement with regard to \(G _{1}\) phase \((Gap\,1)\) of interphase.

The production of gametes by the parents, formation of zygotes, the \(\mathrm{F}_{1}\) and \(\mathrm{F}_{2}\) plants, can be understood from a diagram called:

Conversion of milk to curd improves its nutritional value by increasing the amount of

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current \('I'\) along the same direction as shown in figure. Magnitude of force per unit length on the middle wire \('B'\) is given by 

The partial pressures (in \(\mathrm{mm}\, \mathrm{Hg}\) ) of oxygen \(\left(\mathrm{O}_{2}\right)\) and carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) at alveoli (the site of diffusion) are: