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 \(hc =1230 \,eV - nm\) ).

When \(5\ V\) potential difference is applied across a wire of length \(0.1\ m\), the drift speed of electrons is \(2.5 \times 10^{-4}\) \(ms^{-1}\) . If the electron density in the wire is \(8 \times 10^{28}\) \(m^{-3}\) the resistivity of the material is close to

The maximum velocity of the photoelectrons emitted from the surface is \(v\) when light of frequency \(n\) falls on a metal surface. If the incident frequency is increased to \(3n\) , the maximum velocity of the ejected photoelectrons will be 

A convex lens is put \(10\, cm\) from a light source and it makes a sharp image on a screen, kept \(10\, cm\) from the lens. Now a glass block (refractive index \(1.5\)) of \(1.5\, cm\) thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance \(d\). Then \(d\) is

A battery of \(6\,V\) is connected to the circuit as shown below. The current I drawn from the battery is:

A charge \(q\)  is spread uniformly over an insulated loop of radius \(r\) . If it is rotated with an angular velocity \(\omega \) with respect to normal axis then the magnetic moment of the loop is

An inductor of inductance \(2\,\mu\,H\) is connected in series with a resistance, a variable capacitor and an \(AC\) source of frequency \(7\,kHz\). The value of capacitance for which maximum current is drawn into the circuit is \(\frac{1}{x} F\), where the value of \(x\) is \(.........\). \(\left(\right.\) Take \(\left.\pi=\frac{22}{7}\right)\)

lf \(2 + 3i\) is one of the roots of the equation \(2x^3 -9x^2 + kx- 13 = 0,\) \(k \in R,\) then the real root of this equation

In a survey of \(220\) students of a higher secondary school, it was found that at least \(125\) and at most \(130\) students studied Mathematics; at least \(85\) and at most \(95\) studied Physics; at least \(75\) and at most \(90\) studied Chemistry; \(30\) studied both Physics and Chemistry; \(50\) studied both Chemistry and Mathematics; \(40\) studied both Mathematics and Physics and \(10\) studied none of these subjects. Let \(\mathrm{m}\) and \(\mathrm{n}\) respectively be the least and the most number of students who studied all the three subjects. Then \(\mathrm{m}+\mathrm{n}\) is equal to ...........

Let \( cos(\alpha+\beta)=-\frac{1}{10} \) and \( sin(\alpha-\beta)=\frac{3}{8} \) where \( 0<\alpha<\frac{\pi}{3} \) and \( 0<\beta<\frac{\pi}{4} \). If \( tan~2\alpha=\frac{3(1-r\sqrt{5})}{\sqrt{11}(s+\sqrt{5})}, r, s\in\mathbb{N} \), then \( r+s \) is equal to ___ .

For \(LED's\)  to emit light in visible region of electromagnetic light, it should have energy band gap in the range of

In the given figure, a battery of emf \(E\) is connnected across a conductor \(P Q\) of length \('Y'\) and different area of cross-sections having radii \(r_{1}\) and \(r_{2}\left(r_{2}\,<\,r_{1}\right)\). Choose the correct option as one moves from \(P\) to \(Q\) :

If the shortest distance between the lines \(\frac{x-4}{1}=\frac{y+1}{2}=\frac{z}{-3}\) and \(\frac{x-\lambda}{2}=\frac{y+1}{4}=\frac{z-2}{-5}\) is \(\frac{6}{\sqrt{5}}\), then the sum of all possible values of \(\lambda\) is :