An electron of mass \(\mathrm{m}\) and magnitude of charge \(|e|\) initially at rest gets accelerated by a constant electric field \(\mathrm{E}\). The rate of change of de-Broglie wavelength of this electron at time \(t\) ignoring relativistic effects is 

The work function of a metal is 3 eV. The color of the visible light that is required to cause emission of photoelectrons is _______.

A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius \(\mathrm{R} / 2\) is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.

In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure

\(Sl\). \(No\).	\(R\, (\Omega )\)	\(l\, (cm)\)
\(1\).	\(1000\)	\(60\)
\(2\).	\(100\)	\(13\)
\(3\).	\(10\)	\(1.5\)
\(4\).	\(1\)	\(1.0\)

Which of the readings is inconsistent ?

Two thin convex lenses of focal length 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is :

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R.\) Assertion \(A :\) Moment of inertia of a circular disc of mass \('M'\) and radius \('R'\) about \(X, Y\) axes (passing through its plane) and \(Z-\)axis which is perpendicular to its plane were found to be \(I_{x}, I_{y}\) and \({I}_{z}\) respectively. The respective radii of gyration about all the three axes will be the same. Reason \(R\) : A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below :

A person moved from \(A\) to \(B\) on a circular path as shown in figure. If the distance travelled by him is \(60 \,m\), then the magnitude of displacement would be\(.....\,m\) (Given \(\left.\cos 135^{\circ}=-0.7\right)\)

An average force of \(125\,N\) is applied on a machine gun firing bullets each of mass \(10\,g\) at the speed of \(250\,m / s\) to keep it in position. The number of bullets fired per second by the machine gun 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 \(\left.\pi=\frac{22}{7}\right)\)

Let \([ {\varepsilon _0} ]\) denote the dimensional formula of the permittivity of vacuum. If \(M =\) mass, \(L=\) length, \(T =\) time and \(A=\) electric current, then: