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 \(\left.\cos 135^{\circ}=-0.7\right)\)

The rms value of conduction current in a parallel plate capacitor is \(6.9\,\mu\,A\). The capacity of this capacitor, if it is connected to \(230 V\) ac supply with an angular frequency of \(600\,rad / s\), will be \(....\,pF\)

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to \(\operatorname{arc} \mathrm{AB}\) to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The density of the copper \(\left({ }_{29}^{64} \mathrm{Cu}\right)\) nucleus is greater than that of the carbon \(\left({ }_6^{12} \mathrm{C}\right)\) nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to \(\mathrm{A}^{1 / 3}\).
In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) An electron microscope can achieve better resolving power than an optical microscope. Reason \(R\) : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light. In the light of the above statements, choose the correct answer from the options given below

A thin uniform bar of length \(L\) and mass \(8\,m\) lies on a smooth horizontal table. Two point masses \(m\) and \(2\,m\) moving in the same horizontal plane from opposite sides of the bar with speeds \(2v\) and \(v\) respectively. The masses stick to the bar after collision at a distance \(\frac{L}{3}\) and \(\frac{L}{6}\) respectively from the centre of the bar. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be

In a Young's double slit experiment, the intensity at a point is \(\left(\frac{1}{4}\right)^{\text {th }}\) of the maximum intensity, the minimum distance of the point from the central maximum is _______ \(\mu \mathrm{m}\). (Given : \(\lambda=600 \mathrm{~nm}, d=1.0 \mathrm{~mm}, \mathrm{D}=1.0 \mathrm{~m}\) )

A light beam is described by \(E=800 \sin \omega\left(t-\frac{x}{c}\right)\) An electron is allowed to move normal to the propagation of light beam with a speed of \(3 \times 10^{7}\;{ms}^{-1}\). What is the maximum magnetic force exerted on the electron ?