If \(\vec{A}\) and \(\vec{B}\) are two vectors satisfying the relation \(\vec{A} . \vec{B}=[\vec{A} \times \vec{B}]\). Then the value of \([\vec{A}-\vec{B}]\). will be :

A galvanometer having a resistance of \(20\,\Omega \) and \(30\, divisions\) on both sides has figure of merit \(0.005\, ampere /division\). The resistance that should be connected in series such that it can be used as a voltmeter upto \(15\, volt\) is ........... \(\Omega\)

The internal energy of a monoatomic gas is 3 nRT . One mole of helium is kept in a cylinder having internal cross section area of \(17 cm^2\) and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by \(4^{\circ} C\), then the piston will move ___________ cm.
(atmospheric pressure \(=10^5 Pa\) )

The root mean square velocity of molecules of gas is

A particle of mass ' \(m\) ' and charge ' \(q\) ' is fastened to one end ' \(A\) ' of a massless string having equilibrium length \(l\), whose other end is fixed at point ' \(O\) '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x -axis is

An electron with mass ' \(m\) ' with an initial velocity \((\mathrm{t}=0) \overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\mathrm{i}} \quad\left(\mathrm{v}_0 \gt 0\right)\) enters a magnetic field \(\vec{B}=B_0 \hat{j}\). If the initial de-Broglie wavelength at \(\mathrm{t}=0\) is \(\lambda_0\) then its value after time ' t ' would be :

A radiation is emitted by \(1000\, W\) bulb and it generates an electric field and magnetic field at \(P\), placed at a distance of \(2\, m\). The efficiency of the bulb is \(1.25 \%\). The value of peak electric field at \(P\) is \(x \times 10^{-1} \,V / m\). Value of \(x\) is. (Rounded-off to the nearest integer) [Take \(\varepsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1} m ^{-2}, c =3 \times 10^{8}\) \(ms ^{-1}\) ]

Two particles \(A, B\) are moving on two concentric circles of radii \(R_1\) and \(R_2\) with equal angular speed \(\omega \). At \(t = 0,\) their positions and direction of motion are shown in the figure The relative velocity \(\overrightarrow {{V_A}}  - \overrightarrow {{V_B}} \) at \(t = \frac{\pi }{{2\omega }}\) is given by

The de-Broglie wavelength associated with the electron in the \(n\, = 4\) level is

Two projectiles are projected at \(30^{\circ}\) and \(60^{\circ}\) with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is _______.

The radius of \(R\) of a nucleus of mass number \(A\) can be estimated by the formula \(R =\left(1.3 \times 10^{-15}\right) A ^{1 / 3}\, m .\) It follows that the mass density of a nucleus is of the order of \(\left( M _{\text {prot. }} \cong M _{\text {neut. }}=1.67 \times 10^{-27} kg \right)\)

A point charge of \(10^{-8} C\) is placed at origin. The work done in moving a point charge \(2 \mu C\) from point \(A (4,4,2) m\) to \(B (2,2,1) m\) is _________ J.