A closed organ pipe has a fundamental frequency of \(1.5\, kHz\). The number of overtones that can be distinctly heard by a person with this organ pipe will be : (Assume that the highest frequency a person can hear is \(20,000\, Hz\))

A small bar magnet placed with its axis at \(30^{\circ}\) with an external field of \(0.06\, T\) experiences a torque of \(0.018\, Nm\). The minimum work required to rotate it from its stable to unstable equilibrium position is

A plane electromagnetic wave of frequency \(35\  \mathrm{MHz}\) travels in free space along the \(\mathrm{X}\)-direction. At a particular point (in space and time) \(\overrightarrow{\mathrm{E}}=9.6\  \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}\). The value of magnetic field at this point is _______.

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion A : The nuclear density of nuclides \({ }_5^{10} B ,{ }_3^6 Li ,{ }_{26}^{56} Fe ,{ }_{10}^{20} Ne\) and \({ }_{83}^{209} Bi\) can be arranged as \(\rho_{ Bi }^{ N }>\rho_{ Fe }^{ N }>\rho_{ Ne }^{ N }>\rho_{ B }^{ N }>\rho_{ Li }^{ N }\). Reason \(R\) : The radius \(R\) of nucleus is related to its mass number \(A\) as \(R=R_0 A^{1 / 3}\), where \(R_0\) is a constant. In the light of the above statement, choose the correct answer from the options given below :

The average kinetic energy of a molecule of the gas is

\(512\) identical drops of mercury are charged to a potential of \(2\, V\) each. The drops are joined to form a single drop. The potential of this drop is ......... \(V.\)

A rigid wire consists of a semicircular portion of radius \(R\) and two straight sections. The wire is partially immerged in a perpendicular magnetic field \(B=B_0\ {j}\) as shown in figure. The magnetic force on the wire if it has a current \(i\) is _______.

For ac circuit shown in figure, \(\mathrm{R}=100 \mathrm{k} \Omega\) and \(\mathrm{C}=100 \mathrm{pF}\) and the phase difference between \(\mathrm{V}_{\text {in }}\) and \(\left(V_B-V_A\right)\) is \(90^{\circ}\). The input signal frequency is \(10^x \mathrm{rad} / \mathrm{sec}\), where ' x ' is ______.

If the series limit frequency of the Lyman series is \(v_L\), then the series limit frequency of the \(P\)-fund series is

A block of mass \(1 \mathrm{~kg}\) is pushed up a surface inclined to horizontal at an angle of \(60^{\circ}\) by a force of \(10 \mathrm{~N}\) parallel to the inclined surface as shown in figure. When the block is pushed up by \(10 \mathrm{~m}\) along inclined surface, the work done against frictional force is _______. \(\left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right]\)

A very long wire \(ABDMNDC\) is shown in figure carrying current \(I. AB\) and \(BC\) parts are straight, long and at right angle. At \(D\) wire forms a circular turn \(DMND\) of radius \(R. AB.\) \(\mathrm{BC}\) parts are tangential to circular turn at \(\mathrm{N}\) and \(D\). Magnetic field at the centre of circle is