Two conducting circular loops \(A \) and \(B\) are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is _______.

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is \(30 \;\mathrm{cm}\) and the refractive index of the lens material is \(1.5 .\) then the focal length of the lens (in \(\mathrm{cm}\) ) is

As shown in the figure, the voltmeter reads \(2\,V\) across \(5\,\Omega\) resistor. The resistance of the voltmeter is \(.......\,\Omega\).

Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength \(\lambda\). The value of principal quantum number ' \(n\) ' of the excited state will be: (\(R\): Rydberg constant)

In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength . If wavelength of red light is \(6600\,\mathop A\limits^o\) , then wavelength of first maximum will be.....\(\mathop A\limits^o \)

Three equal masses \(m\) are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At \(t=0\), they are given an initial velocity \(\vec{V}_A=V_0 \overrightarrow{A C}, \vec{V}_B=V_0 \overrightarrow{B A}\) and \(\vec{V}_C=V_0 \overrightarrow{C B}\). Here, \(\overrightarrow{A C}, \overrightarrow{C B}\) and \(\overrightarrow{B A}\) are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

Two streams of photons, possessing energies to five and ten times the work function of metal are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectron emitted, in the two cases respectively, will be.

If the gravitational field in the space is given as \(\left(-\frac{ K }{ r ^2}\right)\). Taking the reference point to be at \(r =2\,cm\) with gravitational potential \(V =10\,J / kg\). Find the gravitational potential at \(r =3\,cm\) in \(SI\) unit (Given, that \(K =6\,J cm / kg\) )

In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards \(A\). If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of ' \(-2^{\prime}\) then the radius of curvature of meniscus is :

Given below are two statements. One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion A :Two identical balls \(A\) and \(B\) thrown with same velocity '\(u\) ' at two different angles with horizontal attained the same range \(R\). If \(A\) and \(B\) reached the maximum height \(h_{1}\) and \(h_{2}\) respectively, then \(R =4 \sqrt{ h _{1} h _{2}}\) Reason R: Product of said heights. \(h _{1} h _{2}=\left(\frac{u^{2} \sin ^{2} \theta}{2 g }\right) \cdot\left(\frac{u^{2} \cos ^{2} \theta}{2 g }\right)\) Choose the \(CORRECT\) answer