At an angle of \(30^{\circ}\) to the magnetic meridian, the apparent dip is \(45^{\circ} .\) Find the true dip :

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 hydrogen atom in ground state is given an energy of \(10.2 \mathrm{eV}\). How many spectral lines will be emitted due to transition of electrons?

 A small speaker delivers \(2\, W\) of audio output. At what distance from the speaker will one detect \(120\, dB\) intensity sound ... \(cm\) ? [Given reference intensity of sound as \(10^{-12}\,W/m^2\)]

A charged particle (mass \(m\) and charge \(q\) ) moves along \(X\) axis with velocity \(V _{0}\). When it passes through the origin it enters a region having uniform electric field \(\overrightarrow{ E }=- E \hat{ j }\) which extends upto \(x = d\). Equation of path of electron in the region \(x > d\) is 

If \({R}_{{E}}\) be the radius of Earth, then the ratio between the acceleration due to gravity at a depth \(' {r} '\) below and a height \(' r '\) above the earth surface is: (Given : \(\left.{r}<{R}_{{E}}\right)\)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R .
Assertion A : If oxygen ion \(\left(\mathrm{O}^{-2}\right)\) and Hydrogen ion \(\left(\mathrm{H}^{+}\right)\)enter normal to the magnetic field with equal momentum, then the path of \(\mathrm{O}^{-2}\) ion has a smaller curvature than that of \(\mathrm{H}^{+}\).
Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.
In the light of the above statements, choose the correct answer from the options given below :

The complex number \(z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}\) is equal to \(.....\)

Let the sum of the maximum and the minimum values of the function \(f(x)=\frac{2 x^2-3 x+8}{2 x^2+3 x+8}\) be \(\frac{m}{n}\), where \(\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1\). Then \(\mathrm{m}+\mathrm{n}\) is equal to :

The weight of a body at the surface of earth is \(18\,N\). The weight of the body at an altitude of \(3200\,km\) above the earth's surface is \(........\,N\) (given, radius of earth \(R _{ e }=6400\,km\) )

In Bohr's atomic model of hydrogen, let \(K\), \(P\) and \(E\) are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level

For the given circuit, in the steady state, \(\left| V _{ B }- V _{ D }\right|=.......V.\)

Let the three sides of a triangle are on the lines \(4 x-7 y+10=0, x+y=5\) and \(7 x+4 y=15\). Then the distance of its orthocentre from the orthocentre of the triangle formed by the lines \(x=0, y=0\) and \(x+y=1\) is