The refractive index of a converging lens is \(1.4.\) What will be the focal length of this lens if it is placed in a medium of same refractive index ? (Assume the radii of curvature of the faces of lens are \(R _{1}\) and \(R _{2}\) respectively)

A toy-car, blowing its horn, is moving with a steady speed of \(5\, m/s\) , away from a wall. An observer, towards whom the toy car is moving, is able to hear \(5\, beats\) per second. If the velocity of sound in air is \(340\, m/s\), the frequency of the horn of the toy car is close to  ... \(Hz\)

A plane electromagnetic wave having a frequency \(n = 23.9\, GHz\) propagates along the positive \(z-\) direction in free space. The peak value of the electric field is \(60\, V/m\). Which among the following is the acceptable magnetic field component in the electromagnetic wave?

For a certain organ pipe, the first three resonance frequencies are in the ratio of \(1:3:5\) respectively. If the frequency of fifth harmonic is \(405\,Hz\) and the speed of sound in air is \(324 \,ms ^{-1}\) the length of the organ pipe is \(..........m.\)

A \(25\,cm\) long solenoid has radius \(2\,cm\) and \(500\) total number of turns. It carries a current of \(15\,A.\) If it is equivalent to a magnet of the same size and magnetization \(\vec M\) ( magnetic moment/ volume), then \(\left| {\vec M} \right|\)  is

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: A diode under reverse-biased condition provides very small current which is nearly independent of voltage until a critical limit at which the current increases drastically.

Reason R: Below the critical voltage limit, only majority charge carriers flow which increases drastically above critical voltage.

Choose the correct answer from the options given below

The momentum of a body is increased by \(50 \%\). The percentage increase in the kinetic energy of the body is \(...........\,\%\)

In free space, a particle \(A\) of charge \(1\,\mu C\) is held fixed at a point \(P.\) Another particle \(B\) of the same charge and mass \(4\,\mu g\) is kept at a distance of \(1\,mm\) from \(P\). If \(B\) is released, then its velocity at a distance of \(9\,mm\) from \(P\) is [ Take \(\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}\,N{m^2}{C^{ - 2}}\) ]

At some location on earth the horizontal component of earth’s magnetic field is \(18\times10^{-6}\,T\). At this location, magnetic needle of length \(0.12\, m\) and pole strength \(1.8\, A\,m\) is suspended from its mid-point using a thread, it makes \(45^o\) angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is

In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when the air column has a length of \(20.0 \,cm\) for a tuning fork of frequency \(400 \,Hz\) is used. The velocity of the sound at room temperature is \(336 \,ms ^{-1}\). The third resonance is observed when the air column has a length of ......... \(cm\)

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude. Reason \(R \): At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below