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 lamp emits monochromatic green light uniformly in all directions. The lamp is \(3\%\) efficient in converting electrical power to electromagnetic waves and consumes \(100\,W\) of power . The amplitude of the electric field associated with the electromagnetic radiation at a distance of \(5\,m\) from the lamp will be nearly.......\(V/m\)

If \(Z=\frac{A^{2} B^{3}}{C^{4}}\), then the relative error in \(Z\) will be

Monochromatic light of wavelength \(500 \mathrm{~nm}\) is used in Young's double slit experiment. An interference pattern is obtained on a screen When one of the slits is covered with a very thin glass plate (refractive index \(=1.5\) ), the central maximum is shifted to a position previously occupied by the \(4^{\text {th }}\) bright fringe. The thickness of the glass-plate is _______\(\mu \mathrm{m}\).

Least count of a vernier caliper is \(\frac{1}{20 \mathrm{~N}} \mathrm{~cm}\). The value of one division on the main scale is \(1 \mathrm{~mm}\). Then the number of divisions of main scale that coincide with \(\mathrm{N}\) divisions of vernier scale is _______.

A diatomic gas \((\gamma=1.4)\) does \(100 \mathrm{~J}\) of work in an isobaric expansion. The heat given to the gas is _______.

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is \(I_0\). If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be :

A physical quantity \(Q\) is found to depend on quantities \(a, b, c\) by the relation \(Q=\frac{a^4 b^3}{c^2}\). The percentage error in \(a\), \(b\) and \(c\) are \(3 \%, 4 \%\) and \(5 \%\) respectively. Then, the percentage error in \(\mathrm{Q}\) is _______.

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be: (Assume the coil to be short circuited.)

A magnetic field vector in an electromagnetic wave is represented by \(\vec{B}=B_0\sin\left(2\pi vt-\dfrac{2\pi x}{\lambda}\right)\hat{j}\). Its associated electric field vector is ______.

In an experiment for determination of refractive index of glass of a prism by \(i - \delta\) , plot it was found thata ray incident at angle \(35 ^o \), suffers a deviation of \(40 ^o \) and that it emerges at angle \(7 9 ^o \). In that case which of the following is closest to the maximum possible value of the refractive index?

A screw gauge has \(50\) divisions on its circular scale. The circular scale is \(4\) units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of \(0.5\, mm\) is noticed on the pitch scale. The nature of zero error involved, and the least count of the screw gauge, are respectively

A uniform thin metal plate of mass \(10 \mathrm{~kg}\) with dimensions is shown. The ratio of \(x\) and \(y\) coordinates of center of mass of plate in \(\frac{n}{9}\). The value of \(n\) is _______.