When a car is approaching the observer, the frequency of horn is \(100 Hz\). After passing the observer, it is \(50\,Hz\). If the observer moves with the car, the frequency will be \(\frac{ x }{3} Hz\) where \(x =.....\)

In a compound microscope the focal length of objective lens is \(1.2\, cm\) and focal length of eye piece is \(3.0\, cm\). When object is kept at \(1.25\, cm\) in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be

A particle is moving in a circular path of radius \(a,\) with a constant velocity \(v\) as shown in the figure.The centre of circle is marked by \('C'\). The angular momentum from the origin \(O\) can be written as

The co-ordinates of a particle moving in \(x-y\) plane are given by :  \(\mathrm{x}=2+4 \mathrm{t}, \mathrm{y}=3 \mathrm{t}+8 \mathrm{t}^2 .\) The motion of the particle is _______.

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity \(\rho_{ C }, \rho_{ T }, \rho_{ M }\) and \(\rho_{ A }\) espectively Then:

The figure shows two solid discs with radius \({R}\) and \({r}\) respectively. If mass per unit area is same for both, what is the ratio of \({MI}\) of bigger disc around axis \({AB}\) (Which is \(\perp\) to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given \('M'\) is the mass of the larger disc. (\(MI\) stands for moment of inertia)

Let \(B_1\) be the magnitude of magnetic field at center of a circular coil of radius \(R\) carrying current \(I\). Let \(B_2\) be the magnitude of magnetic field at an axial distance ' \(x\) ' from the center. For \(x: R=3: 4, \frac{B_2}{B_1}\) is :

The diffraction pattern of a light of wavelength \(400\) \(\mathrm{nm}\) diffracting from a slit of width \(0.2 \mathrm{~mm}\) is focused on the focal plane of a convex lens of focal length \(100 \mathrm{~cm}\). The width of the \(1^{\text {st }}\) secondary maxima will be _______.

If a source of electromagnetic radiation having power \(15 kW\) produces \(10^{16}\) photons per second, the radiation belongs to a part of spectrum is.(Take Planck constant \(h =6 \times 10^{-34}\,Js\) )

A three coulomb charge moves from the point \((0, -2, -5)\) to the point \((5, 1, 2)\) in an electric field expressed as \(\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}\) N/C. The work done in moving the charge is _______ J.