For a specific wavelength \(670 \; nm\) of light coming from a galaxy moving with velocity \(v\), the observed wavelength is \(670.7 \; nm\). The value of \(v\) is ............

Consider the combination of \(2\) capacitors \(C _{1}\) and \(C _{2},\) with \(C _{2}> C _{1},\) when connected in parallel, the equivalent capacitance is \(\frac{15}{4}\) time the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, \(\frac{ C _{2}}{ C _{1}}\)

Moment of inertia of a square plate of side \(l\) about the axis passing through one of the corner and perpendicular to the plane of square plate is given by

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number \(192\) is _______.

A proton, a neutron, an electron and an \(\alpha\,-\)particle have same energy. If \(\lambda_{ p }, \lambda_{ n }, \lambda_{ e }\) and \(\lambda_{\alpha}\) are the de Broglie's wavelengths of proton, neutron, electron and \(\alpha\) particle respectively, then choose the correct relation from the following

The energy \(E\) and momentum \(p\) of a moving body of mass \(m\) are related by some equation. Given that c represents the speed of light, identify the correct equation.

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is \(\frac{x}{8}\), where \(x=\) _______.

Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points A and F are maintained at \( 100^{\circ}C \) and \( 40^{\circ}C \) respectively. Given the thermal conductivity of rod x is three times of that of rod y, the temperature at junction points B and E are (close to):

If \(1000\) droplets of water of surface tension \(0.07\,N / m\). having same radius \(1\,mm\) each, combine to from a single drop. In the process the released surface energy is \(\left(\text { Take } \pi=\frac{22}{7}\right)\)

Two travelling waves produces a standing wave represented by equation, \({y}=1.0\, {mm} \cos \left(1.57 \,{cm}^{-1}\right) {x} \sin \left(78.5\, {s}^{-1}\right) {t}\) The node closest to the origin in the region \({x}>0\) will be at \({x}=\ldots \ldots \ldots\, {cm}\)

In Young's double slit experiment, two slits \(S_1\) and \(S_2\) are ' \(d\) ' distance apart and the separation from slits to screen is \(D\) (as shown in figure). Now if two transparent slabs of equal thickness \(0.1\,mm\) but refractive index \(1.51\) and \(1.55\) are introduced in the path of beam \((\lambda=4000 \mathring A)\) from \(S_1\) and \(S_2\) respectively. The central bright fringe spot will shift by  \(..........\) number of fringes.

A closed organ pipe of length \(L\) and an open organ pipe contain gases of densities \(\rho_{1}\) and \(\rho_{2}\) respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is \(\frac{ x }{3} L \sqrt{\frac{\rho_{1}}{\rho_{2}}}\) where \(x\) is ......... . (Round off to the Nearest Integer)