The equation \(\lambda=\frac{1.227}{ x } nm\) can be used to find the de-Brogli wavelength of an electron. In this equation \(x\) stands for : Where,\(m =\) mass of electron \(P =\) momentum of electron \(K =\) Kinetic energy of electron \(V =\) Accelerating potential in volts for electron

An electrical power line, having a total resistance of \(2 \Omega\), delivers \(1 \,kW\) at \(220\, V\). The efficiency of the transmission line is approximately \(.......\%\)

If two glass plates have water between them and are separated by very small distance ( see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is \(R\) and surface tension of water is \(T\) then the pressure in water between the plates is lower by

Consider the following logic circuit.

The output is \(\mathrm{Y}=0\) when :

The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is \(\frac{4}{3}\).The wavelength of the same light when it is passing through a transparent medium having refractive index of \(\frac{3}{2}\) is __________ nm.

A \(\sqrt{34}\,m\) long ladder weighing \(10\,kg\) leans on a frictionless wall. Its feet rest on the floor \(3\,m\) away from the wall as shown in the figure. If \(F_{f}\) and \(F_{w}\) are the reaction forces of the floor and the wall, then ratio of \(F _{ a } / F _{f}\) will be: (Use \(\left.g=10\,m / s ^{2}\right)\)

A small spherical droplet of density \(d\) is floating exactly half immersed in a liquid of density \(\rho\) and surface tension \(\mathrm{T}\). The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) 

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field \(\vec{E}_1=E_0\hat{x}\). If another electric field \(\vec{E}_2=2E_0(\hat{y}+\hat{z})\) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

A solution containing active cobalt \({}_{27}^{60}Co\) having activity of \(0.8\,\mu Ci\) and decay constant \(\lambda \) is injected in an animal's body. If \(1 \,cm^3\) of blood is drawn from the animal's body after \(10\, hrs\) of injection, the activity found was \(300\, decays\) per minute. What is the volume of blood that is flowing in the body?..........\(litres\) ( \(ICi = 3.7 \times 10^{10}\) decay per second and at \(t = 10\, hrs\) \({e^{ - \lambda t}} = 0.84\) )

Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its \((i)\) second permitted energy level to the first level, and \((ii)\) the highest permitted energy level to the first permitted level.

The workdone by a gas molecule in an isolated system is given by, \(W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},\) where \(x\) is the displacement, \(k\) is the Boltzmann constant and \(T\) is the temperature, \(\alpha\) and \(\beta\) are constants. Then the dimension of \(\beta\) will be

Two simple harmonic motions are represented by the equations \({x}_{1}=5 \sin \left(2 \pi {t}+\frac{\pi}{4}\right)\) and \({x}_{2}=5 \sqrt{2}(\sin 2 \pi {t}+\cos 2 \pi {t})\) The amplitude of second motion is ....... times the amplitude in first motion.