A \(2\,mW\) laser operates at a wavelength of \(500\,nm.\) The number of photons that will be emitted per second is [Given Planck’s constant \(h = 6.6 \times 10^{-34}\,Js,\) speed of light \(c = 3.0\times 10^8\,m/s\) ]

A bicycle tyre is filled with air having pressure of \(270\,kPa\) at \(27^{\circ}\,C\). The approximate pressure of the air in the tyre when the temperature increases to \(36^{\circ}\,C\) is \(............kPa\)

Suppose a uniformly charged wall provides a uniform electric field of \(2 \times 10^4 \mathrm{~N} / \mathrm{C}\) normally. A charged particle of mass \(2 \mathrm{~g}\) being suspended through a silk thread of length \(20 \mathrm{~cm}\) and remain stayed at a distance of \(10 \mathrm{~cm}\) from the wall. Then the charge on the particle will be \(\frac{1}{\sqrt{\mathrm{x}}} \ \mu \mathrm{C}\) where \(\mathrm{x}=\) _______ [use \(g=10 \mathrm{~m} / \mathrm{s}^2\)]

In Bohr's atomic model of hydrogen, let \(K\), \(P\) and \(E\) are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level

The dimension of stopping potential \(\mathrm{V}_{0}\) in photoelectric effect in units of Planck's constant \(h\), speed of light \(c\) and Gravitational constant \(G\) and ampere \(A\) is

Two identical charged spheres are suspended by string of equal lengths. The string make an angle of \(37^{\circ}\) with each other. When suspended in a liquid of density \(0.7 \mathrm{~g} / \mathrm{cm}^3\), the angle remains same. If density of material of the sphere is \(1.4 \mathrm{~g} / \mathrm{cm}^3\), the dielectric constant of the liquid is _______\(\left(\tan 37^{\circ}=\frac{3}{4}\right)\).

The value of the acceleration due to gravity is \(g _{1}\) at a height \(h =\frac{ R }{2}( R =\) radius of the earth) from the surface of the earth. It is again equal to \(g _{1}\) at a depth \(d\) below the surface of the earth. The ratio \(\left(\frac{ d }{ R }\right)\) equals

Identify the correct statements from the following: \((A)\) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. \((B)\) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative. \((C)\) Work done by friction on a body sliding down an inclined plane is positive. \((D)\) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity in zero. \((E)\) Work done by the air resistance on an oscillating pendulum in negative. Choose the correct answer from the options given below:

A ball of mass \(0.5 \mathrm{~kg}\) is attached to a string of length \(50 \mathrm{~cm}\). The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is \(400 \mathrm{~N}\). The maximum possible value of angular velocity of the ball in rad/s is _______.

Let the plane containing the line of intersection of the planes \(P 1: x+(\lambda+4) y+z=1\) and \(P2:\) \(2 x+y+z=2\) pass through the points \((0,1,0)\) and \((1,0,1)\). Then the distance of the point \((2 \lambda, \lambda,-\lambda)\) from the plane \(P 2\) is

The given figure represents two isobaric processes for the same mass of an ideal gas, then ....

\(\mathop {\lim }\limits_{x \to \infty } \,\left( {\frac{n}{{{n^2}\, + {1^2}}} + \frac{n}{{{n^2} + {2^2}}} + \frac{n}{{{n^2} + {3^2}}} + ...\frac{1}{{5n}}} \right)\) is equal to

Let the image of the point \(P (1,2,6)\) in the plane passing through the points \(A (1,2,0), B (1,4,1)\) and \(C(0,5,1)\) be \(Q(\alpha, \beta, \gamma)\). Then \(\left(\alpha^2+\beta^2+\gamma^2\right)\) is equal to :