The radiation corresponding to \(3 \rightarrow 2\) transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of \(5 \times 10^{-4} \,{T}\). Assume that the radius of the largest circular path followed by these electrons is \(7\, {mm}\), the work function of the metal is \(.....\,{eV}\) (Mass of electron \(=9.1 \times 10^{-31} \,{kg}\) )

Shown in the figure is rigid and uniform one meter long rod \(AB\) held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass \('m'\) and has another weight of mass \(2m\) hung at a distance of \(75\, cm\) from \(A\). The tension in the string at \(A\) is\(....mg\)

A string is clamed at both the ends and it is vibrating in its \(4^{th}\) harmonic. The equation of the stationary wave is \(Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)\). The length of the string is ..... \(m\) (all quantities are in \(SI\) units)

A cylindrical container of volume \(4.0 \times 10^{-3} \,{m}^{3}\) contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is \(400 \,{K}\) The pressure of the mixture of gases is: [Take gas constant as \(8.3\, {J} {mol}^{-1} {K}^{-1}\)]

person trying to lose weight by burning fat lifts a mass of \(10\ kg\) upto a height of \(1\ m\) \(1000\) times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies \(3.8 \times 10^7\ J\) of energy per kg which is converted to mechanical energy with a \(20\%\) efficiency rate. Take \(g=9.8\) \(ms^{-2}\) 

A wire \(A\), bent in the shape of an arc of a circle, carrying a current of \(2\, A\) and having radius \(2\, cm\) and another wire \(B ,\) also bent in the shape of arc of a circle, carrying a current of \(3\, A\) and having radius of \(4\, cm ,\) are placed as shown in the figure. The ratio of the magnetic fields due to the wires \(A\) and \(B\) at the common centre \(O\) is

Abeam of unpolarised light of intensity \(I_0\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of \(45^{\circ}\) relative to that of \(A\). The intensity of emergent light is :

Let \( X=\{x\in\mathbb{N}:1\le x\le19\} \) and for some \( a, b\in\mathbb{R}, Y=\{ax+b:x\in X\}. \) If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of b is

Let for \(x \in R , S_0( x )= x\),\(S _{ k }( x )= C _{ k } x + k \int _0^{ x } S _{ k -1}(t) d t\), where \(C _0=1, C _{ k }=1-\int_0^1 S _{ k -1}( x ) dx , k =1,2,3 \ldots\). Then \(S _2(3)+6 C _3\) is equal to \(...........\).

The least count of the main scale of a vernier callipers is \(1\, mm\). Its vernier scale is divided into \(10\) divisions and coincide with \(9\) divisions of the main scale. When jaws are touching each other, the \(7\) th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between \(3.1\, cm\) and \(3.2\, cm\) and \(4^{th}\) \(VSD\) coincides with a main scale division.The length of the cylinder is \(.....cm\) (\(VSD\) is vernier scale division)

Let a variable line of slope \(m>0\) passing through the point \((4,-9)\) intersect the coordinate axes at the points \(A\) and \(B\). the minimum value of the sum of the distances of \(\mathrm{A}\) and \(\mathrm{B}\) from the origin is

Given; A circle \(2{x^2} + 2{y^2} = 5\) and parabola \({y^2} = 4\sqrt 5 x\) Statement \(-1\):An equation of a common tangent to these curve is  \(y = x + \sqrt 5 \) Statement \(-2\): If the line, \(y = mx + \frac{{\sqrt 5 }}{m}\left( {m \ne 0} \right)\) is their common tangent , then \(m\) satisfies \({m^4} - 3{m^2} + 2 = 0\). 

A parallel plate capacitor has plate area \(40\,cm ^2\) and plates separation \(2\,mm\). The space between the plates is filled with a dielectric medium of a thickness \(1\,mm\) and dielectric constant \(5\) . The capacitance of the system is :