A flask contains Hydrogen and Argon in the ratio \(2: 1\) by mass. The temperature of the mixture is \(30^{\circ} C\). The ratio of average kinetic energy per molecule of the two gases ( \(K\) argon/ \(K\) hydrogen) is: (Given: Atomic Weight of \(Ar = 39.9\))

A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image of an object ' O ' is :
( C is the center of curvature of the spherical surface and \(R\) is the radius of curvature)

A \(25\,cm\) long solenoid has radius \(2\,cm\) and \(500\) total number of turns. It carries a current of \(15\,A.\) If it is equivalent to a magnet of the same size and magnetization \(\vec M\) ( magnetic moment/ volume), then \(\left| {\vec M} \right|\)  is

The elastic potential energy stored in a steel wire of length \(20\,m\) stretched through \(2 \,cm\) is \(80\,J\). The cross sectional area of the wire is \(.........\,mm ^2\) (Given, \(y =2.0 \times 10^{11}\,Nm ^{-2}\) )

One end of a straight uniform \(1\; \mathrm{m}\) long bar is pivoted on horizontal table. It is released from rest when it makes an angle \(30^{\circ}\) from the horizontal (see figure). Its angular speed when it hits the table is given as \(\sqrt{\mathrm{n}}\; \mathrm{s}^{-1},\) where \(\mathrm{n}\) is an integer. The value of \(n\) is

The quantities \(\quad x=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}, y=\frac{E}{B}\) and \(z=\frac{l}{C R}\) are defined where \(C-\) capacitance \(R-\)Resistance, \(l-\)length, \(E-\)Electric field, \(B-\)magnetic field and \(\varepsilon_{0}, \mu_{0},\) -free space permittivity and permeability respectively. Then....

Two balls \(A\) and \(B\) are placed at the top of \(180 \,m\) tall tower. Ball \(A\) is released from the top at \(t =0 \,s\). Ball \(B\) is thrown vertically down with an initial velocity \(u\)' at \(t=2\, s\). After a certain time, both balls meet \(100 \,m\) above the ground. Find the value of \(u\) in ............... \(ms ^{-1}\). [use \(g =10 \,ms ^{-2}\) ]

The electric field of an electromagnetic wave in free space is \(\overrightarrow{\mathrm{E}}=57 \cos \left[7.5 \times 10^6 \mathrm{t}-5 \times 10^{-3}(3 x+4 y)\right](4 \hat{i}-3 \hat{j}) N / C\). The associated magnetic field in Tesla is _______.

Three bodies \(A, B\) and \(C\) have equal kinetic energies and their masses are \(400 \mathrm{~g}, 1.2 \mathrm{~kg}\) and \(1.6 \mathrm{~kg}\) respectively. The ratio of their linear momenta is _______.

A beam of electrons of energy \(E\) scatters from a target having atomic spacing of \(1\, A\). The first maximum intensity occurs at \(\theta=60^{\circ} .\) Then \(E\) (in \(eV )\) is\(......\) (Planck constant \(h =6.64 \times 10^{-34}\, Js\) \(1 \,eV =1.6 \times 10^{-19}\,J\), electron mass \(\left. m =9.1 \times 10^{-31}\, kg \right)\) 

For \(LED's\)  to emit light in visible region of electromagnetic light, it should have energy band gap in the range of