If three moles of monoatomic gas \(\left(\gamma=\frac{5}{3}\right)\) is mixed with two moles of a diatomic gas \(\left(\gamma=\frac{7}{5}\right)\), the value of adiabatic exponent \(\gamma\) for the mixture is _______.

A person observes two moving trains, '\(A\)' reaching the station and '\(B\)' leaving the station with equal speed of \(30\,m / s\). If both trains emit sounds with frequency \(300\,Hz\), (Speed of sound : \(330\,m / s\) ) approximate difference of frequencies heard by the person will be \(..........Hz\)

In an unbiased \(n-p\) junction electrons diffuse from \(n-\) region to \(p-\) region because

A body of mass \(0.5\, kg\) travels on straight line path with velocity \(v =\left(3 x ^{2}+4\right) m / s\). The net workdone by the force during its displacement from \(x =0\) to \(x =2\, m\) is\(.......J\)

A convex lens of refractive index \(1.5\) and focal length \(18 cm\) in air is immersed in water. The change in focal length of the lens will be \(...........cm\).\(\left(\right.\) Given refractive index of water \(\left.=\frac{4}{3}\right)\)

A sample of gas at temperature \(T\) is adiabatically expanded to double its volume. The work done by the gas in the process is \(\left(\right.\) given, \(\left.\gamma=\frac{3}{2}\right)\) :

Given below are two statement: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) If an electric dipole of dipole moment \(30 \times 10^{-5}\,Cm\) is enclosed by a closed surface, the net flux coming out of the surface will be zero. Reason \(R\) : Electric dipole consists of two equal and opposite charges. In the light of above, statements, choose the correct answer from the options given below:

An \(AC\) circuit has \(R =100 \Omega, C =2\, \mu F\) and \(L =80\, mH ,\) connected in series. The quality factor of the circuit is\(.......\)

Which of the following equations represents a travelling wave ?

If \(x\) and \(y\) coordinates of a projectile as a function of time \((t)\) are given as \(24t\) and \(43.6t-4.9t^2\), respectively, then the angle (in degrees) made by the projectile with horizontal when \(t=2\) s is ______.

The threshold frequency of a metal with work function \(6.63\  \mathrm{eV}\) is:

An infinite wire has a circular bend of radius a, and carrying a current I as shown in figure. The magnitude of magnetic field at the origin \(O\) of the arc is given by :