A source of sound \(S\) is moving with the velocity of \(50\,m/s\) towards a stationary observer. The observer measures the frequency of the sound as \(1000\,Hz.\) What will be the apparent frequency of the source when it is moving away from the observer after crossing him ... \(Hz\) ? (Take velocity of sound in air is \(350\,m/s\) )

If an electron is moving in the \(n ^{\text {th }}\) orbit of the hydrogen atom, then its velocity \(\left( v _{ n }\right)\) for the \(n ^{\text {th }}\) orbit is given as

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is

Match List-I with List-II.

List-I (Physical Quantity)	List-II (Dimensional Formula)
(A) Coefficient of viscosity	(I) [ML0T-3]
(B) Intensity of wave	(II) [ML-2T-2]
(C) Pressure gradient	(III) [M-1LT2]
(D) Compressibility	(IV) [ML-1T-1]

Choose the correct answer from the options given below :

A point charge \(2 \times 10^{-2}\,C\) is moved from \(P\) to \(S\) in a uniform electric field of \(30\,NC ^{-1}\) directed along positive \(x\)-axis. If coordinates of \(P\) and \(S\) are \((1,2\), \(0) m\) and \((0,0,0) m\) respectively, the work done by electric field will be \(.........\,mJ\)

An electric field of \(1000\,V/m\) is applied to an electric dipole at angle of \(45^o\). The value of electric dipole moment is \(10^{-29}\, C.m.\) What is the potential energy of the electric dipole?

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:

Given below are two statements :
Statement I : \(\lim _{x \rightarrow 0}\left(\frac{\tan ^{-1} x+\log _e \sqrt{\frac{1+x}{1-x}}-2 x}{x^5}\right)=\frac{2}{5}\)
Statement II : \(\lim _{\mathrm{x} \rightarrow 1}\left(\mathrm{x}^{\frac{2}{1-\mathrm{x}}}\right)=\frac{1}{\mathrm{e}^2}\)
In the light of the above statements, choose the correct answer from the options given below :

Two identical blocks \(A\) and \(B\) each of mass \(m\) resting on the smooth horizontal floor are connected by a light spring of natural length \(L\) and spring constant \(K\). A third block \(C\) of mass \(m\) moving with a speed \(v\) along the line joining \(A\) and \(B\) collides with \(A\).The maximum compression in the spring is

Let \(\dfrac{x^2}{f(a^2+7a+3)} + \dfrac{y^2}{f(3a+15)} = 1\) represent an ellipse with major axis along \(y\)-axis, where \(f\) is a strictly decreasing positive function on \(\mathbb{R}\). If the set of all possible values of \(a\) is \(\mathbb{R} - [\alpha, \beta]\), then \(\alpha^2+\beta^2\) is equal to:

A point source of \(100\,W\) emits light with \(5 \%\) efficiency. At a distance of \(5\,m\) from the source, the intensity produced by the electric field component is :

A car is standing \(200\, m\) behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration \(2\,m/s^2\) and the car has acceleration \(4\, m/s^2\) . The car will catch up with the bus after a time of

If the co-efficient of \(x^9\) in \(\left(\alpha x^3+\frac{1}{\beta x}\right)^{11}\) and the co-efficient of \(x^{-9}\) in \(\left(\alpha x-\frac{1}{\beta x^3}\right)^{11}\) are equal, then \((\alpha \beta)^2\) is equal to \(.............\).