A point source is emitting sound waves of intensity \(16 \times 10^{-8} \mathrm{Wm}^{-2}\) at the origin. The difference in intensity (magnitude only) at two points located at a distances of \(2 \mathrm{~m}\) and \(4 \mathrm{~m}\) from the origin respectively will be _______ \(\times 10^{-8} \mathrm{Wm}^{-2}\)

Given below are two statements: Statement \(I\) : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit \(\left( E _{1}\right)\) to higher energy orbit \(\left( E _{2}\right)\), is given as \(hf = E _{1}- E _{2}\). Statement \(II\) : The jumping of electron from higher energy orbit \(\left(E_{2}\right)\) to lower energy orbit \(\left(E_{1}\right)\) is associated with frequency of radiation given as \(f\) \(=\left( E _{2}- E _{1}\right) / h\) This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below

A particle of mass \(250\,g\) executes a simple harmonic motion under a periodic force \(F =(-25\,x) N\). The particle attains a maximum speed of \(4\,m / s\) during its oscillation. The amplitude of the motion is \(...........cm\).

When a hydrogen atom going from \(\mathrm{n}=2\) to \(\mathrm{n}=1\) emits a photon, its recoil speed is \(\frac{\mathrm{x}}{5} \mathrm{~m} / \mathrm{s}\). Where \(\mathrm{x}=\) _______. (Use : mass of hydrogen atom\(\left.=1.6 \times 10^{-27 /} \ \mathrm{kg}\right)\)

A magnetic dipole experiences a torque of \(80 \sqrt{3} \mathrm{~N} \mathrm{~m}\) when placed in uniform magnetic field in such a way that dipole moment makes angle of \(60^{\circ}\) with magnetic field. The potential energy of the dipole is :

\(LED\) is constructed from \(Ga-As-P\) semiconducting material. The energy gap of this \(LED\) is \(1.9\, eV\). Calculate the wavelength of light emitted and its colour. \(\left[ h =6.63 \times 10^{-34} \;Js \right.\) and \(\left. c =3 \times 10^{8}\; ms ^{-1}\right]\)

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved ?

The total number of \(4 -\)digit numbers whose greatest common divisor with \(18\) is \(3,\) is .... .

If \(\int \mathrm{e}^x\left(\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}}+\frac{x}{1-x^2}\right) \mathrm{d} x=\mathrm{g}(x)+\mathrm{C}\), where C is the constant of integration, then \(g\left(\frac{1}{2}\right)\) equals :

A wire of resistance \(R\) and length \(L\) is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be _______.

In a uniform magnetic field, the magnetic needle has a magnetic moment \(9.85 \times 10^{-2} \,{A} / {m}^{2}\) and moment of inertia \(5 \times 10^{-6} \,{kgm}^{2}\). If it performs \(10\) complete oscillations in \(5\, seconds\) then the magnitude of the magnetic field is \(....\,mT.\) [ Take \(\pi^{2}\) as \(9.85\) ]

Let the plane \(ax \,\,+\,\,by \,\,+c z=d\) pass through \((2,3,-5)\) and is perpendicular to the planes \(2 x + y -5 z =10\) and \(3 x+5 y-7 z=12\). If \(a, b, c, d\) are integers \(d>0\) and gcd \((lal, |b|,|c|, d)\) \(=1\), then the value of \(a+7 b+c+20 \,d\) is equal to

In an experiment, a set of reading are obtained \(-1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm\). The expected least count of the instrument used in recording these readings is ___________ mm.