A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by \(100 \,\mu A\), it brings a change of \(10 \,mA\) in collector current. If the load resistance is \(2 \,k \Omega\) and input resistance is \(1 \,k \Omega\), the value of power gain is \(x \times 10^{4}\). The value of \(x\) is_________

Which of the following nuclear fragments corresponding to nuclear fission between neutron \(\left({ }_0^1 \mathrm{n}\right)\) and uranium isotope \(\left({ }_{92}^{235} \mathrm{U}\right)\) is correct:

\(\sqrt{d_{1}}\) and \(\sqrt{d_{2}}\) are the impact parameters corresponding to scattering angles \(60^{\circ}\) and \(90^{\circ}\) respectively, when an \(\alpha\) particle is approaching a gold nucleus. For \(d_{1}=x d_{2}\), the value of \(x\) will be ________

A moving coil galvanometer allows a full scale current of \(10^{-4}\, A\). A series resistance of \(2\, M\,\Omega \) is required to convert the above galvanometer into a voltmeter of range \(0 -5\, V\). Therefore the value of shunt resistance required to convert the above galvanometer into a ammeter of range \(0-10\, mA\) is....\(\Omega \)

A submarine \((A)\) travelling at \(18\, km/hr\) is being chased along the line of its velocity by another submarine \((B)\) travelling at \(27\, km/hr\). \(B\) sends a sonar signal of \(500\, Hz\) to detect \(A\) and receives a reflected sound of frequency \(v\). The value of \(v\) is close to ... \(Hz\) (Speed of sound in water \(= 1500\, ms^{-1}\))

An \(n.p.n\) transistor with current gain \(\beta=100\) in common emitter configuration is shown in figure. The output voltage of the amplifier will be\(.....V\)

\(Y = A \sin \left(\omega t +\phi_{0}\right)\) is the time-displacement equation of a SHM. At \(t=0\) the displacement of the particle is \(Y =\frac{ A }{2}\) and it is moving along negative \(x\) -direction. Then the initial phase angle \(\phi_{0}\) will be ...... .

From the statements given below :
\((A)\) The angular momentum of an electron in \(n^{\text {th }}\) orbit is an integral multiple of \(h\).
\((B)\) Nuclear forces do not obey inverse square law.
\((C)\) Nuclear forces are spin dependent.
\((D)\) Nuclear forces are central and charge independent.
\((E)\) Stability of nucleus is inversely proportional to the value of packing fraction. Choose the correct answer from the options given below :

Using Young's double slit experiment, a monochromatic light of wavelength \(5000\,\mathring A\) produces fringes of fringe width \(0.5 \,mm\). If another monochromatic light of wavelength \(6000\,\mathring A\) is used and the separation between the slits is doubled, then the new fringe width will be ............... \(mm\)