A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle \(60^o\) with ground level. But he finds the aeroplane right vertically above his position. If \(\upsilon \) is the speed of sound, speed of the plane is

An emf of \(20\; \mathrm{V}\) is applied at time \(\mathrm{t}=0\) to a circuit containing in series \(10\; \mathrm{mH}\) inductor and \(5 \;\Omega\) resistor. The ratio of the currents at time \(\mathrm{t}=\infty\) and at \(t=40\; s\) is close to : (Take \(e^{2}=7.389\) )

Velocity \((v)\) and acceleration \((a)\) in two systems of units \(1\) and \(2\) are related as \(V _{2}=\frac{ n }{ m ^{2}} v _{1}\) and \(a_{2}=\frac{a_{1}}{m n}\) respectively. Here \(m\) and \(n\) are constants. The relations for distance and time in two systems respectively are

A particle moving with kinetic energy \(E\) has de Broglie wavelength \(\lambda\). If energy \(\Delta \mathrm{E}\) is added to its energy, the wavelength become \(\frac {\lambda}{2} .\) Value of \(\Delta \mathrm{E},\) is 

The actual value of resistance \(R\), shown in the figure is \(30\,\Omega \). This is measured in an experiment as shown using the standard formula \(R = \frac{V}{I}\) where \(V\) and \(I\) are the readings of the voltmeter and ammeter, respectively. If the measured value of \(R\) is \(5\%\) less, then the internal resistance of the voltmeter is ................. \(\Omega\)

An electromagnetic wave of frequency \(1\times10^{14}\, hertz\) is propagating along \(z-\) axis. The amplitude of electric field is \(4\, V/m\) . lf \({\varepsilon_0}=\, 8.8\times10^{-12}\, C^2/Nm^2\) , then average energy density of electric field will be:

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to : [Boltzmans Constant \(k_B = 1.38\times10^{-23}\, J / K\) Avogadro number \(N_A = 6.02\times10^{26}\, / kg\) Radius of Earth \(: 6.4\times10^6\, m\) Gravitation acceleration on Earth \(= 10\, ms^{-2}\)]

In an experiment to find out the diameter of wire using screw gauge, the following observation were noted. \((a)\) Screw moves \(0.5\,mm\) on main scale in one complete rotation \((b)\) Total divisions on circular scale \(=50\) \((c)\) Main scale reading is \(2.5\,mm\) \((d)\) \(45^{\text {th }}\) division of circular scale is in the pitch line \((e)\) Instrument has \(0.03 \;mm\) negative error Then the diameter of wire is \(...........\,mm\)

A potential divider circuit is connected with a DC source of \(20 \mathrm{~V}\), a light emitting diode of glow in voltage \(1.8 \mathrm{~V}\) and a zener diode of breakdown voltage of \(3.2 \mathrm{~V}\). The length (PR) of the resistive wire is \(20 \mathrm{~cm}\). The minimum length of \(P Q\) to just glow the LED is _______ cm.

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

A resistor develops \(300 \,J\) of thermal energy in \(15 \,s\), when a current of \(2\, A\) is passed through it. If the current increases to \(3 \,A\), the energy developed in \(10\,\,s\)  is........\(J.\)

Imagine that the electron in a hydrogen atom is replaced by a muon \((\mu) .\) The mass of muon particle is \(207\) times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be ............. \(eV\)

Consider the nuclear fission \(Ne^{20} \to 2He^4 + C^{12}\) .Given that the binding energy / nucleon of \(Ne^{20}, He^4\) and \(C^{12}\) are, respectively, \(8.03\, MeV\), \(7.07\, MeV\), and \(7.86\, MeV\), identify the correct statement