The circuit shown below is working as a \(8\; \mathrm{V}\;dc\) regulated voltage source. When \(12 \;\mathrm{V}\) is used as input, the power dissipated (in \(\mathrm{mW}\) ) in each diode is (considering both zener diodes are identical)

The speed of sound in oxygen at \(S.T.P. \)will be approximately _______. (Given, \(\mathrm{R}=8.3 \mathrm{JK}^{-1}, \gamma=1.4\) )

A particle moves from the point \(\left( {2.0\hat i + 4.0\hat j} \right)\,m\), at \(t = 0\) with an initial velocity \(\left( {5.0\hat i + 4.0\hat j} \right)\,m{s^{ - 1  }}\). It is acted upon by a constant force which produces a constant acceleration \(\left( {4.0\hat i + 4.0\hat j} \right)\,m{s^{ - 2}}\). What is the distance of the particle from the origin at time \(2\,s\)

A projectile is projected at \(30^{\circ}\) from horizontal with initial velocity \(40\,ms ^{-1}\). The velocity of the projectile at \(t =2\,s\) from the start will be \(........\) (Given \(g =10\,m / s ^2\) )

A particular hydrogen - like ion emits the radiation of frequency \(3 \times 10^{15} \mathrm{~Hz}\) when it makes transition from \(n=2\) to \(n=1\). The frequency of radiation emitted in transition from \(n=3\) to \(n=1\) is \(\frac{x}{9} \times 10^{15} \mathrm{~Hz}\), when \(x=\) = _____.

A \(100 \,\Omega\) resistance, a \(0.1\, \mu {F}\) capacitor and an inductor are connected in series across a \(250 \,{V}\) supply at variable frequeny. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is \(60\, {Hz}\). (In \({H}\))

The threshold frequency of metal is \(f_0\). When the light of frequency \(2 f_0\) is incident on the metal plate, the maximum velocity of photoelectron is \(v_1\). When the frequency of incident radiation is increased to \(5 f _0\). the maximum velocity of photoelectrons emitted is \(v_2\). The ratio of \(v_1\) to \(v_2\) is:

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A :\) Photodiodes are preferably operated in reverse bias condition for light intensity measurement. Reason \(R\) : The current in the forward bias is more than the current in the reverse bias for a \(p - n\) junction diode. In the light of the above statement, choose the correct answer from the options given below :

The value of the resistor, \(R_S\), needed in the \(dc\) voltage regulator circuit shown here, equals

Light of wavelength \(550\, nm\) falls normally on a slit of width \(22.0 \times 10^{-5}\,cm\). The angular position of the second minima from the central maximum will be (in radians)

In a coil of resistance \(8 \Omega\), the magnetic flux due to an external magnetic field varies with time as \(\phi=\frac{2}{3}\left(9- t ^{2}\right)\). The value of total heat produced in the coil, till the flux becomes zero, will be \(....J\)

An experiment takes \(10\, minutes\) to raise the temperature of water in a container from \(0\,^oC\) to \(100\,^oC\) and another \(55\, minutes\) to convert it totally into steam by a heater supplying heat at a uniform rate . Neglecting the specific heat of the container and taking specific heat of water to be \(1\, cal / g\,^oC\), the heat of vapourization according to this experiment will come out to be ........ \(cal/g\)