GATE PH format:nat PYQs & Answers — Page 18

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Questions 171–180 of 182. Imported answers require independent review unless marked reviewed.

Topic practice 182 questionsPage 18 of 19

Consider a metal with free electron density of

. The lowest frequency electromagnetic radiation to which this metal is transparent is

. If this metal had a free electron density of

instead, the lowest frequency electromagnetic radiation to which it would be transparent is ________

. (up to two decimal places).

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An object travels along the x-direction with velocity

in a frame

. An observer in a frame

sees the same object travelling with velocity

. The relative velocity of

with respect to

in units of

is ________. (up to two decimal places).

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The integral

is equal to ________. (up to two decimal places).

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The imaginary part of an analytic complex function is

. The real part of the function is zero at the origin. The value of the real part of the function at

is ________. (up to two decimal places).

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A uniform solid cylinder is released on a horizontal surface with speed 5 m/s without any rotation (slipping without rolling). The cylinder eventually starts rolling without slipping. If the mass and radius of the cylinder are 10 gm and 1 cm respectively, the final linear velocity of the cylinder is ________ m/s. (up to two decimal places).

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The energy density and pressure of a photon gas are given by

and

, where

is the temperature and

is the radiation constant. The entropy per unit volume is given by

. The value of

is ________. (up to two decimal places).

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The

decays at rest to

and

. Assuming the neutrino to be massless, the momentum of the neutrino is ________ MeV/c. (up to two decimal places) (

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A person weighs

at Earth's north pole and

at the equator. Treating the Earth as a perfect sphere of radius 6400 km, the value

is ________. (up to two decimal places). (Take

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For the transistor amplifier circuit shown below with

, and

. Neglecting the emitter diode resistance, the input impedance of the amplifier looking into the base for small ac signal is ________ k

. (up to two decimal places).

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Consider an ideal operational amplifier as shown in the figure below with

. For an applied input voltage

, the current passing through

is ________

. (up to two decimal places).

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GATE PH format:nat PYQs

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