GATE CY branch:cy PYQs & Answers — Page 13

Questions 121–130 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 13 of 65

Wavefunctions and energies for a particle confined in a cube box are

and

, respectively. The functions

, and

are written as linear combinations of

. Among these functions, the eigenfunction(s) of the Hamiltonian operator for this particle is/are

Your answerSelect all correct options. You can choose more than one.

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If a particle’s state function is an eigenfunction of the operator

with eigenvalue

, then the possible eigenvalue(s) of the operator

for the same state function is/are

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An archaeological specimen containing

gives 45 counts per gram of carbon in 5 minutes. A specimen of freshly cut wood gives 20 counts per gram of carbon per minute. The counter used recorded a background count of 5 counts per minute in the absence of any

containing sample. The age of the specimen is _____ years (in integer).\n\n[Note:

= 5730 years]

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In the following reaction, 13.4 grams of aldehyde P gave a diastereomer mixture of alcohols Q and R in a ratio of 2:1.

If the yield of the reaction is 80%, then the amount of Q (in grams) obtained is _____ (in integer).

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The kinetic energies of an electron (

) and a proton (

) are

and

, respectively. Given that mass of a proton is 1836 times that of an electron, the ratio of their de Broglie wavelengths (

) is_____ (rounded off to two decimal places).

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If a molecule emitting a radiation of frequency

Hz approaches an observer with a relative speed of

m s

, then the observer detects a frequency of _____

Hz. (rounded off to three decimal places)\n\n[Given: Speed of light

m s

]

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The mean energy of a molecule having two available energy states at

J and

J at 300 K is _____

J (rounded off to two decimal places).\n\n[Given: Boltzmann constant (

) =

J K

]

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For the cell reaction,\n\n

\n\nThe standard cell potential is

V, and

V K

. The standard enthalpy change of the reaction (

) at 298 K is

kJ mol

. The value of

is _____ (rounded off to two decimal places).\n\n[Given: Faraday constant

C mol

]

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Consider a Carnot engine with a hot source kept at 500 K. From the hot source, 100 J of energy (heat) is withdrawn at 500 K. The cold sink is kept at 300 K. The efficiency of the Carnot engine is _____ (rounded off to one decimal place).

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The Lineweaver-Burk plot for an enzyme obeying the Michaelis-Menten mechanism is given below.

\n\nThe slope of the line is

s, and the y-intercept is

mol

L s. The value of the Michaelis constant (

) is____

mol L

(in integer).\n\n[Note:

is the initial rate, and

is the substrate concentration]

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GATE CY branch:cy PYQs

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