GATE PH format:mcq PYQs & Answers — Page 16

Questions 151–160 of 380. Imported answers require independent review unless marked reviewed.

Consider two non-identical spin

particles labelled 1 and 2 in the spin product state

. The Hamiltonian of the system is

where

and

are the spin operators of particles 1 and 2, respectively, and

is a constant with appropriate dimensions. What is the expectation value of

in the above state?

Your answerChoose one option.

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A spin

particle is in a spin up state along the

-axis (with unit vector

) and is denoted as

. What is the probability of finding the particle to be in a spin up state along the direction

, which lies in the

-plane and makes an angle

with respect to the positive

-axis, if such a measurement is made?

Your answerChoose one option.

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Different spectral lines of the Balmer series (transitions

, with

being the principal quantum number) fall one at a time on a Young’s double slit apparatus. The separation between the slits is

and the screen is placed at a constant distance from the slits. What factor should

be multiplied by to maintain a constant fringe width for various lines, as

takes different allowed values?

Your answerChoose one option.

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You should ________ when to say ________.

Your answerChoose one option.

no / no

no / know

know / know

know / no

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Two straight lines pass through the origin

. One of them passes through the point

and the other passes through the point

. What is the area enclosed between the straight lines in the interval

on the

-axis?

Your answerChoose one option.

0.5

1.0

1.5

2.0

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and

is 50% more than

, what is the ratio

Your answerChoose one option.

2 : 15

16 : 15

1 : 5

16 : 45

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Given the statements:

• P is the sister of Q. • Q is the husband of R. • R is the mother of S. • T is the husband of P.

Based on the above information, T is ______ of S.

Your answerChoose one option.

the grandfather

an uncle

the father

a brother

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In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is

Your answerChoose one option.

Area of SPQT = Area of RUVZ = Area of PXWR

Area of SPQT = Area of PXWR − Area of RUVZ

Area of PXWR = Area of SPQT − Area of RUVZ

Area of PXWR = Area of RUVZ − Area of SPQT

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Healthy eating is a critical component of healthy aging. When should one start eating healthy? It turns out that it is never too early. For example, babes who start eating healthy in the first year are more likely to have better overall health as they get older.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

Your answerChoose one option.

Healthy eating is important for those with good health conditions, but not for others

Eating healthy can be started at any age, earlier the better

Eating healthy and better overall health are more correlated at a young age, but not older age

Healthy eating is more important for adults than kids

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P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year.

If at the end of that investment year, Q receives

of the total profit, what is the value of

(in ₹)?

Your answerChoose one option.

250

300

687

843

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GATE PH format:mcq PYQs

Question 52

Question 53

Question 54

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Question 7