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JEE Main 2020 Question Paper With Solution 08 Jan 2020 Shift 1 Memory BasedMiso Study
JEE Main 2020 Question Paper With Solution 08 Jan 2020 Shift 1 Memory Based, which helps you to understand the chapter in easy way also downaload sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
Current Affairs Notes for December MonthSOURAV DAS
🌟 Stay updated with the latest Current Affairs for December Month! 📅 Dr. Sourav Sir's Classes presents comprehensive Current Affairs Notes curated by experts to keep you ahead in your preparation. 📝 Get insights into crucial events, developments, and news from around the globe in a student-friendly format.
🔍 Dive deep into the significant happenings of December with our meticulously crafted notes, designed to aid your competitive exam preparations. From politics to economics, from science to sports, we've got you covered with all the essential topics you need to know.
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Competitive Mathematics Model Question Paper || Sourav Sir's ClassesSOURAV DAS
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JEE Main 2020 Question Paper With Solution 08 Jan 2020 Shift 1 Memory BasedMiso Study
JEE Main 2020 Question Paper With Solution 08 Jan 2020 Shift 1 Memory Based, which helps you to understand the chapter in easy way also downaload sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
Current Affairs Notes for December MonthSOURAV DAS
🌟 Stay updated with the latest Current Affairs for December Month! 📅 Dr. Sourav Sir's Classes presents comprehensive Current Affairs Notes curated by experts to keep you ahead in your preparation. 📝 Get insights into crucial events, developments, and news from around the globe in a student-friendly format.
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Competitive Mathematics Model Question Paper || Sourav Sir's ClassesSOURAV DAS
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CAT 2018 Slot 1 (Morning Session) Question Paper With Solution || Sourav Sir'...SOURAV DAS
The full form of CAT is the Common Admission Test. CAT is a computer-based examination of admission to a graduate management programme. The test includes three sections. QA (Quantitative Ability).
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Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
"Protectable subject matters, Protection in biotechnology, Protection of othe...
GATE - Graduate Aptitude Test in Engineering || Physics Question Paper 2016 || Sourav Sir's Classes
1. GATE 2016 General Aptitude - GA Set-2
1/3
Q. 1 – Q. 5 carry one mark each.
Q.1 The volume of a sphere of diameter 1 unit is ________ than the volume of a cube of side 1 unit.
(A) least (B) less (C) lesser (D) low
Q.2 The unruly crowd demanded that the accused be _____________ without trial.
(A) hanged (B) hanging (C) hankering (D) hung
Q.3 Choose the statement(s) where the underlined word is used correctly:
(i) A prone is a dried plum.
(ii) He was lying prone on the floor.
(iii) People who eat a lot of fat are prone to heart disease.
(A) (i) and (iii) only (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only
Q.4 Fact: If it rains, then the field is wet.
Read the following statements:
(i) It rains
(ii) The field is not wet
(iii) The field is wet
(iv) It did not rain
Which one of the options given below is NOT logically possible, based on the given fact?
(A) If (iii), then (iv). (B) If (i), then (iii).
(C) If (i), then (ii). (D) If (ii), then (iv).
Q.5 A window is made up of a square portion and an equilateral triangle portion above it. The base of
the triangular portion coincides with the upper side of the square. If the perimeter of the window is
6 m, the area of the window in m2
is ___________.
(A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88
2. GATE 2016 General Aptitude - GA Set-2
2/3
Q. 6 – Q. 10 carry two marks each.
Q.6 Students taking an exam are divided into two groups, P and Q such that each group has the same
number of students. The performance of each of the students in a test was evaluated out of 200
marks. It was observed that the mean of group P was 105, while that of group Q was 85. The
standard deviation of group P was 25, while that of group Q was 5. Assuming that the marks were
distributed on a normal distribution, which of the following statements will have the highest
probability of being TRUE?
(A) No student in group Q scored less marks than any student in group P.
(B) No student in group P scored less marks than any student in group Q.
(C) Most students of group Q scored marks in a narrower range than students in group P.
(D) The median of the marks of group P is 100.
Q.7 A smart city integrates all modes of transport, uses clean energy and promotes sustainable use of
resources. It also uses technology to ensure safety and security of the city, something which critics
argue, will lead to a surveillance state.
Which of the following can be logically inferred from the above paragraph?
(i) All smart cities encourage the formation of surveillance states.
(ii) Surveillance is an integral part of a smart city.
(iii) Sustainability and surveillance go hand in hand in a smart city.
(iv) There is a perception that smart cities promote surveillance.
(A) (i) and (iv) only (B) (ii) and (iii) only
(C) (iv) only (D) (i) only
Q.8 Find the missing sequence in the letter series.
B, FH, LNP, _ _ _ _.
(A) SUWY (B) TUVW (C) TVXZ (D) TWXZ
Q.9 The binary operation □ is defined as a □ b = ab+(a+b), where a and b are any two real numbers.
The value of the identity element of this operation, defined as the number x such that a □ x = a, for
any a, is .
(A) 0 (B) 1 (C) 2 (D) 10
3. GATE 2016 General Aptitude - GA Set-2
3/3
Q.10 Which of the following curves represents the function = ln(| | (| |)|
|) for | | < 2 ?
Here, represents the abscissa and represents the ordinate.
(A)
(B)
(C)
(D)
END OF THE QUESTION PAPER
4. GATE 2016 Physics
PH 1/10
Q. 1 – Q. 25 carry one mark each.
Q.1
Consider the linear differential equation .
xy
dx
dy
If ,
0
at
2
x
y then the value of y at x=2 is
given by
(A) 2
e (B) 2
2
e
(C) 2
e (D) 2
2e
Q.2 Which of the following magnetic vector potentials gives rise to a uniform magnetic field k
B ˆ
0 ?
(A) k
z
B ˆ
0 (B) j
x
B ˆ
0
(C)
j
x
i
y
B ˆ
ˆ
2
0
(D)
j
x
i
y
B ˆ
ˆ
2
0
Q.3 The molecule 2
17
O is
(A) Raman active but not NMR (nuclear magnetic resonance) active.
(B) Infrared active and Raman active but not NMR active.
(C) Raman active and NMR active.
(D) Only NMR active.
Q.4 There are four electrons in the 3d shell of an isolated atom. The total magnetic moment of the atom
in units of Bohr magneton is ________.
Q.5 Which of the following transitions is NOT allowed in the case of an atom, according to the electric
dipole radiation selection rule?
(A) 2s-1s (B) 2p-1s (C) 2p-2s (D) 3d-2p
Q.6 In the SU(3) quark model, the triplet of mesons
,
, 0
has
(A) Isospin = 0 , Strangeness = 0
(B) Isospin = 1 , Strangeness = 0
(C) Isospin = 1/2, Strangeness = +1
(D) Isospin = 1/2, Strangeness = -1
Q.7 The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a
steady current I is m. If this loop is changed to a circular shape with the same current I passing
through it, the magnetic dipole moment becomes
pm
. The value of p is ______.
Q.8 The total power emitted by a spherical black body of radius R at a temperature T is P1. Let P2 be the
total power emitted by another spherical black body of radius R/2 kept at temperature 2T. The ratio,
P1/P2 is _______. (Give your answer upto two decimal places)
5.
6. GATE 2016 Physics
PH 3/10
Q.17 The kinetic energy of a particle of rest mass 0
m is equal to its rest mass energy. Its momentum in
units of c
m0 , where c is the speed of light in vacuum, is _______. (Give your answer upto two
decimal places)
Q.18 The number density of electrons in the conduction band of a semiconductor at a given temperature
is 19
10
2 3
m
. Upon lightly doping this semiconductor with donor impurities, the number density
of conduction electrons at the same temperature becomes 20
10
4 3
m
. The ratio of majority to
minority charge carrier concentration is ________.
Q.19 Two blocks are connected by a spring of spring constant k . One block has mass m and the other
block has mass 2m. If the ratio k/m = 4 2
s
, the angular frequency of vibration ω of the two block
spring system in 1
s
is _______. (Give your answer upto two decimal places)
Q.20 A particle moving under the influence of a central force r
k
r
F
)
( (where r
is the position
vector of the particle and k is a positive constant) has non-zero angular momentum. Which of the
following curves is a possible orbit for this particle?
(A) A straight line segment passing through the origin.
(B) An ellipse with its center at the origin.
(C) An ellipse with one of the foci at the origin.
(D) A parabola with its vertex at the origin.
Q.21 Consider the reaction Mn
54
25 +
e Cr
54
24 + X . The particle X is
(A) γ (B) e
(C) n (D) π0
Q.22 The scattering of particles by a potential can be analyzed by Born approximation. In particular, if
the scattered wave is replaced by an appropriate plane wave, the corresponding Born approximation
is known as the first Born approximation. Such an approximation is valid for
(A) large incident energies and weak scattering potentials.
(B) large incident energies and strong scattering potentials.
(C) small incident energies and weak scattering potentials.
(D) small incident energies and strong scattering potentials.
Q.23 Consider an elastic scattering of particles in 0
l states. If the corresponding phase shift 0
is
0
90 and the magnitude of the incident wave vector is equal to
2 fm-1
then the total scattering
cross section in units of fm2
is _______.
Q.24 A hydrogen atom is in its ground state. In the presence of a uniform electric field ,
ˆ
0 z
E
E
the
leading order change in its energy is proportional to
n
E )
( 0 . The value of the exponent n is _______.
7. GATE 2016 Physics
PH 4/10
Q.25 A solid material is found to have a temperature independent magnetic susceptibility, .
C
Which
of the following statements is correct?
(A) If C is positive, the material is a diamagnet.
(B) If C is positive, the material is a ferromagnet.
(C) If C is negative, the material could be a type I superconductor.
(D) If C is positive, the material could be a type I superconductor.
Q. 26 – Q. 55 carry two marks each.
Q.26 An infinite, conducting slab kept in a horizontal plane carries a uniform charge density .
Another infinite slab of thickness t, made of a linear dielectric material of dielectric constant k, is
kept above the conducting slab. The bound charge density on the upper surface of the dielectric slab
is
(A)
k
2
(B)
k
(C)
k
k
2
)
2
(
(D)
k
k )
1
(
Q.27 The number of spectroscopic terms resulting from the S
L coupling of a 3p electron and a 3d
electron is _______.
Q.28 Which of the following statements is NOT correct?
(A) A deuteron can be disintegrated by irradiating it with gamma rays of energy 4 MeV.
(B) A deuteron has no excited states.
(C) A deuteron has no electric quadrupole moment.
(D) The 1
S0 state of deuteron cannot be formed.
Q.29 If 1
s
and 2
s
are the spin operators of the two electrons of a He atom, the value of 2
1 s
s
for the
ground state is
(A) 2
2
3
(B) 2
4
3
(C) 0 (D) 2
4
1
Q.30 A two-dimensional square rigid box of side L contains six non-interacting electrons at T = 0 K. The
mass of the electron is m. The ground state energy of the system of electrons, in units of 2
2
2
2mL
is
_______.
Q.31 An alpha particle is accelerated in a cyclotron. It leaves the cyclotron with a kinetic energy of 16
MeV. The potential difference between the D electrodes is 50 kilovolts. The number of revolutions
the alpha particle makes in its spiral path before it leaves the cyclotron is ______.
Q.32 Let be the component of a vector field ⃗, which has zero divergence. If ≡ / , the
expression for is equal to
(A) i
k
j V
(B) i
k
j V
(C) i
jV
2
(D) i
jV
2
8. GATE 2016 Physics
PH 5/10
Q.33 The direction of ∇
⃗ for a scalar field ( , , ) = − + at the point (1, 1,2) is
(A)
5
ˆ
2
ˆ k
j
(B)
5
ˆ
2
ˆ k
j
(C)
5
ˆ
2
ˆ k
j
(D)
5
ˆ
2
ˆ k
j
Q.34 z
and
,
y
x are the Pauli matrices. The expression x
y
y
x
2 is equal to
(A) z
i
3
(B) z
i
(C) z
i (D) z
i
3
Q.35 A particle of mass = 0.1 kg is initially at rest at origin. It starts moving with a uniform
acceleration 2
ms
ˆ
10
i
a
at = 0. The action of the particle, in units of J-s, at = 2 is
______. (Give your answer upto two decimal places)
Q.36 A periodic function ( ) of period 2 is defined in the interval (− < < ) as:
( ) =
−1, − < < 0
1, 0 < <
The appropriate Fourier series expansion for ( ) is
(A) ...]
5
/
)
5
(sin
3
/
)
3
(sin
[sin
/
4
)
(
x
x
x
x
f
(B) ...]
5
/
)
5
(sin
3
/
)
3
(sin
[sin
/
4
)
(
x
x
x
x
f
(C) ...]
5
/
)
5
(cos
3
/
)
3
(cos
[cos
/
4
)
(
x
x
x
x
f
(D) ...]
5
/
)
5
(cos
3
/
)
3
(cos
[cos
/
4
)
(
x
x
x
x
f
Q.37 Atoms, which can be assumed to be hard spheres of radius R, are arranged in an fcc lattice with
lattice constant a, such that each atom touches its nearest neighbours. Take the center of one of the
atoms as the origin. Another atom of radius r (assumed to be hard sphere) is to be accommodated at
a position (0, a/2, 0) without distorting the lattice. The maximum value of r/R is ________. (Give
your answer upto two decimal places)
Q.38 In an inertial frame of reference S, an observer finds two events occurring at the same time at co-
ordinates 0
1
x and .
2 d
x A different inertial frame S moves with velocity v with respect to S
along the positive x-axis. An observer in S also notices these two events and finds them to occur
at times 1
t and 2
t and at positions 1
x and ,
2
x respectively. If 1
2 t
t
t
, 1
2 x
x
x
and
2
2
v
1
1
c
, which of the following statements is true ?
(A) d
x
t
,
0 (B)
d
x
t
,
0
(C) d
x
c
d
t
,
v 2
(D)
d
x
c
d
t
,
v 2
9. GATE 2016 Physics
PH 6/10
Q.39 The energy vs. wave vector
k
E relationship near the bottom of a band for a solid can be
approximated as
4
2
)
(
)
( ka
B
ka
A
E
, where the lattice constant a = 2.1 Å. The values of A and
B are J,
10
2
.
3
and
J
10
3
.
6 20
19
respectively. At the bottom of the conduction band, the ratio
of the effective mass of the electron to the mass of free electron is _______. (Give your answer
upto two decimal places)
(Take =1.05x10-34
J-s, mass of free electron= 9.1x10-31
kg)
Q.40 The electric field component of a plane electromagnetic wave travelling in vacuum is given by
i
t
z
k
E
t
z
E ˆ
)
cos(
)
,
( 0
. The Poynting vector for the wave is
(A) j
t
z
k
E
c ˆ
)
(
cos
2
/ 2
2
0
0
(B) k
t
z
k
E
c ˆ
)
(
cos
2 2
2
0
0
(C) j
t
z
k
E
c ˆ
)
(
cos2
2
0
0
(D) k
t
z
k
E
c ˆ
)
(
cos2
2
0
0
Q.41 Consider a system having three energy levels with energies 0,
2 and ,
3 with respective
degeneracies of 2, 2 and 3. Four bosons of spin zero have to be accommodated in these levels such
that the total energy of the system is
10 . The number of ways in which it can be done is
________.
Q.42 The Lagrangian of a system is given by
constants.
are
and
,
where
,
cos
sin
2
1 2
2
2
2
g
l
m
mgl
ml
L
Which of the following is conserved?
(A)
2
sin
(B)
sin
(C)
sin
(D)
2
sin
Q.43 Protons and α-particles of equal initial momenta are scattered off a gold foil in a Rutherford
scattering experiment. The scattering cross sections for proton on gold and α-particle on gold are
p
and
respectively. The ratio p
is ________.
10. GATE 2016 Physics
PH 7/10
Q.44 For the digital circuit given below, the output X is
(A) C
B
A
(B) C)
(B
A
(C) C)
(B
A
(D) C)
(B
A
Q.45 The Fermi energies of two metals X and Y are 5 eV and 7 eV and their Debye temperatures are 170
K and 340 K, respectively. The molar specific heats of these metals at constant volume at low
temperatures can be written as 3
T
A
T
C X
X
X
V
and ,
3
T
A
T
C Y
Y
Y
V
where γ and A
are constants. Assuming that the thermal effective mass of the electrons in the two metals are same,
which of the following is correct?
(A) 8
,
5
7
Y
X
Y
X
A
A
(B)
8
1
,
5
7
Y
X
Y
X
A
A
(C)
8
1
,
7
5
Y
X
Y
X
A
A
(D) 8
,
7
5
Y
X
Y
X
A
A
Q.46 A two-level system has energies zero and E . The level with zero energy is non-degenerate, while
the level with energy E is triply degenerate. The mean energy of a classical particle in this system
at a temperature T is
(A) T
k
E
T
k
E
B
B
e
Ee
/
/
3
1
(B) T
k
E
T
k
E
B
B
e
Ee
/
/
1
(C) T
k
E
T
k
E
B
B
e
Ee
/
/
1
3
(D) T
k
E
T
k
E
B
B
e
Ee
/
/
3
1
3
A
B
C
X
11. GATE 2016 Physics
Q.47 A particle of rest mass M is moving along the positive x-direction. It decays into two photons 1
and 2
as shown in the figure. The energy of 1
is 1 GeV and the energy of 2
is 0.82 GeV. The
value of M (in units of GeV/c2
) is ________. (Give your answer upto two decimal places)
Q.48 If x and p are the x components of the position and the momentum operators of a particle
respectively, the commutator ]
,
[ 2
2
p
x is
(A) )
( px
xp
i
(B) )
(
2 px
xp
i
(C) )
( px
xp
i
(D) )
(
2 px
xp
i
Q.49 The x-y plane is the boundary between free space and a magnetic material with relative
permeability r
. The magnetic field in the free space is k
B
i
B z
x
ˆ
ˆ . The magnetic field in the
magnetic material is
(A) k
B
i
B z
x
ˆ
ˆ (B) k
B
i
B z
r
x
ˆ
ˆ
(C) k
B
i
B z
x
r
ˆ
ˆ
1
(D) k
B
i
B z
x
r
ˆ
ˆ
Q.50 Let m
l, be the simultaneous eigenstates of 2
L and z
L . Here L
is the angular momentum
operator with Cartesian components ( )
,
, z
y
x L
L
L , l is the angular momentum quantum number
and m is the azimuthal quantum number. The value of is
1
,
1
)
(
0
,
1
y
x iL
L
(A) 0 (B) (C)
2 (D)
3
Q.51 For the parity operator P, which of the following statements is NOT true?
(A) = (B) P
P
2
(C) I
P
2
(D) =
12. GATE 2016 Physics
Q.52 For the transistor shown in the figure, assume VBE = 0.7 V and βdc = 100. If Vin = 5V, Vout (in Volts)
is _________. (Give your answer upto one decimal place)
Q.53 The state of a system is given by
3
2
1 3
2
where 1
, 2
and 3
form an orthonormal set. The probability of finding the system in the
state 2
is ________. (Give your answer upto two decimal places)
Q.54 According to the nuclear shell model, the respective ground state spin-parity values of O
15
8 and
O
17
8 nuclei are
(A)
2
1
,
2
1
(B)
2
5
,
2
1
(C)
2
5
,
2
3
(D)
2
1
,
2
3
13. GATE 2016 Physics
PH 10/10
Q.55 A particle of mass m and energy E, moving in the positive x direction, is incident on a step potential
at x = 0, as indicated in the figure. The height of the potential is V0, where V0 > E. At
0
where
, 0
0
x
x
x , the probability of finding the electron is 1/e times the probability of finding
it at x = 0. If 2
0 )
(
2
E
V
m
, the value of x0 is
(A)
2
(B)
1
(C)
2
1
(D)
4
1
END OF THE QUESTION PAPER
x = x0
V0
E
x = 0