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GATE (Graduate Aptitude Test in Engineering) Physics is an online examination conducted to get admission in M-Tech (Masters in Technology), ME (Master of Engineering ) and PhD at IITs (Indian Institutes of Technology), NITs (National Institutes of Technology), IIITs (Indian Institutes of Information Technology) and other universities in India. GATE exam is jointly conducted by IIT Bombay, IIT Delhi, IIT Guwahati, IIT Kanpur, IIT Kharagpur, IIT Madras, IIT Roorkee and Indian Institute for Science, Bangalore (IISC Bangalore). The exam is divided into two different parts General Aptitude (GA) and Candidate’s Selected Subject (Core Subjects). GATE Physics online mock tests help candidates in preparing for the GATE exam. By attempting GATE online mock tests candidates get familiar with the pattern of actual question paper. BrPaper provides all GATE question papers completely free. Here you can practice free online mock tests of complete exam of GATE Physics. We advise candidates to solve the online GATE Physics mock tests to get good marks in the exam. Start practicing PhysicsGATE 2020 Mock tests here online for free

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Category: GATE Physics 2020 General Aptitude

Question 1:

He is known for his unscrupulous ways. He always sheds___________ tears to deceive people.

fox\'s

crocodile\'s

crocodile

fox

Category: GATE Physics 2020 General Aptitude

Question 2:

Jofra Archer, the England fast bowler, is ________ than accurate.

more fast

faster

less faster

more faster

Category: GATE Physics 2020 General Aptitude

Question 3:

Define [x] as the greatest integer less than or equal to x, for each

x \in (- \infty, \infty) . If y = [x]

, then area under y for

x \in [1, 4]

is ________.

Category: GATE Physics 2020 General Aptitude

Question 4:

P, Q, R, and S are to be uniquely coded using

α and β .

If P is coded as

αα and Q as αβ,

then R and S, respectively, can be coded as ____________.

A	$βα and αβ$	B	$ββ and αα$
C	$αβ and ββ$	D	$βα and ββ$

Category: GATE Physics 2020 General Aptitude

Question 5:

Select a graph that schematically represents BOTH undefined properly in the interval undefined for integer values of m, where m>1.

A		B
C		D

Category: GATE Physics 2020 General Aptitude

Question 6:

Select the word that fits the analogy: Build: Building: : Grow: ____________

Grown

Grew

Growth

Growed

Category: GATE Physics 2020 General Aptitude

Question 7:

I do not think you know the case well enough to have opinions. Having said that, I agree with your other point. Was does the phase "having said that" mean in the given text?

as opposed to what I have said

despite what I have said

in addition to what I have said

contrary to what I have said

Category: GATE Physics 2020 General Aptitude

Question 8:

Crowdfunding deals with the mobilization of funds for a project from a large number of people, who would be willing to invest a smaller amount through web-based platforms in the project. Based on the above paragraph, which of the following is correct about crowdfunding?

funds raised through unwilling contributions on web-based platforms

funds raised through large contributions on web-based platforms

funds raised through coerced contributions on web-based platforms

funds raised through voluntary contributions on web-based platforms

Category: GATE Physics 2020 General Aptitude

Question 9:

The sum of the first n terms in the sequence 8, 88, 888, 8888,... is ____________.

A	$\frac{81}{80} (10^{n} - 1) + \frac{9}{8} n$	B	$\frac{81}{80} (10^{n} - 1) - \frac{9}{8} n$
C	$\frac{81}{80} (10^{n} - 1) + \frac{8}{9} n$	D	$\frac{81}{80} (10^{n} - 1) - \frac{8}{9} n$

Category: GATE Physics 2020 General Aptitude

Question 10:

The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q< R, and S. The average of success rates (in percentage) of these four schools is ______________.

58.5%

58.8%

59.0%

59.3%

Category: GATE Physics 2020

Question 11:

Which one of the following is a solution of

\frac{d^{2} u (x)}{d x^{2}} = k^{2} u (x), for k real ?

A	$e^{- k x}$	B	$\sin k x$
C	$\cos k x$	D	$\sinh x$

Category: GATE Physics 2020

Question 12:

A real, invertible 3x3 matrix M has eigenvalues

λ_{1}, (i = 1, 2, 3)

and the corresponding eigenvectors are

e_{1} >, (i = 1, 2, 3)

respectively. Which one of the following is correct?

A	$M e_{i} > = \frac{1}{λ_{1}} e_{i} >, f o r i = 1, 2, 3$	B	$M^{- 1} e_{i} > = \frac{1}{λ_{1}} e_{i} >, f o r i = 1, 2, 3$
C	$M^{- 1} e_{i} > = λ_{i} e_{i} >, f o r i = 1, 2, 3$	D	The eigenvalues of M and $M^{- 1}$ are not related

Category: GATE Physics 2020

Question 13:

A quantum particle is subject to the potential

V (x) = \{\begin{matrix} \infty, & x \leq - \frac{a}{2} \\ 0, & 1 - \frac{a}{2} < x > \frac{a}{2} \\ \infty, & x \geq \frac{a}{2} . \end{matrix}

The ground state wave function of the particle is proportional to

A	$\sin [\frac{πx}{2 a}]$	B	$\sin [\frac{πx}{a}]$
C	$\cos [\frac{πx}{2 a}]$	D	$\cos [\frac{πx}{a}]$

Category: GATE Physics 2020

Question 14:

Let

\hat{a} a n d {\hat{a}}^{+},

respectively denote the lowering and raising operators of a one-dimensional simple harmonic oscillator. oscillator. Let

n >

be the energy eigenstate of the simple harmonic oscillator. Given that

n >

is also an eigenstate of

{\hat{a}}^{+} {\hat{a}}^{+} \hat{a} \hat{a}

, the corresponding eigenvalue is

A	$n (n - 1)$	B	$n (n + 1)$
C	${(n + 1)}^{2}$	D	$n^{2}$

Category: GATE Physics 2020

Question 15:

Which one of the following is a universal logic gate?

AND

NOT

NAND

Category: GATE Physics 2020

Question 16:

Which one of the following is the correct binary equivalent of the hexadecimal F6C?

0110 1111 1100

1111 0110 1100

1100 0110 1111

0110 1100 0111

Category: GATE Physics 2020

Question 17:

The total angular momentum j of the ground state of

the O_{8}^{17}

nucleus is

A	$\frac{1}{2}$	B	$1$
C	$\frac{3}{2}$	D	$\frac{5}{2}$

Category: GATE Physics 2020

Question 18:

A particle X is produced in the process

π^{+} + p \to K^{+} + X

via the strong interaction. If the quark content of the

K^{=} i s u \bar{s}

, the quark content of X is

A	$c \bar{s}$	B	$u u d$
C	$u u s$	D	$u \bar{d}$

Category: GATE Physics 2020

Question 19:

A medium

(ε_{r} > 1, μ_{r} = 1, σ > 0)

is semi-transparent to an electromagnetic wave when

A	Conduction current >> Displacement current	B	Conduction current << Displacement current
C	Conduction current = Displacement current	D	Both Conduction current and Displacement current are zero

Category: GATE Physics 2020

Question 20:

A particle is moving in a central force field given by

\vec{F} = - \frac{k}{r^{3}} \hat{r,} w h e r e \hat{r}

is the unit vector pointing away from the center of the field. The potential energy of the particle is given by

A	$\frac{k}{r^{2}}$	B	$\frac{k}{2 r^{2}}$
C	$- \frac{k}{r^{2}}$	D	$- \frac{k}{2 r^{2}}$

Category: GATE Physics 2020

Question 21:

Choose the correct statement related to the Fermi energy

(E_{F})

and the chemical potential (μ) of metal.

A	$μ = E_{F} o n l y a t 0 K$	B	$μ = E_{F} a t f i n i t e t e m p e r a t u r e$
C	$μ < E_{F} a t 0 K$	D	$μ > E_{F} f i n i t e t e m p e r a t u r e$

Category: GATE Physics 2020

Question 22:

Consider a diatomic molecule formed by identical atoms. If

E_{v} a n d E_{e}

represent the energy of the vibrational nuclear motion and electronic motion respectively, then in terms of the electronic mass m and nuclear mass

M, \frac{E_{V}}{E_{e}}

is proportional to

A	${(\frac{m}{M})}^{1 / 2}$	B	$\frac{m}{M}$
C	${(\frac{m}{M})}^{3 / 2}$	D	${(\frac{m}{M})}^{2}$

Category: GATE Physics 2020

Question 23:

Which one of the following relations determines the manner in which the electric field lines are refracted across the interface between two dielectric media having dielectric constants undefined (see figure)?

A	undefined	B	undefined
C	undefined	D	undefined

Category: GATE Physics 2020

Question 24:

\vec{E} and \vec{B}

are the electric and magnetic fields respectively, then

\vec{E} . \vec{B}

odd under parity and even under time reversal

even under parity and odd under time reversal

odd under parity and odd under time reversal

even under parity and even under time reversal

Category: GATE Physics 2020

Question 25:

A small disc is suspended by a fiber such that it is free to rotate about the fiber axis (see figure). For small angular deflections, the Hamiltonian for the disc is given by undefined , where I is the moment of inertia and α is the restoring torque per unit deflection. The disc is subject to angular deflections (θ) due to thermal collisions from the surrounding gas at temperature undefined is the momentum conjugate to θ. The average and the root-mean square angular deflection, undefined respectively are

A	undefined	B	undefined
C	undefined	D	undefined

Category: GATE Physics 2020

Question 26:

As shown in the figure, an ideal gas is confined to chamber A of an insulated container, with vacuum in chamber B. When the plug in the wall separating the chambers A and B is removed, the gas fills both the chambers. Which one of the following statements is true?

The temperature of the gas remains unchanged

Internal energy of the gas decreases

Temperature of the gas decrease as it expands to fill the space in chamber B

Internal energy of the gas increases as its atoms have more space to move around

Category: GATE Physics 2020

Question 27:

Particle A with angular momentum

j = \frac{3}{2}

decays into particles B and C with angular momenta

j_{1} a n d j_{2}

, respectively. If

\frac{3}{2}, \frac{3}{2} >_{A} = α 1, 1 >_{B} \otimes \frac{1}{2}, \frac{1}{2} >_{c},

the value of α is ________.

0 to 10

1 to 1

2 to 2

3 to 3

Category: GATE Physics 2020

Question 28:

Far from the Earth, the Earth's magnetic fields can be approximated as due to a bar magnet of magnetic pole strength

4 x 10^{14}

Am. Assume this magnetic fields is generated by a current carrying loop encircling the magnetic equator. The current required to do so is about

4 x 10^{n}

A, where n is an integer. The value of n is __________. (Earth 's circumference:

4 x 10^{7}

5 to 5

6 to 6

7 to 7

8 to 8

Category: GATE Physics 2020

Question 29:

The number of distinct ways the primitive unit cell can be constructed for the two dimensional lattice as shown in the figure is ________.

2 to 2

3 to 3

4 to 4

5 to 5

Category: GATE Physics 2020

Question 30:

A hydrogenic atom is subjected to a strong magnetic field. In the absence of spin-orbit coupling, the number of doubly degenerate states created out of the d-level is ________.

1 to 1

2 to 2

3 to 3

4 to 4

Category: GATE Physics 2020

Question 31:

A particle Y undergoes strong decay

Y \to π^{-} + π^{-} .

The isospin of Y is_______.

2 to 2

4 to 4

6 to 6

8 to 8

Category: GATE Physics 2020

Question 32:

For a complex variable z and the contour

c : |z| = 1

taken in the counter clockwise direction,

\frac{1}{2 π i} \oint_{c} (z - \frac{2}{z} + \frac{3}{z^{2}}) d z =________.

-2 to -2

-2 to 0

0 to 2

2 to 2

Category: GATE Physics 2020

Question 33:

Let p be the momentum conjugate to the generalized coordinate q. If the transformation

Q = \sqrt{2} q^{m} \cos p P = \sqrt{2} q^{m} \sin p

is canonical, then m =__________.

0.1 to 0.1

0.3 to 0.3

0.5 to 0.5

0.7 to 0.7

Category: GATE Physics 2020

Question 34:

A conducting sphere of radius 1 m is placed in air. The maximum number of electrons that can be put on the sphere to avoid electrical breakdown is about

7 x 10^{n}

, where n is an integer. The value of n is __________. Assume: Breakdown electric fields strength in air is

|E| = 3 x 10^{6} V / m

Permittivity of free space

ε_{0} = 8.85 x 10^{- 12} F / m

Electron charge e

e = 1.60 x 10^{- 19} C

11 to 12

12 to 13

13 to 14

14 to 15

Category: GATE Physics 2020

Question 35:

If a particle is moving along a sinusoidal curve, the number of degrees of freedom of the particle is ________.

0 to 0

1 to 1

2 to 2

3 to 3

Category: GATE Physics 2020

Question 36:

The product of eigenvalues of

(\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix})

-1

Category: GATE Physics 2020

Question 37:

Let

e_{1} > \equiv (\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}), e_{2} > \equiv (\begin{matrix} 1 \\ 1 \\ 0 \end{matrix}) a n d e_{3} \equiv (\begin{matrix} 1 \\ 1 \\ 1 \end{matrix}) . L e t S = \{e_{1} >, |e_{2} >,| e_{3} >\} . L e t ℝ^{3} denote

the three-dimensional real vector space. Which one of the following is correct?

A	S is an orthonormal set	B	S is a linearly dependent set
C	S is a basis for $ℝ^{3}$	D	$\sum_{i = 1}^{3} \|e_{i} > < e_{i}\| = (\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix})$

Category: GATE Physics 2020

Question 38:

{\hat{S}}_{x}

denotes the spin operator defined as

{\hat{S}}_{x} = \frac{h}{2} (\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}) .

Which one of the following is correct?

A	The eigenstates of spin operator ${\hat{S}}_{x} a r e ↑ >_{x} \equiv (\begin{matrix} \begin{matrix} 1 \\ 0 \end{matrix} \end{matrix}) and ↓ >_{x} \equiv (\begin{matrix} 0 \\ 1 \end{matrix})$
B	The eigenstates of spin operator ${\hat{S}}_{x} a r e ↑ >_{x} \equiv \frac{1}{\sqrt{2}} (\begin{matrix} \begin{matrix} 1 \\ - 1 \end{matrix} \end{matrix}) and ↑ >_{x} \equiv \frac{1}{\sqrt{2}} (\begin{matrix} 1 \\ 1 \end{matrix})$
C	In the spin state $\frac{1}{2} (\begin{matrix} 1 \\ \sqrt{3} \end{matrix})$ , upon the measurement of ${\hat{S}}_{x}$ , the probability for obtaining $↑ >_{x} i s \frac{1}{4}$
D	In the spin state $\frac{1}{2} (\begin{matrix} 1 \\ \sqrt{3} \end{matrix})$ , upon the measurement of ${\hat{S}}_{x}$ , the probability for obtaining $↑ >_{x} i s \frac{2 + \sqrt{3}}{4}$

Category: GATE Physics 2020

Question 39:

The input voltage undefined to the circuit shown in the figure is 2 cos(100t) V. The output voltage undefined is 2 cos undefined V. If R = 1 kΩ, the value of C (in μF) is

0.1

100

Category: GATE Physics 2020

Question 40:

Consider a 4-bit counter constructed out of four flip-flops. It is formed by connecting the J and K inputs to logic high and feeding the Q output to the clock input of the following flip-flop (see the figure). The input signal to the counter is series of square pulses and the change of state is triggered by the falling edge. At time undefined the output are in logic low state undefined . Then at undefined logic state of the output is

A	undefined	B	undefined
C	undefined	D	undefined

Category: GATE Physics 2020

Question 41:

Consider the Lagrangian

L = a {(\frac{d x}{d t})}^{2} + b {(\frac{d y}{d t})}^{2} + c x y, w h e r e a, b a n d c a r e c o n s \tan t s . I f p_{x} a n d p_{y}

are the momenta conjugate to the coordinates x and y respectively, then the Hamiltonian is

A	$\frac{p_{x}^{2}}{4 a} + \frac{p_{y}^{2}}{4 b} - c x y$	B	$\frac{p_{x}^{2}}{2 a} + \frac{p_{y}^{2}}{2 b} - c x y$
C	$\frac{p_{x}^{2}}{2 a} + \frac{p_{y}^{2}}{2 b} + c x y$	D	$\frac{p_{x}^{2}}{a} + \frac{p_{y}^{2}}{b} + c x y$

Category: GATE Physics 2020

Question 42:

Which one of the following matrices does NOT represent a proper rotation in a plane ?

A	$(\begin{matrix} - \sin θ & \cos θ \\ - \cos θ & - \sin θ \end{matrix})$	B	$(\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix})$
C	$(\begin{matrix} \sin θ & \cos θ \\ - \cos θ & \sin θ \end{matrix})$	D	$(\begin{matrix} - \sin θ & \cos θ \\ - \cos θ & \sin θ \end{matrix})$

Category: GATE Physics 2020

Question 43:

A uniform magnetic field

\vec{B} = B_{0} \hat{y}

exists in an inertial frame K. A perfect conducting sphere moves with a constant velocity undefined with respect to this inertial frame. The rest frame of the sphere is K' (see figure). The electric and magnetic fields in K and K' are related as undefined The induced surface charge density on the sphere (to the lowest order in v/c) in the frame K' is

A	maximum along z'	B	maximum along y'
C	maximum along x'	D	uniform over the sphere

Category: GATE Physics 2020

Question 44:

A charge q moving with uniform speed enters a cylindrical region in free space at t = 0 and exits the region at t = τ (see figure). Which one of the following options best describes the time dependence of the total electric flux φ(t), through the entire surface of the cylinder?

A		B
C		D

Category: GATE Physics 2020

Question 45:

Consider a one-dimensional non-magnetic crystal with one atom per unit cell. Assume that the valence electrons (i) do not interact with each other and (ii) interact weakly with the ions. If n is the number of valence electrons per unit cell, then at 0 K,

the crystal is metallic for any value of n

the crystal is non-metallic for any value of n

the crystal is metallic for even values of n

the crystal is metallic for odd values of n

Category: GATE Physics 2020

Question 46:

According to the Fermi gas model of the nucleus, the nucleus, the nucleons move in a sphere volume of radius

R (= R_{0} A^{\frac{1}{3}},

where A is the mass number and

R_{0}

is an empirical constant with the dimensions of length). The Fermi energy of the nucleus

E_{F}

is proportional to

A	$R_{0}^{2}$	B	$\frac{1}{R_{0}}$
C	$\frac{1}{R_{0}^{2}}$	D	$\frac{1}{R_{0}^{3}}$

Category: GATE Physics 2020

Question 47:

Consider a two dimensional crystal with 3 atoms in the basis. The number of allowed optical branches (n) and acoustic branches (m) due to the lattice vibrations are

(n, m)=(2, 4)

(n, m)=(3, 3)

(n, m)=(4, 2)

(n, m)=(1, 5)

Category: GATE Physics 2020

Question 48:

The internal energy U of a system is given by

U (S, V) = λ V^{- 2 / 3} S^{2}

, where

λ

is a constant of appropriate dimensions; V and S denote the volume and entropy, respectively. Which one of the following gives the correct equations of state of the system?

A	$\frac{P V^{1 / 3}}{T^{2}} = c o n s \tan t$	B	$\frac{P V}{T^{1 / 3}} = c o n s \tan t$
C	$\frac{P}{V^{1 / 3} T} = c o n s \tan t$	D	$\frac{P V^{2 / 3}}{T} = c o n s \tan t$

Category: GATE Physics 2020

Question 49:

The potential energy of a particle of mass m is given by

U (x) = a \sin (k^{2} x - π / 2), a > 0, k^{2} > 0 .

The angular frequency of small oscillations of the particle about x = 0 is

A	$k^{2} \sqrt{\frac{2 a}{m}}$	B	$k^{2} \sqrt{\frac{a}{m}}$
C	$k^{2} \sqrt{\frac{a}{2 m}}$	D	$2 k^{2} \sqrt{\frac{a}{m}}$

Category: GATE Physics 2020

Question 50:

The radial wave function of a particle in a central potential is given by

R (r) = A \frac{r}{a} e x p (- \frac{r}{2 a}),

where A is the normalization constant and a is positive constant of suitable dimensions. If γα is the most probable distance of the particle from the force center, the value of γ is___________.

1 to 4

2 to 4

3 to 4

4 to 4

Category: GATE Physics 2020

Question 51:

A free particle of mass M is located in a three-dimensional cubic potential well with impenetrable walls. The degeneracy of the fifth excited state of the particle is _________.

3 to 3

6 to 6

9 to 9

12 to 12

Category: GATE Physics 2020

Question 52:

Consider the circuit given in the figure. Let the forward voltage drop across each diode be 0.7 V. The current 1 (in mA) through the resistor is _____________.

2 to 2

4 to 4

6 to 6

8 to 8

Category: GATE Physics 2020

Question 53:

Let

u^{μ}

denote the 4-velocity of a relativistic particle whose square

u^{μ} u_{μ} = 1 . If ε_{μ v p σ}

is the Levi-Civita tensor then value of

ε_{μ v p σ} u^{μ} u^{v} u^{p} u^{σ}

is __________.

0 to 0

0 to 1

0 to 2

0 to 3

Category: GATE Physics 2020

Question 54:

Consider a simple cubic monoatomic Bravais lattice which has a basis with vectors

{\vec{r}}_{1} = 0, {\vec{r}}_{2} = \frac{α}{4} (\hat{x} + \hat{y} + \hat{z}), α

is the lattice parameter. The Bragg reflection is observed due to the change in the wave vector between the incident and the scattered beam as given by

\vec{K} = n_{1} {\vec{G}}_{1} + n_{2} {\vec{G}}_{2} + n_{3} {\vec{G}}_{3}

, where

{\vec{G}}_{1}, {\vec{G}}_{2}, a n d {\vec{G}}_{3}

are primitive reciprocal lattice vectors. For

n_{1} = 3 n_{2} = 3 and n_{3} = 2

, the geometrical structure factor is ____________.

0 to 0

0 to 2

2 to 2

-2 to -2

Category: GATE Physics 2020

Question 55:

A plane electromagnetic wave of wavelength λ is incident on a circular loop of conducting wire. The loop radius is

a (a < < λ)

. The angle (in degrees), made by the Poynting vector with normal to the plane of the loop to generate a maximum induced electrical signal, is ________.

-270 to -270 or -90 to -90

90 to 90 or 270 to 270

-270 to -270 or -90 to -90 or 90 to 90 or 270 to 270

None of above

Category: GATE Physics 2020

Question 56:

An electron in a hydrogen atom is in the state n = 3, l = 2, m = - 2. Let

{\hat{L}}_{y}

denote the y-component of the orbital angular momentum operator. If

{(∆ {\hat{L}}_{y})}^{2} = a h^{2}

, the value of

α

is __________.

1 to 1

1 to 2

1 to 3

1 to 4

Category: GATE Physics 2020

Question 57:

A sinusoidal voltage of from V(t) =

V_{0}

cos(ωt) is applied across a parallel plate capacitor placed in vacuum. Ignoring the edge effects, the induced emf within the region between the capacitor plates can be expressed as a power series in ω. The lowest non-vanishing exponent in ω is _________.

0 to 0

1 to 1

2 to 2

3 to 3

Category: GATE Physics 2020

Question 58:

If x = \sum_{k = 1}^{\infty} a_{k} \sin k x, for - π \leq x \leq π,

the value of

a_{2}

is___________.

-1 to 0

0 to -1

-1 to -1

1 to 1

Category: GATE Physics 2020

Question 59:

Let f_{n} (x) = \{\begin{matrix} 0, x < - \frac{1}{2 n} \\ n, - \frac{1}{2 n} < x < \frac{1}{2 n} \\ 0, \frac{1}{2} < x . \end{matrix}

The value of

\lim_{n \to \infty} \int_{- \infty}^{\infty} f_{n} (x) \sin x d x i s_____.

0 to 0

0 to 1

0 to 2

0 to 3

Category: GATE Physics 2020

Question 60:

Consider the Hamiltonian

\hat{H} = {\hat{H}}_{0} + \hat{H}'

where

{\hat{H}}_{0} = (\begin{matrix} E & 0 & 0 \\ 0 & E & 0 \\ 0 & 0 & E \end{matrix}) a n d \hat{H}

' is the time independent given by

\hat{H}' = (\begin{matrix} 0 & k & 0 \\ k & 0 & k \\ 0 & k & 0 \end{matrix}), where k > 0

. If , the maximum energy eigenvalue of

\hat{H} i s 3 e V

corresponding to E = 2 e V, the value of K (rounded off to three decimal places) in eV is __________.

0.702 to 0.704

0.704 to 0.706

0.706 to 0.708

0.708 to 0.710

Category: GATE Physics 2020

Question 61:

A hydrogen atom is in an orbital momentum state

l, m = l >

. If

\vec{L}

lies on a cone which makes a half angle 30° with respect to the z-axis, the value of l is __________.

3 to 3

6 to 6

9 to 9

12 to 12

Category: GATE Physics 2020

Question 62:

In the center of mass frame, two protons each having 7000 GeV, collide to produced protons and anti-protons . The maximum number of anti-protons produced is _____________. (Assume the proton mass to be

1 G e V / c^{2})

6990 to 6990

6993 to 6993

6996 to 6996

6999 to 6999

Category: GATE Physics 2020

Question 63:

Consider a gas of hydrogen atoms in the atmosphere of the sun where the temperature is 5800 K. If a sample from this atmosphere contains

6.023 x 10^{23}

of hydrogen atoms in the ground state, the number of hydrogen atoms in the first excited sate is approximately

8 x 10^{n}

, where n is an integer. The value of n is ________ (Boltmann constant:

8.617 x 10^{- 5} e V / K)

12 to 13

14 to 15

16 to 17

18 to 19

Category: GATE Physics 2020

Question 64:

For a gas of non-interacting particles, the probability that a particle has a speed v in the interval v to v+dv is given by

f (v) d v = 4 π v^{2} d v {(\frac{m}{2 π k_{B} T})}^{3 / 2} e^{- m v^{2} / 2 k_{B} T}

If E is the energy of a particle, then maximum in the corresponding energy distribution in unit of

E / k_{B} T

occurs at _______(round off to one decimal place).

0.5 to 0.5

1.5 to 1.5

2.5 to 2.5

3.5 to 3.5

Category: GATE Physics 2020

Question 65:

The Planck's energy density distribution is given by

u (ω) = \frac{h ω^{3}}{π^{2} c^{3} (e^{h ω / k_{B} T} - 1)} .

At long wavelengths, the energy density of photons in thermal equilibrium with a cavity at temperature T varies as

T^{a}

, where a is ___________.

0 to 0

1 to 1

2 to 2

3 to 3

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Answered & Marked for Review (will be considered for evaluation)

Question 1:

He is known for his unscrupulous ways. He always sheds___________ tears to deceive people.

Correct Answer : crocodile

Question 2:

Jofra Archer, the England fast bowler, is ________ than accurate.

Correct Answer : more fast

Question 3:

Define [x] as the greatest integer less than or equal to x, for each

x \in (- \infty, \infty) . If y = [x]

, then area under y for

x \in [1, 4]

is ________.

Correct Answer : 6

Question 4:

P, Q, R, and S are to be uniquely coded using

α and β .

If P is coded as

αα and Q as αβ,

then R and S, respectively, can be coded as ____________.

A	$βα and αβ$	B	$ββ and αα$
C	$αβ and ββ$	D	$βα and ββ$

Correct Answer : D

Question 5:

Select a graph that schematically represents BOTH undefined properly in the interval undefined for integer values of m, where m>1.

A		B
C		D

Correct Answer : A

Question 6:

Select the word that fits the analogy: Build: Building: : Grow: ____________

Correct Answer : Growth

Question 7:

I do not think you know the case well enough to have opinions. Having said that, I agree with your other point. Was does the phase "having said that" mean in the given text?

Correct Answer : despite what I have said

Question 8:

Correct Answer : funds raised through voluntary contributions on web-based platforms

Question 9:

The sum of the first n terms in the sequence 8, 88, 888, 8888,... is ____________.

A	$\frac{81}{80} (10^{n} - 1) + \frac{9}{8} n$	B	$\frac{81}{80} (10^{n} - 1) - \frac{9}{8} n$
C	$\frac{81}{80} (10^{n} - 1) + \frac{8}{9} n$	D	$\frac{81}{80} (10^{n} - 1) - \frac{8}{9} n$

Correct Answer : D

Question 10:

Correct Answer : 59.0%

Question 11:

Which one of the following is a solution of

\frac{d^{2} u (x)}{d x^{2}} = k^{2} u (x), for k real ?

A	$e^{- k x}$	B	$\sin k x$
C	$\cos k x$	D	$\sinh x$

Correct Answer : A

Question 12:

A real, invertible 3x3 matrix M has eigenvalues

λ_{1}, (i = 1, 2, 3)

and the corresponding eigenvectors are

e_{1} >, (i = 1, 2, 3)

respectively. Which one of the following is correct?

A	$M e_{i} > = \frac{1}{λ_{1}} e_{i} >, f o r i = 1, 2, 3$	B	$M^{- 1} e_{i} > = \frac{1}{λ_{1}} e_{i} >, f o r i = 1, 2, 3$
C	$M^{- 1} e_{i} > = λ_{i} e_{i} >, f o r i = 1, 2, 3$	D	The eigenvalues of M and $M^{- 1}$ are not related

Correct Answer : B

Question 13:

A quantum particle is subject to the potential

V (x) = \{\begin{matrix} \infty, & x \leq - \frac{a}{2} \\ 0, & 1 - \frac{a}{2} < x > \frac{a}{2} \\ \infty, & x \geq \frac{a}{2} . \end{matrix}

The ground state wave function of the particle is proportional to

A	$\sin [\frac{πx}{2 a}]$	B	$\sin [\frac{πx}{a}]$
C	$\cos [\frac{πx}{2 a}]$	D	$\cos [\frac{πx}{a}]$

Correct Answer : D

Question 14:

Let

\hat{a} a n d {\hat{a}}^{+},

respectively denote the lowering and raising operators of a one-dimensional simple harmonic oscillator. oscillator. Let

n >

be the energy eigenstate of the simple harmonic oscillator. Given that

n >

is also an eigenstate of

{\hat{a}}^{+} {\hat{a}}^{+} \hat{a} \hat{a}

, the corresponding eigenvalue is

A	$n (n - 1)$	B	$n (n + 1)$
C	${(n + 1)}^{2}$	D	$n^{2}$

Correct Answer : A

Question 15:

Which one of the following is a universal logic gate?

Correct Answer : NAND

Question 16:

Which one of the following is the correct binary equivalent of the hexadecimal F6C?

Correct Answer : 1111 0110 1100

Question 17:

The total angular momentum j of the ground state of

the O_{8}^{17}

nucleus is

A	$\frac{1}{2}$	B	$1$
C	$\frac{3}{2}$	D	$\frac{5}{2}$

Correct Answer : D

Question 18:

A particle X is produced in the process

π^{+} + p \to K^{+} + X

via the strong interaction. If the quark content of the

K^{=} i s u \bar{s}

, the quark content of X is

A	$c \bar{s}$	B	$u u d$
C	$u u s$	D	$u \bar{d}$

Correct Answer : C

Question 19:

A medium

(ε_{r} > 1, μ_{r} = 1, σ > 0)

is semi-transparent to an electromagnetic wave when

A	Conduction current >> Displacement current	B	Conduction current << Displacement current
C	Conduction current = Displacement current	D	Both Conduction current and Displacement current are zero

Correct Answer : B

Question 20:

A particle is moving in a central force field given by

\vec{F} = - \frac{k}{r^{3}} \hat{r,} w h e r e \hat{r}

is the unit vector pointing away from the center of the field. The potential energy of the particle is given by

A	$\frac{k}{r^{2}}$	B	$\frac{k}{2 r^{2}}$
C	$- \frac{k}{r^{2}}$	D	$- \frac{k}{2 r^{2}}$

Correct Answer : D

Question 21:

Choose the correct statement related to the Fermi energy

(E_{F})

and the chemical potential (μ) of metal.

A	$μ = E_{F} o n l y a t 0 K$	B	$μ = E_{F} a t f i n i t e t e m p e r a t u r e$
C	$μ < E_{F} a t 0 K$	D	$μ > E_{F} f i n i t e t e m p e r a t u r e$

Correct Answer : A

Question 22:

Consider a diatomic molecule formed by identical atoms. If

E_{v} a n d E_{e}

represent the energy of the vibrational nuclear motion and electronic motion respectively, then in terms of the electronic mass m and nuclear mass

M, \frac{E_{V}}{E_{e}}

is proportional to

A	${(\frac{m}{M})}^{1 / 2}$	B	$\frac{m}{M}$
C	${(\frac{m}{M})}^{3 / 2}$	D	${(\frac{m}{M})}^{2}$

Correct Answer : A

Question 23:

A	undefined	B	undefined
C	undefined	D	undefined

Correct Answer : D

Question 24:

\vec{E} and \vec{B}

are the electric and magnetic fields respectively, then

\vec{E} . \vec{B}

Correct Answer : odd under parity and odd under time reversal

Question 25:

A	undefined	B	undefined
C	undefined	D	undefined

Correct Answer : B

Question 26:

Correct Answer : The temperature of the gas remains unchanged

Question 27:

Particle A with angular momentum

j = \frac{3}{2}

decays into particles B and C with angular momenta

j_{1} a n d j_{2}

, respectively. If

\frac{3}{2}, \frac{3}{2} >_{A} = α 1, 1 >_{B} \otimes \frac{1}{2}, \frac{1}{2} >_{c},

the value of α is ________.

Correct Answer : 1 to 1

Question 28:

Far from the Earth, the Earth's magnetic fields can be approximated as due to a bar magnet of magnetic pole strength

4 x 10^{14}

Am. Assume this magnetic fields is generated by a current carrying loop encircling the magnetic equator. The current required to do so is about

4 x 10^{n}

A, where n is an integer. The value of n is __________. (Earth 's circumference:

4 x 10^{7}

Correct Answer : 7 to 7

Question 29:

The number of distinct ways the primitive unit cell can be constructed for the two dimensional lattice as shown in the figure is ________.

Correct Answer : 5 to 5

Question 30:

A hydrogenic atom is subjected to a strong magnetic field. In the absence of spin-orbit coupling, the number of doubly degenerate states created out of the d-level is ________.

Correct Answer : 3 to 3

Question 31:

A particle Y undergoes strong decay

Y \to π^{-} + π^{-} .

The isospin of Y is_______.

Correct Answer : 2 to 2

Question 32:

For a complex variable z and the contour

c : |z| = 1

taken in the counter clockwise direction,

\frac{1}{2 π i} \oint_{c} (z - \frac{2}{z} + \frac{3}{z^{2}}) d z =________.

Correct Answer : -2 to -2

Question 33:

Let p be the momentum conjugate to the generalized coordinate q. If the transformation

Q = \sqrt{2} q^{m} \cos p P = \sqrt{2} q^{m} \sin p

is canonical, then m =__________.

Correct Answer : 0.5 to 0.5

Question 34:

A conducting sphere of radius 1 m is placed in air. The maximum number of electrons that can be put on the sphere to avoid electrical breakdown is about

7 x 10^{n}

, where n is an integer. The value of n is __________. Assume: Breakdown electric fields strength in air is

|E| = 3 x 10^{6} V / m

Permittivity of free space

ε_{0} = 8.85 x 10^{- 12} F / m

Electron charge e

e = 1.60 x 10^{- 19} C

Correct Answer : 14 to 15

Question 35:

If a particle is moving along a sinusoidal curve, the number of degrees of freedom of the particle is ________.

Correct Answer : 1 to 1

Question 36:

The product of eigenvalues of

(\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix})

Correct Answer : -1

Question 37:

Let

e_{1} > \equiv (\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}), e_{2} > \equiv (\begin{matrix} 1 \\ 1 \\ 0 \end{matrix}) a n d e_{3} \equiv (\begin{matrix} 1 \\ 1 \\ 1 \end{matrix}) . L e t S = \{e_{1} >, |e_{2} >,| e_{3} >\} . L e t ℝ^{3} denote

the three-dimensional real vector space. Which one of the following is correct?

A	S is an orthonormal set	B	S is a linearly dependent set
C	S is a basis for $ℝ^{3}$	D	$\sum_{i = 1}^{3} \|e_{i} > < e_{i}\| = (\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix})$

Correct Answer : C

Question 38:

{\hat{S}}_{x}

denotes the spin operator defined as

{\hat{S}}_{x} = \frac{h}{2} (\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}) .

Which one of the following is correct?

A	The eigenstates of spin operator ${\hat{S}}_{x} a r e ↑ >_{x} \equiv (\begin{matrix} \begin{matrix} 1 \\ 0 \end{matrix} \end{matrix}) and ↓ >_{x} \equiv (\begin{matrix} 0 \\ 1 \end{matrix})$
B	The eigenstates of spin operator ${\hat{S}}_{x} a r e ↑ >_{x} \equiv \frac{1}{\sqrt{2}} (\begin{matrix} \begin{matrix} 1 \\ - 1 \end{matrix} \end{matrix}) and ↑ >_{x} \equiv \frac{1}{\sqrt{2}} (\begin{matrix} 1 \\ 1 \end{matrix})$
C	In the spin state $\frac{1}{2} (\begin{matrix} 1 \\ \sqrt{3} \end{matrix})$ , upon the measurement of ${\hat{S}}_{x}$ , the probability for obtaining $↑ >_{x} i s \frac{1}{4}$
D	In the spin state $\frac{1}{2} (\begin{matrix} 1 \\ \sqrt{3} \end{matrix})$ , upon the measurement of ${\hat{S}}_{x}$ , the probability for obtaining $↑ >_{x} i s \frac{2 + \sqrt{3}}{4}$

Correct Answer : D

Question 39:

The input voltage undefined to the circuit shown in the figure is 2 cos(100t) V. The output voltage undefined is 2 cos undefined V. If R = 1 kΩ, the value of C (in μF) is

Correct Answer : 10

Question 40:

A	undefined	B	undefined
C	undefined	D	undefined

Correct Answer : B

Question 41:

Consider the Lagrangian

L = a {(\frac{d x}{d t})}^{2} + b {(\frac{d y}{d t})}^{2} + c x y, w h e r e a, b a n d c a r e c o n s \tan t s . I f p_{x} a n d p_{y}

are the momenta conjugate to the coordinates x and y respectively, then the Hamiltonian is

A	$\frac{p_{x}^{2}}{4 a} + \frac{p_{y}^{2}}{4 b} - c x y$	B	$\frac{p_{x}^{2}}{2 a} + \frac{p_{y}^{2}}{2 b} - c x y$
C	$\frac{p_{x}^{2}}{2 a} + \frac{p_{y}^{2}}{2 b} + c x y$	D	$\frac{p_{x}^{2}}{a} + \frac{p_{y}^{2}}{b} + c x y$

Correct Answer : A

Question 42:

Which one of the following matrices does NOT represent a proper rotation in a plane ?

A	$(\begin{matrix} - \sin θ & \cos θ \\ - \cos θ & - \sin θ \end{matrix})$	B	$(\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix})$
C	$(\begin{matrix} \sin θ & \cos θ \\ - \cos θ & \sin θ \end{matrix})$	D	$(\begin{matrix} - \sin θ & \cos θ \\ - \cos θ & \sin θ \end{matrix})$

Correct Answer : D

Question 43:

A uniform magnetic field

\vec{B} = B_{0} \hat{y}

A	maximum along z'	B	maximum along y'
C	maximum along x'	D	uniform over the sphere

Correct Answer : A

Question 44:

A		B
C		D

Correct Answer : D

Question 45:

Correct Answer : the crystal is metallic for odd values of n

Question 46:

According to the Fermi gas model of the nucleus, the nucleus, the nucleons move in a sphere volume of radius

R (= R_{0} A^{\frac{1}{3}},

where A is the mass number and

R_{0}

is an empirical constant with the dimensions of length). The Fermi energy of the nucleus

E_{F}

is proportional to

A	$R_{0}^{2}$	B	$\frac{1}{R_{0}}$
C	$\frac{1}{R_{0}^{2}}$	D	$\frac{1}{R_{0}^{3}}$

Correct Answer : C

Question 47:

Consider a two dimensional crystal with 3 atoms in the basis. The number of allowed optical branches (n) and acoustic branches (m) due to the lattice vibrations are

Correct Answer : (n, m)=(4, 2)

Question 48:

The internal energy U of a system is given by

U (S, V) = λ V^{- 2 / 3} S^{2}

, where

λ

is a constant of appropriate dimensions; V and S denote the volume and entropy, respectively. Which one of the following gives the correct equations of state of the system?

A	$\frac{P V^{1 / 3}}{T^{2}} = c o n s \tan t$	B	$\frac{P V}{T^{1 / 3}} = c o n s \tan t$
C	$\frac{P}{V^{1 / 3} T} = c o n s \tan t$	D	$\frac{P V^{2 / 3}}{T} = c o n s \tan t$

Correct Answer : A

Question 49:

The potential energy of a particle of mass m is given by

U (x) = a \sin (k^{2} x - π / 2), a > 0, k^{2} > 0 .

The angular frequency of small oscillations of the particle about x = 0 is

A	$k^{2} \sqrt{\frac{2 a}{m}}$	B	$k^{2} \sqrt{\frac{a}{m}}$
C	$k^{2} \sqrt{\frac{a}{2 m}}$	D	$2 k^{2} \sqrt{\frac{a}{m}}$

Correct Answer : B

Question 50:

The radial wave function of a particle in a central potential is given by

R (r) = A \frac{r}{a} e x p (- \frac{r}{2 a}),

where A is the normalization constant and a is positive constant of suitable dimensions. If γα is the most probable distance of the particle from the force center, the value of γ is___________.

Correct Answer : 4 to 4

Question 51:

A free particle of mass M is located in a three-dimensional cubic potential well with impenetrable walls. The degeneracy of the fifth excited state of the particle is _________.

Correct Answer : 6 to 6

Question 52:

Consider the circuit given in the figure. Let the forward voltage drop across each diode be 0.7 V. The current 1 (in mA) through the resistor is _____________.

Correct Answer : 8 to 8

Question 53:

Let

u^{μ}

denote the 4-velocity of a relativistic particle whose square

u^{μ} u_{μ} = 1 . If ε_{μ v p σ}

is the Levi-Civita tensor then value of

ε_{μ v p σ} u^{μ} u^{v} u^{p} u^{σ}

is __________.

Correct Answer : 0 to 0

Question 54:

Consider a simple cubic monoatomic Bravais lattice which has a basis with vectors

{\vec{r}}_{1} = 0, {\vec{r}}_{2} = \frac{α}{4} (\hat{x} + \hat{y} + \hat{z}), α

is the lattice parameter. The Bragg reflection is observed due to the change in the wave vector between the incident and the scattered beam as given by

\vec{K} = n_{1} {\vec{G}}_{1} + n_{2} {\vec{G}}_{2} + n_{3} {\vec{G}}_{3}

, where

{\vec{G}}_{1}, {\vec{G}}_{2}, a n d {\vec{G}}_{3}

are primitive reciprocal lattice vectors. For

n_{1} = 3 n_{2} = 3 and n_{3} = 2

, the geometrical structure factor is ____________.

Correct Answer : 2 to 2

Question 55:

A plane electromagnetic wave of wavelength λ is incident on a circular loop of conducting wire. The loop radius is

a (a < < λ)

. The angle (in degrees), made by the Poynting vector with normal to the plane of the loop to generate a maximum induced electrical signal, is ________.

Correct Answer : -270 to -270 or -90 to -90 or 90 to 90 or 270 to 270

Question 56:

An electron in a hydrogen atom is in the state n = 3, l = 2, m = - 2. Let

{\hat{L}}_{y}

denote the y-component of the orbital angular momentum operator. If

{(∆ {\hat{L}}_{y})}^{2} = a h^{2}

, the value of

α

is __________.

Correct Answer : 1 to 1

Question 57:

A sinusoidal voltage of from V(t) =

V_{0}

Correct Answer : 2 to 2

Question 58:

If x = \sum_{k = 1}^{\infty} a_{k} \sin k x, for - π \leq x \leq π,

the value of

a_{2}

is___________.

Correct Answer : -1 to -1

Question 59:

Let f_{n} (x) = \{\begin{matrix} 0, x < - \frac{1}{2 n} \\ n, - \frac{1}{2 n} < x < \frac{1}{2 n} \\ 0, \frac{1}{2} < x . \end{matrix}

The value of

\lim_{n \to \infty} \int_{- \infty}^{\infty} f_{n} (x) \sin x d x i s_____.

Correct Answer : 0 to 0

Question 60:

Consider the Hamiltonian

\hat{H} = {\hat{H}}_{0} + \hat{H}'

where

{\hat{H}}_{0} = (\begin{matrix} E & 0 & 0 \\ 0 & E & 0 \\ 0 & 0 & E \end{matrix}) a n d \hat{H}

' is the time independent given by

\hat{H}' = (\begin{matrix} 0 & k & 0 \\ k & 0 & k \\ 0 & k & 0 \end{matrix}), where k > 0

. If , the maximum energy eigenvalue of

\hat{H} i s 3 e V

corresponding to E = 2 e V, the value of K (rounded off to three decimal places) in eV is __________.

Correct Answer : 0.706 to 0.708

Question 61:

A hydrogen atom is in an orbital momentum state

l, m = l >

. If

\vec{L}

lies on a cone which makes a half angle 30° with respect to the z-axis, the value of l is __________.

Correct Answer : 3 to 3

Question 62:

1 G e V / c^{2})

Correct Answer : 6999 to 6999

Question 63:

Consider a gas of hydrogen atoms in the atmosphere of the sun where the temperature is 5800 K. If a sample from this atmosphere contains

6.023 x 10^{23}

of hydrogen atoms in the ground state, the number of hydrogen atoms in the first excited sate is approximately

8 x 10^{n}

, where n is an integer. The value of n is ________ (Boltmann constant:

8.617 x 10^{- 5} e V / K)

Correct Answer : 14 to 15

Question 64:

For a gas of non-interacting particles, the probability that a particle has a speed v in the interval v to v+dv is given by

f (v) d v = 4 π v^{2} d v {(\frac{m}{2 π k_{B} T})}^{3 / 2} e^{- m v^{2} / 2 k_{B} T}

If E is the energy of a particle, then maximum in the corresponding energy distribution in unit of

E / k_{B} T

occurs at _______(round off to one decimal place).

Correct Answer : 0.5 to 0.5

Question 65:

The Planck's energy density distribution is given by

u (ω) = \frac{h ω^{3}}{π^{2} c^{3} (e^{h ω / k_{B} T} - 1)} .

At long wavelengths, the energy density of photons in thermal equilibrium with a cavity at temperature T varies as

T^{a}

, where a is ___________.

Correct Answer : 1 to 1

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