## ==> Sticky: User Created 70 Sample Questions with answers

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

physics_auth wrote:
noospace wrote:Where did there questions come from? Are they really official ETS? If so how come they're not available on the website?

What's going on here?
It is a bit irritating to have to apologize again ... but I will do it once and for all ... . Questions 1-42 in this post are not ETS official questions, but questions that imitate those of the real PGRE test. Above all, to post ETS questions is plagiarism! Furthermore, I give directions (in green color somewhere in the 1st page) in this post how to find a pdf archive with ETS questions (about 30 questions with their brief solutions). The pdf mentioned contains ETS official questions. Is that clear? For those of you who want to practise only on ETS official questions there are directions on how to do this (the pdf I mentioned... the 4 practice tests etc.), the questions I post here periodically are for those who want to practise on PGRE questions beyond the official material. Ok?
I think you should mention this paragraph in the first page, before the 1st question, so that no further doubts arise in anyone's head.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

blackcat007 wrote:
physics_auth wrote:
noospace wrote:Where did there questions come from? Are they really official ETS? If so how come they're not available on the website?

What's going on here?
It is a bit irritating to have to apologize again ... but I will do it once and for all ... . Questions 1-42 in this post are not ETS official questions, but questions that imitate those of the real PGRE test. Above all, to post ETS questions is plagiarism! Furthermore, I give directions (in green color somewhere in the 1st page) in this post how to find a pdf archive with ETS questions (about 30 questions with their brief solutions). The pdf mentioned contains ETS official questions. Is that clear? For those of you who want to practise only on ETS official questions there are directions on how to do this (the pdf I mentioned... the 4 practice tests etc.), the questions I post here periodically are for those who want to practise on PGRE questions beyond the official material. Ok?
I think you should mention this paragraph in the first page, before the 1st question, so that no further doubts arise in anyone's head.
Thanks Blackcat007. It think that now the whole issue is crystal clear. I have already done it ... . However, the fact that some people are confused about if these questions are official or not could mean that the questions are good imitations of the official ones . (For example, REA's questions can easily be recognized that are poles apart ... .)

noospace
Posts: 46
Joined: Fri Feb 22, 2008 9:14 pm

### Re: ==> Sticky: User Created Sample Questions and Discussion

Hi physics_auth,

Thanks for the clarification. When you talk about these 30 ETS questions. I'm pretty sure you're referring to the ETS Major Field Questions right?

Wouldn't it have been a lot easier just to give the link (below) to avoid confustion. Anyway.

http://www.nocheating.org/Media/Tests/M ... hysics.pdf

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: User Created Sample Questions and Discussion

noospace wrote:Hi physics_auth,

Thanks for the clarification. When you talk about these 30 ETS questions. I'm pretty sure you're referring to the ETS Major Field Questions right?

Wouldn't it have been a lot easier just to give the link (below) to avoid confustion. Anyway.

http://www.nocheating.org/Media/Tests/M ... hysics.pdf
No, I don't refer to the ETS Major Field Questions, but to another pdf under the name GRE_practice. In the first page is quoted the PGRE committee ... .

noospace
Posts: 46
Joined: Fri Feb 22, 2008 9:14 pm

### Re: ==> Sticky: User Created Sample Questions and Discussion

Hi physics_auth,

Can you please post the url for these questions? It tried your google steps and got zero hits.

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Re: ==> Sticky: User Created Sample Questions and Discussion

noospace wrote:Hi physics_auth,

Can you please post the url for these questions? It tried your google steps and got zero hits.
http://www.princeton.edu/~jdpeters/docs/ETS_extra.pdf

hk
Posts: 16
Joined: Wed Jun 24, 2009 3:43 am

### Re: ==> Sticky: User Created 44 Sample Questions & Discussion

Many thanks for the sample questions!

I would like to ask something about the ETS extra problems. Is there any full solution available for it? I've seen in this forum several topics discussing one particular question from the problem set though.
Thanks.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: User Created 44 Sample Questions & Discussion

hk wrote:Many thanks for the sample questions!

I would like to ask something about the ETS extra problems. Is there any full solution available for it? I've seen in this forum several topics discussing one particular question from the problem set though.
Thanks.
The extra problems (i.e. the 2 pdfs which contain 30 questions each) are accompanied only by brief solutions (i.e. the number of the question and the correct answer-letter). Furthermore, as I know there are analytic solutions only for the 4 released full-tests by ETS.
If you want any help with any of that questions, post your query in some thread (this one or any other) or send a private message (if you don't want to post openly). It is up to you!
Physics_auth

hk
Posts: 16
Joined: Wed Jun 24, 2009 3:43 am

### Re: ==> Sticky: User Created 44 Sample Questions & Discussion

Okay, I think I'll start a new thread then..

joshfr3
Posts: 1
Joined: Fri May 28, 2010 3:31 am

### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

blackcat007 wrote:
colonblow wrote:hi, shouldn't the answer to #1 problem be letter D, which is 3g/L? If 3g/2L is the correct answer, can someone please tell me how it was solved? thanks thanks!
the only torque that is acting is that due to the weight of the beam. so mgl/2 =Ia
I=(ml^2)/3

equate and solve..

I have attempted to solve this problem quickly using a lagrangian. Clearly, I must be doing something wrong. Shouldn't the lagrangian yield the same answer? Would anyone be so kind as to include a light draft of this?

I used T = rotational kinetic energy + translational

and U = mgLcos/2

Thanks!

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: More ETS and 42 "active" Sample Questions

joshfr3 wrote: I have attempted to solve this problem quickly using a lagrangian. Clearly, I must be doing something wrong. Shouldn't the lagrangian yield the same answer? Would anyone be so kind as to include a light draft of this?

I used T = rotational kinetic energy + translational

and U = mgLcos/2

Thanks!
Here is what I did: Take +z-axis downwards and x-axis horizontal. Take as a generalized coordinate the angle θ between the axis of the rod (I refer to the axis along its length) and x-axis. You decided to solve the problem focusing on the motion of the center of mass. The potential energy of the center of mass is V = (1/2)*MgLsinθ with this selection of the generalized coordinate. The translational kinetic energy of the CM is (1/8)*Μ*(L^2)*(dθ/dt)^2 and its rotational kinetic energy is (1/24)*M*(L^2)*(dθ/dt)^2 since the rotation axis passes through the center of mass in this case (and is parallel to the fixed axis of rotation). Add the aforementioned quantities to form the Lagrangian L

L = (1/6)*Μ*(L^2)*(dθ/dt)^2 + (1/2)*MgLsinθ

and the equation of motion is: (1/3)*Μ*(L^2)*[d(dθ/dt)/dt] = (1/2)*MgLcosθ
solve for d(dθ/dt)/dt (the acceleration asked to find) and finally set θ = 0, because you want to find the angular acceleration when the rod is set free from the horizontal position.

letocharm
Posts: 1
Joined: Thu Nov 08, 2012 4:43 pm

### Re: ==> Sticky: User Created 60 Sample Questions with answers

Hi good post. Some corrections, for number 50, I think none of them have the correct units. A is right but drop the m next to the l if you mean q=ml being the heat of fusion. If you mean l to be the entire amount of heat I think you'll need to make it l/m sinc you appeared to factor out m. Also perhaps it was assumed but it should be made explicit the masses of the two are the same.

Also neutrinos do have a magnetic moment though it's small.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: User Created 60 Sample Questions with answers

letocharm wrote:Hi good post. Some corrections, for number 50, I think none of them have the correct units. A is right but drop the m next to the l if you mean q=ml being the heat of fusion. If you mean l to be the entire amount of heat I think you'll need to make it l/m sinc you appeared to factor out m. Also perhaps it was assumed but it should be made explicit the masses of the two are the same.

Also neutrinos do have a magnetic moment though it's small.
Hi there, I will take care ... it has been a long time since I posted this pool around 2009 ... therefore some rectifications might be necessary ... anyway thanks for your comments.

physics_auth

superderec
Posts: 3
Joined: Fri Aug 02, 2013 1:25 am

### Re: ==> Sticky: User Created 60 Sample Questions with answers

I think that there is no correct answer to question 25 and that the answer to number 23 is wrong

Aether73
Posts: 27
Joined: Wed Jun 19, 2013 10:52 pm

### Re: ==> Sticky: User Created 60 Sample Questions with answers

superderec wrote:I think that there is no correct answer to question 25 and that the answer to number 23 is wrong
I'm getting $$\frac{Q}{6\epsilon_{0}}$$ for number 25. The flux on each side of the cube should be equal (unless I've missed something here), and any cube has six sides. You know the rest.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: User Created 60 Sample Questions with answers

Aether73 wrote:
superderec wrote:I think that there is no correct answer to question 25 and that the answer to number 23 is wrong
I'm getting $$\frac{Q}{6\epsilon_{0}}$$ for number 25. The flux on each side of the cube should be equal (unless I've missed something here), and any cube has six sides. You know the rest.
You are right; thanks for the typo (this question was modified).
Question 23 has to do with the behavior of the resistor in terms of temperature ... resistance normally increases vs temperature ... .

superderec
Posts: 3
Joined: Fri Aug 02, 2013 1:25 am

### Re: ==> Sticky: User Created 60 Sample Questions with answers

I think that the answer to question 58 should be E and that of No. 59 should be C instead of those answers given. Pls check.

+ answer to TRIAL QUESTION 1 is B

somy
Posts: 1
Joined: Sat Dec 20, 2014 2:54 am

### Re: ==> Sticky: User Created 60 Sample Questions with answers

Hey guys

At the first of this thread, it has been written that there are the solutions of these question, but few of them are just argued . I would be appreciate to tell me where the solutions have been written. I am in a hurry, please

Thanks for the nice froum

sishoueta
Posts: 1
Joined: Tue Oct 20, 2015 12:30 pm

### Re: ==> Sticky: User Created 60 Sample Questions with answers

My results for Questions 51 and 56 are A and C respectively! I would like to know your opinion about these questions my friends!

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: User Created 60 Sample Questions with answers

Anwers to questions (51) and (56) were supplied ... I will extend this pool up to 100 questions at some point.

bugaboo
Posts: 1
Joined: Thu Sep 08, 2016 12:43 am

### Re: ==> Sticky: User Created 60 Sample Questions with answers

In question 1 statement A is false unless the barrier between the wells is infinite. Statement B is false even if it is infinite. Statement D is also false, it should mention ground state, not just state.

SzwedyBallz
Posts: 1
Joined: Tue Feb 21, 2017 8:00 pm

### Re: ==> Sticky: User Created 60 Sample Questions with answers

I'm a bit confused about question 56. The solutions say that the answer is A, both constants should be real for the operator to be Hermitian, but I don't see how kappa can be real. Suppose that lambda is equal to zero. Then the operator is just kappa*d/dx, which is just the momentum operator with the substitution of kappa=-i*hbar. Since the momentum operator is Hermitian, it seems that kappa must be imaginary. Please let me know what your thoughts are on the subject

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: User Created 60 Sample Questions with answers

bugaboo wrote:In question 1 statement A is false unless the barrier between the wells is infinite. Statement B is false even if it is infinite. Statement D is also false, it should mention ground state, not just state.
Do not agree with your answers - study the ammonia molecule quantum mechanical problem to resolve your points of confusion.

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: ==> Sticky: User Created 60 Sample Questions with answers

SzwedyBallz wrote:I'm a bit confused about question 56. The solutions say that the answer is A, both constants should be real for the operator to be Hermitian, but I don't see how kappa can be real. Suppose that lambda is equal to zero. Then the operator is just kappa*d/dx, which is just the momentum operator with the substitution of kappa=-i*hbar. Since the momentum operator is Hermitian, it seems that kappa must be imaginary. Please let me know what your thoughts are on the subject
Correct answer is fixed now! ... thanks

physics_auth
Posts: 163
Joined: Sat Jul 18, 2009 7:24 pm

### Re: 8 NEW SAMPLE PHYSICS GRE QUES. WITH THEIR ANSWERS (24-42)

physics_auth wrote:SAMPLE QUESTION 24:
A neutral particle is at rest in a uniform magnetic field of magnitude B. At time t = 0 it decays into two charged particles each of mass m. The two particles move off in separate orbits, both of which lie in a plane perpendicular to the magnetic field. The charge of one of the particles is +q. What is going to happen at a future time t > 0?

(A) The particles will collide after a time interval equal to 2πm/qB.
(B) The particles will collide after a time interval equal to πm/qB.
(C) The particles will collide after a time interval equal to πm/2qB.
(D) The particles will recede from each other until they are infinitely apart.
(E) The particles will recede from each other, moving along a straight line and subsequently approach each other (moving along the same line) under the action of the mutual Coulomb attraction.

SAMPLE QUESTION 25:
A point charge +Q is placed at the vertex of a cube. What is the electric flux through the cube?

(A) 0
(B) +$$\frac{Q}{\epsilon_0}$$
(C) +$$\frac{Q}{2\epsilon_0}$$
(D) +$$\frac{Q}{6\epsilon_0}$$
(E) +$$\frac{Q}{8\epsilon_0}$$

SAMPLE QUESTION 26:
The mass density of a certain planet has spherical symmetry but varies in such a way that the mass inside every spherical surface with center at the center of the planet is proportional to the radius of the surface. If r is the distance from the center of the planet to a point mass inside the planet, the gravitational force on this mass is:

(A) not dependent on r

(B) proportional to $$r^2$$

(C) proportional to r

(D) proportional to $$1/r$$

(E) proportional to $$1/r^2$$

SAMPLE QUESTION 27: (This is a tough question - a more analytical answer is provided in the thread below)
A soap film immersed in air is illuminated by white light almost normal to its surface. The index of refraction of the film is 1.50. Wavelengths of 480 nm and 800 nm are ONLY intensified in the reflected beam. (No other wavelengths between them are intensified.) The thickness of the film is:

(A) 150 nm
(B) 240 nm
(C) 360 nm
(D) 400 nm
(E) 600 nm

SAMPLE QUESTION 28:
A certain nucleus, after absorbing a neutron, undergoes beta minus decay and then splits into two alpha particles. Which of the following can be the A and Z of the original nucleus?

(A) A = 6 _____ Z = 2
(B) A = 6 _____ Z = 3
(C) A = 7 _____ Z = 3
(D) A = 7 _____ Z = 2
(E) A = 8 _____ Z = 4

SAMPLE QUESTION 29:
The energy supplied by a thermal neutron in an induced fission event is essentially equal to:

(A) its rest energy
(B) its kinetic energy
(C) its binding energy to the nucleus which undergoes fission
(D) the total energy of the initial fission fragments
(E) the energy released during the fission process

SAMPLE QUESTION 30:
A baryon with strangeness 0 decays into two particles, one of which is a baryon with strangeness +1. Which of the following could be the other particle?

(A) a baryon with strangeness 0
(B) a baryon with strangeness -1
(C) a lepton
(D) a meson with strangeness +1
(E) a meson with strangeness -1

SAMPLE QUESTION 31:
Two bodies move with speeds 0.8c and 0.6c respectively. If the two bodies have the same rest mass, what is the ratio of their relativistic kinetic energies?

(A) 16/9
(B) 4/3
(C) 3/2
(D) 8/3
(E) 32/27

SAMPLE QUESTION 32:
A large transparent slab of uniform thickness and index of refraction $$n$$ is initially immersed in the air. A monochromatic beam of light is incident on the slab at an angle $$\theta$$ such that the reflected and the refracted beam emerge on mutually orthogonal directions. The previous experiment is then repeated (i.e. same angle of incidence for the aforementioned monochromatic beam), this time with the slab immersed in a liquid with index of refraction $$n_l$$. In terms of the angle of incidence $$\theta$$ and the refraction indices $$n$$ and $$n_l$$, what is the angle between the emergent reflected and refracted beams in the latter case?

(A) They are still orthogonal to each other.

(B) It is equal to $$$$\arcsin \left( {\frac{{{n_l}}}{{{n^2}}} \cdot \sqrt {1 + {n^2}} } \right) - \theta$$$$.

(C) It is equal to $$$$\arcsin \left( {{n_l }/\sqrt {1 + {n^2}} } \right) - \theta$$$$.

(D) It is equal to $$$$\arcsin \left( {\frac{{{n_l } \cdot n}}{{1 + {n^2}}}} \right) - \theta$$$$.

(E) It is equal to $$$$\arcsin \left( {\frac{{{n_l }}}{n} \cdot \sqrt {1 - {n^2}} } \right) - \theta$$$$.

SAMPLE QUESTION 33:
The largest number of beats per second will be heard from which of the following pairs of tuning forks?

(A) 200 and 201 Hz
(B) 256 and 260 Hz
(C) 534 and 540 Hz
(D) 763 and 774 Hz
(E) 8420 and 8422 Hz

SAMPLE QUESTION 34:
A beam of particles of energy E = 9 eV strikes on a step potential and 25% of the beam's particles is reflected back. What is the height of the step potential?

(A) 4 eV
(B) 8 eV
(C) 3 eV
(D) 1 eV
(E) 5 eV

SAMPLE QUESTION 35:
The magnetic dipole moment of a current-carrying loop of wire is in the positive z direction. The magnetic dipole is placed in space where there is a magnetic field $$\vec{B}=B_0\hat {\vec{i}}+B_0 \hat{\vec{j}}$$, where $$B_0$$ is some positive constant and $$\hat{\vec{i}}$$, $$\hat{\vec{j}}$$ the unit vectors along directions x and y respectively. What is the direction of the magnetic torque on the loop?

(A) It is along the negative z direction.
(B) It is along the line y = -x in the forth quadrant.
(C) It is along the line y = x, in the third quadrant.
(D) It is along the line y = -x, in the second quadrant.
(E) It is along the line x = y = z towards positive x,y and z.

SAMPLE QUESTION 36:
A system is composed of 4000 non-interacting particles distributed among three possible energy states $$E_1 = 0$$, $$E_2 = \epsilon$$ and $$E_2 = 2\epsilon$$. A particular partition corresponds to the occupation numbers $$n_1 = 2000$$ and $$n_2 = 1500$$ for the first two energy states. The total number of particles of the system remains constant. What is approximately the average energy of this configuration?

(A) $$2500 \epsilon$$
(Β) $$0.63 \epsilon$$
(C) $$5000 \epsilon$$
(D) $$1.25 \epsilon$$
(E) $$0.38 \epsilon$$

SAMPLE QUESTION 37:
The positive terminals of two batteries with emf's of $$E_1$$ and $$E_2$$, respectively, are connected together. It is $$E_2 > E_1$$. The circuit is completed by connecting the negative terminals. If each battery has an internal resistance r, what is the rate with which electrical energy is converted to chemical energy in the smaller battery?

(A) $$\frac{E_1^2}{r}$$
(B) $$\frac{E_1^2}{2r}$$
(C) $$\frac{(E_2-E_1)E_1}{r}$$
(D)$$\frac{(E_2-E_1)E_1}{2r}$$
(E) $$\frac{E_2^2}{2r}$$

SAMPLE QUESTION 38:
The Lagrangian for a mechanical system is $$L(q,\dot{q})=\frac{\dot{q}^3 + q^3}{3}$$, where $$q$$ is a generalized coordinate and $$\dot{q}=dq/dt>0$$. What is the Hamiltonian $$H$$ of this system?

(A) $$H=pq-\frac{p^{\frac{3}{2}}+q^3}{3}$$
(B) $$H=\frac{2p^{\frac{1}{2}}-q^3}{3}$$
(C) $$H=\frac{2p^{\frac{3}{2}}-q^3}{3}$$
(D) $$H=\frac{2 \dot{q}^3-q^3}{3}$$
(E) $$H=\frac{p^{\frac{3}{2}}+q^3}{3}$$

SAMPLE QUESTION 39:
Massless and inextensible string is wrapped around the periphery of a homogeneous cylinder of radius R = 0.5 m and mass m = 2 kg. The string is pulled straight away from the upper part of the periphery of the cylinder, without relative slipping. The cylinder moves on a horizontal floor, for which the friction coefficient (μ) is 0.4. What is most nearly the maximum force $$F_{max}$$ that can be exerted on the free end of the string so that the cylinder rolls without sliding?

(A) $$F_{max}$$ = 24 N
(B) $$F_{max}$$= 12 N
(C) $$F_{max}$$ = 8 N
(D) $$F_{max}$$ = 6 N
(E) $$F_{max}$$ = 8/3 N

SAMPLE QUESTION 40:
Which of the following facts could be a remnant of the Big Bang theory for the evolution of the universe from a space-time singularity?

I. Uniform distribution of microwave background radiation.
II. Uniform distribution of background electrons.
III. Uniform distribution of background neutrinos.
IV. Uniform distribution of gluons and quarks.

(A) I and II only
(B) I, II and III only
(C) I and III only
(D) I, III and IV only
(E) II and III only

SAMPLE QUESTION 41:
Six identical point charges +q are placed on the vertices of a regular hexagon of side of length l. There is one charge on each vertex. The hexagon is rotated about an axis that passes through its center of symmetry and is perpendicular to its plane. If the frequency of revolution is f, what is the magnitude of the induced magnetic field B at the center of the hexagon?

(A) $$B = \frac{\mu_0 q f}{2l}$$
(B) $$B = \frac{\mu_0 q f}{l}$$
(C) $$B = \frac{\mu_0 q f}{6l}$$
(D) $$B = \frac{3 \mu_0 q f}{l}$$
(E) $$B = \frac{3 \mu_0 q f}{2l}$$

$$\mu_0$$= magnetic susceptibility of free space

SAMPLE QUESTION 42:
A Carnot engine operates using a monoatomic gas as its working substance. Which of the following procedures could lead to the greatest possible increase of the efficiency of the Carnot thermal engine?

(A) The increase of the temperature of the hot reservoir by 40 K.
(B) The lowering of the temperature of the cold reservoir down to 0 K.
(C) The substitution of the monoatomic gas by a diatomic gas.
(D) The increase of the temperature of the hot reservoir by 20 K and the simultaneous decrease of the temperature of the cold reservoir by 20 K.
(E) The substitution of the reversible mode of operation of the engine by an irreversible one.

entrancei
Posts: 1
Joined: Sun Jun 30, 2019 11:57 am

### Re: ==> Sticky: User Created 70 Sample Questions with answers

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