The document is the physics test paper for JAM 2006. It contains 25 questions, the first 15 being objective questions worth 6 marks each and the remaining 10 being subjective questions worth 21 marks each. The questions cover topics in physics including electromagnetic waves, quantum mechanics, solid state physics, thermodynamics and optics.
At Apex Institute, we endeavour to amalgamate the ancient values of uttermost dedication and responsibility that gave teaching a very pious and sacred status, with latest teaching methodologies so as to make the act of learning, a delectable experience. The arduous task is accomplished by a team of diligent academicians and entrepreneurs, who with the years of experience have mastered the techniques to transform even the most abstruse topics easy to comprehend.
Great emphasis is laid on the concepts and fundamentals with a smooth and systematic transition to the advanced levels of teaching. The interaction between students and teachers is always encouraged so as to provide a very healthy environment for growth and learning. During the process of training the students for IIT-JEE/Engg./Medical entrance examinations, great emphasis is laid on the fundamentals so as to excel in the CBSE examination also.
Illustrious faculty and excellent teaching techniques provide you will an infallible approach to success only at Apex Institute.
Our Mission
Generating excellence both in academic and competitive aspects thereby training the youth for most gruelling entrance level exams viz. IIT-JEE/Engg.& Medical entrance.
Our Vision
Generating excellence in academic, exploring creative areas of the dormant self, nurturing talent & aptitude & including perseverance among the students to keep themselves abreast of the latest developments in the field of competitive examinations.
Our Objectives
1. Striving for the best possible education to ambitious students aspiring to join corporate world as medical professionals.
2. Creating a comprehensive understanding of the subjects & help developing strategies to meet arduous competitions among the students to match, excel & ameliorate the competition oriented education.
At Apex Institute, we endeavour to amalgamate the ancient values of uttermost dedication and responsibility that gave teaching a very pious and sacred status, with latest teaching methodologies so as to make the act of learning, a delectable experience. The arduous task is accomplished by a team of diligent academicians and entrepreneurs, who with the years of experience have mastered the techniques to transform even the most abstruse topics easy to comprehend.
Great emphasis is laid on the concepts and fundamentals with a smooth and systematic transition to the advanced levels of teaching. The interaction between students and teachers is always encouraged so as to provide a very healthy environment for growth and learning. During the process of training the students for IIT-JEE/Engg./Medical entrance examinations, great emphasis is laid on the fundamentals so as to excel in the CBSE examination also.
Illustrious faculty and excellent teaching techniques provide you will an infallible approach to success only at Apex Institute.
Our Mission
Generating excellence both in academic and competitive aspects thereby training the youth for most gruelling entrance level exams viz. IIT-JEE/Engg.& Medical entrance.
Our Vision
Generating excellence in academic, exploring creative areas of the dormant self, nurturing talent & aptitude & including perseverance among the students to keep themselves abreast of the latest developments in the field of competitive examinations.
Our Objectives
1. Striving for the best possible education to ambitious students aspiring to join corporate world as medical professionals.
2. Creating a comprehensive understanding of the subjects & help developing strategies to meet arduous competitions among the students to match, excel & ameliorate the competition oriented education.
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
SCRUTINY TO THE NON-AXIALLY DEFORMATIONS OF AN ELASTIC FOUNDATION ON A CYLIND...P singh
This paper is devoted to homogenization of partial differential operators to use in special structure that is a plate allied to an elastic foundation when it is situated through the basic loads (especially with the harmonic forces) with a Non-axially deformation of the cantilever. Furthermore, it contains the Equations of motion that they can be derived from degenerate Non-linear elliptic ones. Through the mentioned processes, there exists many excess works related to computing the bounded conditions for this special application form of study (when the deformation phenomenon has occurred). At the end of the article whole results of the study on a circular plate are debated and new ways assigned to them are discussed. Afterwards all the processes are formulised with the collection of contracting sequences and expanding sequences integrable functions that are intrinsically joints with the characteristic functions to expanding the behaviour of an elastic foundation. Thenceforth all the resultant functions are sets and compared with the other ones (without the loads). Sample pictures and analysis of the study were employed with the ANSYS software to obtain the better observations and conclusions.
GATE - Graduate Aptitude Test in Engineering || Physics Question Paper 2016 |...SOURAV DAS
Graduate Aptitude Test in Engineering (GATE) 2016 Question Paper
Physics Previous Years Question Paper
GATE Preparation
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Download the previous year NEET question paper with the answer key for the years 2022–2023 only on Zephyr.
https://zephyrentrance.in/neet-quiestion-papers
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.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
A Strategic Approach: GenAI in EducationPeter 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.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
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.
2. Useful Data
1. Speed of light in free space, c = 3 x 108 m s-1
2. Planck’s constant, h = 6.6 x 10-34 J s
3. Electron charge, e = 1.6 x 10-19 C
4. Electron mass, me = 9.1 x 10-31 kg
5. Use e3 ≈ 20
NOTE: Attempt ALL the 25 questions. Questions 1-15 (objective questions) carry six marks
each and questions 16-25 (subjective questions) carry twenty one marks each.
Write the answers to the objective questions in the Answer Table for Objective Questions
provided on page 12 only.
1. In a crystalline solid, the energy band structure (E-k relation) for an electron of mass m
h 2 k (2k − 3)
is given by E = . The effective mass of the electron in the crystal is
2m
(A) m
2
(B) m
3
m
(C)
2
(D) 2m
2. Two electric dipoles P1 and P2 are placed at (0, 0, 0) and (1, 0, 0) respectively, with both
of them pointing in the +z direction. Without changing the orientations of the dipoles, P2
is moved to (0, 2, 0). The ratio of the electrostatic potential energy of the dipoles after
moving to that before moving is
1
(A)
16
1
(B)
2
1
(C)
4
1
(D)
8
2
3. 3. The truth table for the given circuit is
J
Q
K
J K Q
(A)
0 0 1
0 1 0
1 0 1
1 1 0
(B) J K Q
0 0 1
0 1 0
1 0 0
1 1 1
(C)
J K Q
0 0 0
0 1 1
1 0 0
1 1 1
(D)
J K Q
0 0 0
0 1 1
1 0 1
1 1 0
3
4. 4. At a given point in space the total light wave is composed of three phasors P1 = a ,
a a
P2 = ei θ and P3 = e − i θ . The intensity of light at this point is
2 2
⎛θ ⎞
(A) 4 a 2 cos 2 ⎜ ⎟
⎝2⎠
⎛θ ⎞
(B) 4 a 2 cos 4 ⎜ ⎟
⎝2⎠
(C) a 2 cos 2 (θ )
(D) 4 a 2 cos 2 (2 θ )
5. A small magnetic dipole is kept at the origin in the x-y plane. One wire L1 is located at
z = − a in the x-z plane with a current I flowing in the positive x direction. Another wire
L2 is at z = + a in y-z plane with the same current I as in L1, flowing in the positive y
direction. The angle ϕ made by the magnetic dipole with respect to the positive x-axis is
(A) 225°
(B) 120°
(C) 45°
(D) 270°
6. The ratio of the inner radii of two glass tubes of same length is 2 . A fluid of viscosity
8.0 cP flows through the first tube, and another fluid of viscosity 0.8 cP flows through
the second one when equal pressure difference is applied across both of them. The ratio
of the flow rate in the first tube to that in the second tube is
(A) 1.6
(B) 10 2
(C) 2
(D) 0.4
7. The relation between angular frequency ω and wave number k for given type of waves
is ω 2 = α k + β k 3 . The wave number k0 for which the phase velocity equals the group
velocity is
α
(A) 3
β
⎛1⎞ α
(B) ⎜ ⎟
⎝3⎠ β
α
(C)
β
4
5. ⎛1⎞ α
(D) ⎜ ⎟
⎝2⎠ β
8. A neutron of mass mn = 10−27 kg is moving inside a nucleus. Assume the nucleus to be a
cubical box of size 10−14 m with impenetrable walls. Take h ≈ 10−34 Js and
1MeV ≈ 10−13 J. An estimate of the energy in MeV of the neutron is
(A) 80 MeV
1
(B) MeV
8
(C) 8 MeV
1
(D) MeV
80
9. A spring-mass system has undamped natural angular frequency ω0 = 100 rad s-1. The
solution x(t) at critical damping is given by x(t ) = x0 (1 + ω0 t ) exp(−ω0 t ) , where x0 is a
constant. The system experiences the maximum damping force at time
(A) 0.01 s
(B) 0.1 s
(C) 0.0 1π s
(D) 0.1 π s
10. In an intrinsic semiconductor, the free carrier concentration n (in cm-3) varies with
temperature T (in Kelvin) as shown in the figure below. The band gap of the
semiconductor is (use Boltzmann constant k B = 8.625 × 10 −5 eV K-1)
36.5
35.5
(n)
ln
34.5
33.5
32.5
2 3 1000/T
(A) 1.44 eV
(B) 0.72 eV
(C) 1.38 eV
(D) 0.69 eV
5
6. r
11. E ( x, y, z, t ) = A(3 i + 4 ˆ) exp[i (ω t − k z )] represents an electromagnetic wave. Possible
ˆ j
directions of the fast axis of a quarter wave plate which converts this wave into a
circularly polarized wave are
(A)
1
[7 iˆ + ˆj ] and
1
[−i +7 ˆ
ˆ j ]
2 2
(B)
1 ˆ [
3i + 4ˆ
j ] and
1
[
4i −3 ˆ
ˆ j ]
2 2
(C)
1 ˆ [
3 i − 4 ˆ and
j
1
2
]
4i +3 ˆ
ˆ j [ ]
2
(D)
1
[
7i − ˆ
ˆ j ] and [
1 ˆ
i +7 ˆ
j ]
2 2
12. A particle of rest mass m0 is moving uniformly in a straight line with relativistic
velocity β c , where c is the velocity of light in vacuum and 0 < β < 1. The phase velocity
of the de Broglie wave associated with the particle is
(A) βc
c
(B)
β
(C) c
c
(D)
β2
13. Electrons of energy E coming in from x = − ∞ impinge upon a potential barrier of width
2a and height V0 centered at the origin with V0 > E , as shown in the figure below. Let
2m (V0 − E )
k= . In the region − a ≤ x ≤ a , the wave function for the electrons is a
h
linear combination of
V
V0
-a a x
6
7. (A) e k x and e − k x
(B) e i k x and e − k x
(C) e i k x and e − i k x
(D) e − i k x and e k x
14. A solid melts into a liquid via first order phase transition. The relationship between the
pressure P and the temperature T of the phase transition is P = −2T + P0 , where P0 is a
constant. The entropy change associated with the phase transition is 1.0 J mole-1 K-1. The
⎛ dP ⎞
Clausius-Clapeyron equation for the latent heat is L = T ⎜ ⎟ Δv. Here Δv = vliquid – vsolid
⎝ dT ⎠
is the change in molar volume at the phase transition. The correct statement relating the
values of the volumes is
(A) vliquid = vsolid
(B) vliquid = vsolid − 1
1
(C) vliquid = vsolid −
2
(D) vliquid = vsolid + 2
⎛a⎞
15. The symmetric part of P = ⎜ ⎟ (a − 2 b ) is
⎜b ⎟
⎝ ⎠
⎛a2 − 2 ba − 1⎞
(A) ⎜ ⎟
⎜ ba − 1 b −2⎟
2
⎝ ⎠
⎛ a (a − 2) b⎞
(B) ⎜ ⎟
⎜
⎝ b b2 ⎟
⎠
⎛ a (a − 1) b(a − 1) ⎞
(C) ⎜ ⎟
⎜ b(a − 1)
⎝ b2 ⎟ ⎠
⎛ a (a − 2) b(a − 1) ⎞
(D) ⎜ ⎟
⎜ b(a − 1)
⎝ b2 ⎟ ⎠
16. Consider a Body Centered Cubic (BCC) crystal with lattice constant ‘a’. Determine
(a) the Miller indices for the (1, 0, 0) plane, [9]
(b) the number of atoms per unit area in the (1, 1, 1) plane. [12]
⎛ a2 ⎞
17. The equation of state of a gas is P ⎜V − ⎟ = n R T , while during an adiabatic process
⎜
⎝ V ⎟⎠
γ
the gas obeys P V = K , where a and K are positive constants. All other symbols have
their usual meaning. Find the work done by the gas when it is expanded first isothermally
P
from (P, V) to (P1, 2V) and then adiabatically from (P1, 2V) to ( 1 , V1), where P1 < P.
2
[21]
7
8. 18. A conducting sphere of radius RA has a charge Q. It is surrounded by a dielectric
spherical shell of inner radius RA and outer radius RB (as shown in the figure below)
B
having electrical permittivity ε (r ) = ε 0 r .
(a) Find the surface bound charge density at r = RA. [12]
(b) Find the total electrostatic energy stored in the dielectric (region B). [9]
RA
A B
RB B
19. For the transistor circuit shown below, evaluate VE, RB and RC, given IC = 1 mA,
VCE = 3.8 V, VBE = 0.7 V and VCC = 10 V. Use the approximation IC ≈ IE.
[21]
VCC = 10 V
RC
RB VC
VE
24 kΩ
1.3 kΩ
r
20. ( )ˆ
For the vector field V = x z 2 i − y z 2 ˆ + z x 2 − y 2 k ,
ˆ j
r
(a) calculate the volume integral of the divergence of V over the region defined by
− a ≤ x ≤ a , − b ≤ y ≤ b and 0 ≤ z ≤ c .
[12]
r
(b) Calculate the flux of V out of the region through the surface at z = c. Hence
deduce the net flux through the rest of the boundary of the region. [9]
21. The spherical surface of a plano-convex lens of radius of curvature R = 1m is gently
placed on a flat plate. The space between them is filled with a transparent liquid of
refractive index 1.55. The refractive indices of the lens and the flat plate are 1.5 and 1.6
8
9. respectively. The radius of the sixteenth dark Newton’s ring in the reflected light of
wavelength λ is found to be 5 mm.
(a) Determine the wavelength λ (in microns) of the light. [12]
(b) Now the transparent liquid is completely removed from the space between the
lens and the flat plate. Find the radius (in mm) of the twentieth dark ring in the
reflected light after this change. [9]
22. A resistor of 1 kΩ and an inductor of 5 mH are connected in series with a battery of emf
4 V through a switch. The switch is closed at time t = 0. In the following, you may use
e 3 ≈ 20 .
(a) Find the current flowing in the circuit at t = 15 micro-second. [9]
(b) Find the heat dissipated through the resistor during the first 15 micro-second.
[12]
23. A photon of energy Eph collides with an electron at rest and gets scattered at an angle 60°
with respect to the direction of the incident photon. The ratio of the relativistic kinetic
energy T of the recoiled electron and the incident photon energy Eph is 0.05.
(a) Determine the wavelength of the incident photon in terms of the Compton
⎛ h ⎞
wavelength λc ⎜ =
⎜ m c ⎟ , where h, me, c are Planck’s constant, electron rest mass
⎟
⎝ e ⎠
and velocity of light respectively. [12]
(b) What is the total energy Ee of the recoiled electron in units of its rest mass ?
[9]
r ˆ 3
24. A particle moves in a plane with velocity v = v r r + v θ θ such that vr = vθ . The time
ˆ
4
r
dependence of the magnitude of the velocity | v | = 5t. It is given that r = 1, θ = 0 and
v r > 0 at t = 0. (In the following, you may use e 3 ≈ 20 .)
(a) Determine the trajectory r(θ ) of the particle. [9]
(b) At what time will θ become 4 radian? [12]
25. A body of mass 1 kg moves under the influence of a central force, with a potential energy
exp(−3r / 2)
function V (r ) = − Joule, where r is in meters. It is found to move in a
5r 2
circular orbit of radius r = 2 m. (In the following, you may use e 3 ≈ 20 ).
(a) Find its angular momentum L and total energy E. [12]
(b) A piece of mass m1 = 0.5 kg breaks off suddenly from the body and begins to fall
radially inwards with velocity v = 10 cm s-1. What are the values of angular
momentum L2 and total energy E2 of the remaining piece, assuming that the
potential energy function remains the same? [9]
9