GATE PH 2010 Question Paper & Solutions

Linear Algebra & Vector Calculus

Consider an anti-symumetric tensor P, with the indices i and j running from 1 lo S. The number of independent components of the rensor is (A) 3 (B) 10 (C) 9 (D) 6 D2 The value oi ene integrad fel imfldi, where the comtour e is the unit cirele: (2-2|=1, is (A) 2ri (B) 4 тà (С) пі (D) 0 12 30)

Linear Algebra & Vector Calculus

The cigenvalues of the matrix (A) 5, 2, -2 12 3 0) 3 10 \cdot 1) are (B) - 5, - 1, -1 for x < 3, (C) 5.1, -1 (D) - 5. 1, 1

Complex analysis

The cigenvalues of the mnatrix 320 are 1o 01, (A) 5,2,-2 (В) -5, -1, -1 (C) 5.1, -1 (D) -5. 1,1

Fourier and Laplace transforms

for x < 3, ihen the Laplace transform of f(x) is 11 () =fx-3 forx23, (A) 833 (B) s'e" (C) 52 (D) 5*e-"

Schrodinger equation & Wave Mechanics

The valence clectrons do not directly determine the following property of a metal. (A) Electrical conductivity (B) Thermal conductivity (C) Shear modulus (D) Metallic lustre 0.6 Consider X-ray diffraction from a crystal with a face-centered-cubic (fcc) lattice. The lattice plane for which there is NO diffraction peak is (A) (2.1,2) (B) (1, 1, 1) (C) (2,0.0) (D) (3, 1. 1) 0.7 The Hall coefficient, Rg, of sodium depends on (A) The effective charge carrier mass and catrier density (B) The charge carrier density and rclaxation lime (C) The charge carrier density only (D) The effective charge carrier mass PH 224 2010 0.8 The Bloch theoremn states that within a crystal, the wavefunction, w(F), of an clectron has the form (A) W(F) =u(r)eti where u(f) is an arbitrary function and & is an arbitrary vector (B) w(F) = u(F)eltir where u(F) is an arbitrary function and & is a reciprocal lattice vector (C) W(7) =u(F)elGi where «(F) =u(P+ À), À is a lattice vector and & is a reciprocal lattice vector (D) W(F) =u(F)elr where u(F) =u(ї + À). À is a lattice vector and & is an arbitrary vector

Crystal Structure & Lattice Dynamics

Consider X-ray diffraction from a crystal with a face-centered-cubic (fec) lattice. The lattice plane for which there is NO diffraction peak is (A) (2, 1,2) (B) (1,1, 1) (C) (2,0.0) (D) (3, 1, 1) 0.7 The Hall coefficient, Ry, of sodium depends on (A) The effective charge carrier mass and carrier density (B) The charge carrier density and relaxation time (C) The charge carrier density only (D) The effective charge carrier mass PH 2024 3010

Schrodinger equation & Wave Mechanics

0.9 The Bloch theorem states that within a crystal, the wavefunction, @(F), of an clectron has the form (A) w(r) = «(r)e where «(7) is an arbitrary function and k is an arbitrary vector (B) w(F) = «(F)er where u(F) is an arbitrary function and & is a reciprocal lattice vector (C) y(F) = (F)el where «(F) =u(P+À), À is a lattice vector and G is a reciprocal lattice vector (D) (r) = (r)ed where u(F) = u(i +À). À is a lattice vector and l is an arbitrary vector In an experiment involving a ferromagnetic medium, the following observations were made. Which one of the plots does NOT correctly represent the property of the medium? (I, is the Curie temperature) (B) Spontaneous Magnetization lagnetization (D) Magnetic Susceptibility Specific Heat T.

Schrodinger equation & Wave Mechanics

The Bloch theorem states that within a crystal, the wavefunction, \psi(\vec{r}), of an electron has the form (A) \psi(\vec{r}) = u(\vec{r})e^{i\vec{k}\cdot\vec{r}} where u(\vec{r}) is an arbitrary function and \vec{k} is an arbitrary vector (B) \psi(\vec{r}) = u(\vec{r})e^{i\vec{G}\cdot\vec{r}} where u(\vec{r}) is an arbitrary function and \vec{G} is a reciprocal lattice vector (C) \psi(\vec{r}) = u(\vec{r})e^{i\vec{G}\cdot\vec{r}} where u(\vec{r}) = u(\vec{r}+\vec{R}), \vec{R} is a lattice vector and \vec{G} is a reciprocal lattice vector (D) \psi(\vec{r}) = u(\vec{r})e^{i\vec{k}\cdot\vec{r}} where u(\vec{r}) = u(\vec{r}+\vec{R}), \vec{R} is a lattice vector and \vec{k} is an arbitrary vector

Electrostatics and Magnetostatics

In an experiment involving a ferromagnetic medium, the following observations were made. Which one of the plots does NOT correctly represent the property of the medium? (T_c is the Curie temperature) (A) Spontaneous Magnetization vs Temperature (B) Magnetization vs Applied Magnetic Field (C) Magnetic Susceptibility vs Temperature (D) Specific Heat vs Temperature

Atomic Spectra & Multi-Electron Atoms

The thermal conductivity of a given material reduces when it undergoes a transition from its normal state to the superconducting state. The reason is: (A) The Cooper pairs cannot transfer energy to the lattice (B) Upon the formation of Cooper pairs, the lattice becomes less efficient in heat transter (C) The electrons in the normal state lose their ability to transfer heal because of their coupling to the Cooper pairs (D) The heal capacity increases on transition to the superconducting state leading to a reduction in thermal conductivity PH VZd 2010

Nuclear Models & Decays

The basic process underlying the neutron B - decay is (A) d →uté +F, (B) d→uté (C) s→4+6+7. (D) u→dté+7,

Nuclear Models & Decays

In the nuclear shell model the spin parily of "N is given by (A) }

Complex analysis

Match the reactions on the left with the associaled interactions on the right. (1) s" → pi +V, (i) Strong (2) 5° →1+1 (ii) Electromagnetic (3) П° +П →П + P (iii) Weak (A) (1, jii), (2, ii), (3, i) (B) (1, i), (2, ii), (3, ii) (C) (1, ii), (2, i), (3, iü) (D) (l, iii), (2, i), (3, ii)

Atomic Spectra & Multi-Electron Atoms

To detect trace amounts of a gaseous species in a mixture of gases, the preferred probing tool is (A) Ionization spectroscopy with X-rays (B) NMR spectroscopy (C) ESR spectroscopy (D) Laser spectroscopy

Electrostatics and Magnetostatics

Two states of an atom have definite parities. An electric dipole transition between these states is (A) Allowed if both the states have even parily (B) Allowed if both the states have odd parily (C) Allowed if the two states have opposite parities (D) Not allowed unless a static electric field is applied 4/24 2010 PH

Electrostatics and Magnetostatics

Two states of an atom have definite parities. An electric dipole transition beiween these states is (A) Allowed if both the states have even parily (B) Allowed if both the states have odd parily (C) Allowed if the two states have opposite parities (D) Not allowed unless a stalic electric field is applied PH 4/24 2010 PH

Statistical Ensembles & Partition Functions

The spectrum of radiation emitted by a black body at a temperature 1000 K peaks in the (A) Visible range of frequencies (B) Infrared range of frequencies (C) Ultraviolet range of frequencies (D) Microwave range of frequencies

Electrostatics and Magnetostatics

An insulating sphere of radius a carries a charge density p(F) = po(a'-r*) cos0; r<a. The leading order term for the electric field al a distance d, far away from the charge distribution, is proportional to (A) d' (B) d (C) d (0) d

Complex analysis

The voltage resolution of a 12 - bit digital to analog converter (DAC), whose output varies from -10 V 10 +10 V is, approximately (A) 1 mV (B) 5 mV (C) 20 mV (D) 100 mV

Complex analysis

In one of the following circuits, negative feedback does not operate for a negative input. Which one is it? The opamps are running from $15 V supplies. (A) (B) 5.IV (C) (D)

Complex analysis

A system of N non-interacting classical poini particies is constrained to move on the iwo-dimensional surface of a sphere. The intemal energy of the system is (A) ENK,T (B) NK,T (C) NkJT (D) ENK,T

Statistical Ensembles & Partition Functions

Wincip of the following atoms cunnol exhibit Bose Einsicin condenstion, even in (1)'Il, (В) "Не, (C) "Na,, (D) "K,o PH 3024 2010 "H

Special theory of relativity

For the set of all Lorentz transformations with velocities along the x-axis, consider the two stutements given below: P: If L is a Lorentz transformation then. L'is also a Lorentz transformation. Q: If 4, and Ly are Lorentz transformations then, 44, is necessarily a Lorentz transformation. Choose the correct option. (A) P is true and Q is false. (B) Both P and Q are true. (C) Both P and Q are false. (D) P is false and Q is true.

Schrodinger equation & Wave Mechanics

Which of the following is an allowed wavefunction for a particle in a bound state? Nis a constant and a, B> 0. (A) WEN$ (B) yr= N(1-ear) (C) W= Ne""'eAity+*) ( v e(mnen zero constant if r sp ifr>R

Complex analysis

A particle is confined within a spherical region of radius one femtorneter (10-"m). Its momentum can be expected to be about (A) 20 keV (B) 200 keV (C) 200- Mel (D) 2GeV

Complex analysis

0.26 For the compiex funcion, S(z) =e-e fi which of the following stalements is sin (Vz) correct? (A) z = 0 is a branch point (B) z =0 is a pole of order one (C) z =0 is a removable singularity (D) z = 0 is an essential singularity

Differential equations

The solution of the differential equation for y(f): ix-y-2codtri) sulject 10 the initial conditions y(0) = 0 and dy =0. is dt liao (A) - cosh(l) +rsinh(t) (B) - sinh(f) + z cosh(f) (C) /cosh(f) (D) /sinh(t) 624 2010 PH 0.28 Given the recurrence relation for the Legendre polynomials (2m +1) * P. (x) = (11+1) Pot, (x) + n PM- (x). which of the following integrals has a non-zero value? (A) j P'P,()P.,(x) ds (B) (xP(XP,(x) dk (oij* leco) ar (DI xr () (7) dx 0.29 Fir, are redimeasional free electron gas, the electronic densily n, and the Fermi energy (A) n = (2mЕ, ) 3 n' (B) n= MEe nh (C) n=-- 2nh mEr (D) ^=- 2%. (mЕ,; ) Tch

Complex analysis

Official Question 28 from GATE PH 2010 Examination.

Electrostatics and Magnetostatics

Far away from any of the resonance frequencies of a medium, the real part of the dielectric permittivity is (A) Always independent of frequency (C) Monotonically increasing with (B) Monotonically decreasing with frequency (D) A non-monotonic function of frequency frequency

Electrostatics and Magnetostatics

Far away fromn any of the resonance frequencies of a medium, the real part of the dielectric permittivity is (A) Always independent of frequency (B) Monotonically decreasing with frequency (C) Monotonically increasing with (D) A non-monotonic function of frequency frequency

Lagrangian & Hamiltonian Dynamics

The ground state avefunction of deuteron is in a superposition of s and d states. Which of the following is NOT true as a consequence? (A) li has a non-zero quadruple moment (B) The neutron-proton potential is non-central (C) The orbital wavefunction is not spherically symmetric (D) The Hamiltonian does not conserve the total angular momenturn

Complex analysis

The first three energy leveis of ?Thes are shown below 187 keV 2+ 57.5 keV 0 keV The expected spin-parity and energy of the nexi level are given by (A) (6* : 400 keV) (B) (6": 300 kcV) (C) (2" ; 400 keV) (D) (4* ; 300 kcV) .7124 2010 PH

Nuclear Models & Decays

The guark content of E',K*-t and p is indicated: (5) = (uus): (R) =|s): (=) =|ued): (p) =|/und). In the process, n +p→K +&*, considering strong interactions only, which of the following slatements is true? (A) The process is allowed because 45 = 0 (B) The process is allowed because 4/, =0 (C) The process is nol allowed because AS # 0 and A/, # 0 (D) The process is not allowed because the baryon number is violated

Linear Algebra & Vector Calculus

The three principal moments of inertia of a methanol (CH,OH) molecule have the property I, = 1, =/ and /, # /. The rotational cnergy eigenvalues are (A) E1I+1) +nmg | (8) 1+1) (C) 1) ECA+) Em (2+4)

Schrodinger equation & Wave Mechanics

A particle of mass m is confined in the poiential V(x) = -mc"x' for x >0, V(x) for x S0. Let the wavefunction of the particle be given by W(0) =-7540+-3543- where y, and yf, are the eigenfunctions of the ground state 0 ** and the first excited state respectively. The expectation value of the energy is (A) 3 n00 (в) 25 ra 10 co) Ln D) "ro 10 FH 8/24

Electrostatics and Magnetostatics

Match the typical spectra of stable molecules with the corresponding wave-number range 1. Electronic spectra i. 10° cm' and above 2. Rotational spectra ii. 10% -10° cm' 3. Molecular dissociation iii. 10" -10'cm"' (A) 1 - ii, 2 -1, 3 -ilі (В) 1 -ії, 2 - üї, 3-і (C) I - iii, 2 - іi, 3 - і (D) 1 - i, 2-ji, 3 -iji 37 Consider the operations P:f →-7 (parity) and T: -> -1 (time-reversal). For the electri nd magnetic fields E and B, which of the following set of transformations is correct' (A) P:Ê →-E,B → B; 1B) P: Ê→ E.B →B: T: Ё →Ë,B→-B T:Ë→Ё,B→ B (c) P: Ê →-E.B → B. (D) P:È → E.B → - B. T:Ё→-Ё,B→-B T:Ё→-Ё,B-В

Electrostatics and Magnetostatics

Consider the operations P. 7 → (parity) (parity) and T: ->- (time-reversal. For the electric and magnetic fields E and B, which of the following set of transformations is correct? P:Ê→-Ë,B→ B; P: E→ E,B → B; (A) (B) T:Ẻ →Ë,B→-B T: Ẽ →Ë,B→B (0) P: E→-E, B → B DIP: E- E.B→-B. T: Ë→-Ë,8→ -B T: Ê→-E,B→ B

Complex analysis

Two magnetic dipoles of magnitude m each are placed in a plane as shown. 427 The energy of interaction is given by 143 (A) Zero (В) Ho т7' 4n d (c) Зм.m° 27 dà (D)-340 17? 8r d 9/24 2010 PH

Electrostatics and Magnetostatics

Consider a conducting joop of radius a and total loop resistance R placed in a region with a magnetic field & thereby enclosing a flux d. The luop is connecied to an electronic circuit as shown, the capacitor being initially uncharged. xxXXXXXXXx xXxXXXXxxx xxxxxxxxxx - Yout xxxxxxxxxx If the loop is pulled out of the region of the magnetic field at a constant speed u, the final output voltage Vou is independent of (А) Ф (B) и (C) R (D) C

Complex analysis

The figure shows a constant current source charging a capacitor that is initially uncharged. - Vout If the switch is closed at t = 0, which of the follawing plots depicts correctly the outpul voltage of the circuit as a function of timc? (A) (B) Yout Your (C) (D) Your! Vout PH 10/24

Complex analysis

For any set of inputs, A and B, the following circuits give the same output, Q, except one. Which one is it? (A) A (B) B - A B (C) De A- (D)

Statistical Ensembles & Partition Functions

CO, molecule has the first few energy levels uniformly separated by approximately 2.5 meV. Al a temperature of 300 K, the ratio of the number of molecules in the 4'"' excited slate to the number in the 200 excited siale is about (A) 0.5 (B) 0.6 (C) 0.8 (D) 0.9 243 Whieh apy: he callowine yee oet syaxwell edaios is eneret? (- inicrmal energy. CA) T -(2V) and p-(95), (8) V -(**), and T=lasl (0) P--(38) mar-(38), (D) p=-(%), and s = (3A).

Classical Thermodynamics

Which among the following sets of Maxwell relations is correct? (U - internal energy. H - enthalpy, A - Helmholtz free energy and G - Gibbs froe energy) (A) =(a) and prai (2s), (B) -(**), and - (?),

Electrostatics and Magnetostatics

For a spin-s particle, in the eigen basis of 5%. S, the expoctation value (sm|S; (sm) is (A) - Nfs(s+1)-m'} (B) s°(s(s+1)-2m*) 2 (C) 1°{s(s+1)-mi*} (D) n'm PH 11/24 2010 0.45 A paricle is placed in a region with the porenial V(x)==xx'- 3'*", where k.A>0. (A) r=D and x=ê are points or stable equiliorium (B) x = 0 is a point of stable cquilibrium and *=* is a point of unstable equilibrium (C) x =0 and x =. - are points of unstable equilibrium (D) There are no points of stable or únstable equilibrium 0.46 A a" meson at rest decays into Iwo pholons, which move along the x- axis. They are both detecied simultaneously after a time, t = 10 s. In an inertial frame moving with a velocity V = 0.6c in the direction of one of the photons, the lime interval belween the lwo detections is (A) 15 s (B) 0s (C) 10s (D) 20 s 0.47 A particle of mass m is confined in an infinite porential well: if O< x<L. V(x)=1 otherwise. I is sulbiected 1o a perurtbing porential V,(+) - V,sin(2Zt) Vợ) within the well. Lel E"" and E'" be the corrections to the ground state energy in the first and second order in V, Vр(х) respectively. Which of the following are true? L (A) E"' = 0; E3<0 (В) Е"> 0; E:=0 (C) E"'= 0; E*" depends on the sign of Vo (D) E'" <0: E3<0 Common Data Questions Common Data for Questions 48 and 49: In the presence of a weak magnetic field, alomic hydrogen undergoes the transition: 3Py →'Sy, by emision of radiation.

Complex analysis

Official Question 45 from GATE PH 2010 Examination.

Complex analysis

Official Question 46 from GATE PH 2010 Examination.

Atomic Spectra & Multi-Electron Atoms

The number of distinct spectral lines that are observed in the resuitant Zeeman spectrum is (A) 2 (B) 3 (C) 4 (D) 6 PH 1224 2010

Atomic Spectra & Multi-Electron Atoms

The number of distinet spectral lines that are observed in the resultant Zeeman spectrum is (A) 2 (B) 3 (C) 4 (D) 6 PH 1224 2010 PH

Electrostatics and Magnetostatics

The spectral line cortesponding to the transition =Px (m,=+2) →'Sy(m,==}) is observed along the direction of the applied magnetic field. The emitted electromagnetic fieid is (A) Circularly polarized (B) Linearly polarized (C) Unpolarized (D) Nol emitted along the magnetic field direction Common Data for Questions 50 and 51: The partition function for a gas of photons is given by 1n2 -F VKT

Statistical Ensembles & Partition Functions

The specific heat of the photon gas varies with temperalure as (A) (B) Cy cv T* (C) (D) T T

Bose-Einstein and Fermi-Dirac statistics

The pressure of the photon gas is (A) P' (k9T)" 15 tỉc (8) 7 4) (C) T (KT)" 45 h'c3 (D) 2 (K,T)% 45 h'c' PH 13/24 2010 PH Linked Answer Questions Stalement for Linked Answer Questions 52 and 53: Consider the propagation of electromagnetic waves in a linear, homogeneous and isotropic material medium with electric permittivitye, and magnetic permeabilily i.

Electrostatics and Magnetostatics

For a plane wave of angular frequency « and propagation vector i propagating in the medium Maxwell's equations reduce to (A) k -Ë =0; *\cdotR =0; kxÊ=шеЙ; k×R=-шuË (в) к-Ё=0; К.F=0; КхË=-шЕÑ; К×Ä=шиË (С) Й\cdotЁ=0; К-Н=0; k×Ё=-шиH; R×П=wEÊ (Đ) К \cdotË=0; Ä\cdotЙ =0; КxË=шиH; k×Ñ=-wєË

Lagrangian & Hamiltonian Dynamics

Il & and je assume negalive values in a cenain frequency range, then the directions of the propagation vector & and the Poynting vector § in that frequency range are relared as (A) & and § are parallel (B) K and § are anti-parallcl (C) Á and are perpendicular to cach other (D) l and § make an angle that depends on the magnitude of jel and le Staternent for Linked Answer Questions 54 and 55: The Lagrangian for a simple pendulum is given by: L==mi'Ö'-mgí(l-cos0)

Complex analysis

Hamilion's equations are then given by (A) Po =-mgl sin 0; =Po (B) po =mglsind: d=ml (C) Pa =-mề; (D) P=: \cdot=Pe

Lagrangian & Hamiltonian Dynamics

The Poisson bracket between & and ó is (A) (0,0)=1 (8) 10.0)= ml (0) 10.0)= 1 (D) /0.0}=4 PH T4/24 2010 PH General Aptitude (GA) Questions

Complex analysis

. Choose the most appropriate word from the options given below ra complese the following sentence: His rather casual remarks on polítics .._ Iils lack of seriousness about the subject. (A) masked (B) belied (C) betrayed (D) suppressed 0.57. Which of the following options is the closest in meaning io she word below: Circuitous (A) cyclic (B) indirect (C) confusing (D) crooked 0.58. Choose the most appropriase word from the options given below to complere the following sensence: Il we manage to _ our natural respurces, we would leave a better planet for our children. (A) uphold (B) restrain (C) cherish (D) conserve 0.59. 25 persons are in a room. 15 of them play hockey, I7 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is: (A) 2 (B) 17 (C) 13 (D) 3

Complex analysis

Official Question 57 from GATE PH 2010 Examination.

Complex analysis

Choose the most appropriate word from the options given below to complete the following sentence: If we manage to _______ our natural resources, we would leave a better planet for our children. (A) uphold (B) restrain (C) cherish (D) conserve

Complex analysis

25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is: (A) 2 (B) 17 (C) 13 (D) 3

Complex analysis

. If 137 + 276 = 435 how much is 731 + 6727 (A) 534 (B) 1403 (C) 1623 (D) 1513 PH 15/24 2010 PH Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). Ail were born on I" January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts: i. Hari's age + Gita's age » Irfan's age + Saira's age. ii. The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is nol the youngest. iii. There are no iwins. In what order were they born (oldest first)? (A) HSIG (B) SGHI (C) IGSH (D) IHSG

Complex analysis

. If 137 + 276 = 435 hou' much is 731 + 6727 (A).534 (B) 1403 (C) 1623 (D) 1513 PH 15/24 2010 Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). Ail were born on I" January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given Ihe foilowing facts: i. Hari's age + Gita's age > Irfan's age + Saira's age. üj. The age difference belween Gita and Saira is 1 year. However, Gita is nol the iii. There are no iwins. oldest and Saira is nor the youngest. In what order were they born (oldest first)? (A) HSIG (B) SGHI (C) IGSH (D) IHSG

Complex analysis

. Moderu warfare has changed from large scale clashes of armies to suppression of civiliso populations. Chemical agents that do their work silently appear to be suited to such wartare; and regretfully, there exist people in military establishments who think that chemical agents are usefut tools for their cause. Which of the following starements bes sums up the meaning of the above parsage: (A) Modern warfare has resulted in civil strife.

Complex analysis

. Moderu warfare has changed from large scale clashes of armles to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause. Which of the following starements hest sums up the meaning of the above passage: (A) Modern warfare has resulted in civil strife.

Complex analysis

. S skilied workers can build a wall in 20 days; 8 semi-skilled workers can build a wall in 25 days: ) unskilled workers can build a wall in 30 days. If a team has 2 skilled, & semi-skilled an unskilled workers, how long will it take to build the wall (A) 20 days (B) 18 days (C) 16 days (D) 15 days Q,65. Comme digis 2, 2. 3, 3, 3,4, 4, 4, 4 how many distince a digit numbers gireater than 300 can be (A) 50 (B) 51 (C) 52 (D) 54 END OF THE QUESTION PAPER PH 1624 2010 PH Space for Rough Work PH 2010 PH Space for Rough Work PH 1{24 2010 PH Space for Rough Work FH 1924 2010 PS1 Space for Rough Work 2024 2010 Space for Rough Work PH 21/24 2010 Space for Rough Work PH 22724 2010 PH Space for Rough Work 171 2,224 2010 PH Space for Rough Work SFAI 24724

Complex analysis

Official Question 65 from GATE PH 2010 Examination.