271 Official GATE PH Questions with Verified Solutions & Answer Keys
A power amplifier gives 150W output for an input of 1.5W. The gain, in dB, is (A) 10 (B) 20 (C) 54 (D) 100...
When liquid oxygen is poured down close to a strong bar magnet, the oxygen stream (A) repelled towards the lower field because it is diamagnetic. (B) attracted towards the higher f...
Fission fragments are generally radioactive as (A) they have excess of neutrons. (B) they have excess of protons. (C) they are products of radioactive nuclides. (D) their total kin...
The allowed states for He (2p') configuration are (A) 'So, 'S1, 'P1, 3Po,1,2, 'D2 and 'D1,2; (B) 'So, 3Po.1,2 and 'D2 (C) 'P, and 'Po,13 (D) 'So and 'P;...
The contour integral g z* + a' is to be evaluated on a cirele of radius 2a centered at the origin. It will have contributions only from the points (A) 1+i -a and - 1+1 a (B) ia and...
A toroidal coil has N closely-wound turns. Assume the current through the coil to be I and the toroid is filled with a magnetic material of relative permittivity H,. The magnitude ...
An electromagnetic wave with E(z,f) = E, cos(w t - kz) / is traveling in free space and crosses a disc of radius 2 m placed perpendicular to the z-axis. If E, = 60 V m'' the averag...
If [x,p ]= ih, the value of [x',p] is (A) 2ihx? (B) - 2ihx? (C) 3ihx' (D) - 3ihx?...
A system has energy levels Eo, 2Eo, 3Eo,..., where the excited states are triply degenerate. Four non-interacting bosons are placed in this system. If the total energy of these bos...
A ferromagnetic mixture of iron and copper having 75% atoms of Fe exhibits a saturation magnetization of 1.3 x10° A m''. Assume that the total number of atoms per unit volume is 8x...
In the deuterium + tritium (d + t) fusion more energy is released as compared to deuterium + deuterium (d + d) fusion because (A) tritium is radioactive. (B) more nucleons particip...
Identify the function F generated by the logic network shown → F x. (A) F = (X + Y) Z (B) F =Z+Y+ YX (C) F = ZY (Y + X) (D) F = XYZ...
For arbitrary matrices E,F,G and H, if EF - FE = 0 then Trace(EFGH) is equal to (A) Trace(HGFE) (B) Trace(E)Trace(F).Trace(G).Trace(H) (C) Trace(GFEH) (D) Trace(EGHF)...
The last two terms of the electronic configuration of manganese (Mn) atom is 3d'4s'. The term factor of Mn** ion is (A) *D12 (B) *F32 (C) 'F92 (D) 'D1/2...
Metallic monovalent sodium crystallizes in body centered cubic structure. If the length of the unit cell is 4×10-8 cm, the concentration of conduction electrons in metallic sodium ...
to Q.75, 0.5 mark will be deducted for each wrong answer. For the pairs of questions with linked answers, there will be negative marks only for wrong answer to the first question, ...
If the Fourier transform F[8(x- a)]= exp(-i2mv a), then F' (cos 2r av) will correspond to (A) 8(x-a)- 8(x+a) (B) a constant (0) {[ô(x=a)+iô(x+a)] (D) =[0(r-a)+ô(x+a)] If / = gdz Ln...
The value of [7 (z + 1)dz is (A) 0 (B) 2тi (C) -2тi (D) (-1+ 2i)r PH 5/24 2008 MAIN PAPER - PH - + y =0. Which one of the following Consider the Bessel equation (v = 0), d'y statem...
The value of [r (z + 1)dz is (A) 0 (B) 2mi (C) -2mi (D) (-1+2i)7 PH 5/24 2008 MAIN PAPER - PH| Consider the Bessel equation (v = 0), d'y - + y =0. Which one of the following statem...
Under a certain rotation of coordinate axes, a rank-1 tensor Va (a=1,2,3) transforms according to the orthogonal transformation defined by the relations vi (v, + ½2) ; ½2= VE (-v, ...
Under a certain rotation of coordinate axes, a rank-1 tensor va (a=1,2,3) transforms according to the orthogonal transformation defined by the relations vj (v, +½) : ½= Tz(-v, +v2)...
A mass m is constrained to move on a horizontal frictionless surface. It is set in circular motion with radius ro and angular speed @, by an applied force F communicated through an...
A particle is placed in a one dimensional box of size L along the x-axis (0< x < L). Which of the following is true? (A) In the ground state, the probability of finding the particl...
Consider a system of two non-interacting classical particles which can occupy any of the three energy levels with energy values E =0,e and 2e having degeneracies g(E)=1,2 and 4 res...
Three consecutive absorption lines at 64.275 cm', 77.130 cm' and 89.985 cm' have been observed in a microwave spectrum for a linear rigid diatomic molecule. The moments of inertia ...
The molecular spectra of two linear molecules O-C-O and O-C-S are recorded in the microwave region. Which one of the following statement is correct? (A) Both the molecules would sh...
An a.c. voltage of 220 Vms is applied to the primary of a 10:1 step-down transformer. The secondary of the transformer is centre tapped and connected to a full wave rectifier with ...
The value of the contour integral, fix dãl , fora cirele C of radius r with center at the origin is (A) 2mr (в) ½ (C) тr? (D)г...
If p and q are the position and momentum variables, which one of the following is NOT a canonical transformation ? (A) Q= aq and P =- P, for a # 0 (B) Q=aq+ Bp and P = Bq+ap for a,...
In an insulating solid which one of the following physical phenomena is a consequence of Pauli's exclusion principle ? (A) Ionic conductivity (B) Ferromagnetism (C) Paramagnetism (...
In a diatomic molecule, the internuclear separation of the ground and first excited electronic state are the same as shown in the figure. If the molecule is initially in the lowest...
Assuming the mean life time of a muon (in its rest frame) to be 2x10's, its life time in the laboratory frame, when it is moving with a velocity 0.95c is (A) 6.4x10€s (B) 0.62x10-6...
10 92 15 V \cdot10 g RL above circuit are Assuming an ideal voltage source, Thevenin's resistance and Thevenin's voltage respectively for the (A) 152 and 7.5 V (B) 2052 and 5 V (C)...
An amplifier of gain 1000 is made into a feedback amplifier by feeding 9.9 % of its output voltage in series with the input opposing. If fi = 20 Hz and fu = 200 kHz for the amplifi...
Rs=1 kQ Vin 15-25 V Vz = 10 V RL /Iz Pick the correct statement based on the above circuit. (A) The maximum Zener current, Iz(max), when R_ = 10 kS is 15 mA (B) The minimum Zener c...
 and B represent two physical characteristics of a quantum system. If  is Hermitian, then for the product Âß to be Hermitian, it is sufficient that (A) Ô is Hermitian (B) B is an...
Consider the set of vectors in three-dimensional real vector space R3, S = {(1,1,1), (1,-1,1), (1,1,-1)} . Which one of the following statements is true ? (A) S is not a linearly i...
The minimized logic expression for the above map is (A) Y = PR+@ (B) Y = Q\cdotPR (C) Y =Q+PR (D) Y =Q\cdotPR...
The corresponding logic implementation using gates is given as: P P (A) R- -Y (B) R -Y Q- P P (C) Q (D) Q R R - Y PH END OF THE QUESTION PAPER 14/16...
Official Question 61 from GATE PH 2009 Examination....
Official Question 62 from GATE PH 2009 Examination....
Official Question 63 from GATE PH 2009 Examination....
Official Question 64 from GATE PH 2009 Examination....
Official Question 65 from GATE PH 2009 Examination....
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...
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),...
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...
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)...
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...
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...
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 removabl...
Official Question 28 from GATE PH 2010 Examination....
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 ...
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 9/2...
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...
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)...
Official Question 45 from GATE PH 2010 Examination....
Official Question 46 from GATE PH 2010 Examination....
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...
. 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 sub...
Official Question 57 from GATE PH 2010 Examination....
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 ...
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 footb...
. 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)...
. 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). ...
. 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 wart...
. 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 warf...
. 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, & sem...
Official Question 65 from GATE PH 2010 Examination....
Two charges q and 2q are placed along the x-axis in front of a grounded, infinite conducting plane, as shown in the figure. They are located respectively at a distance of 0.5 m and...
A neutron passing through a detector is detected because of (A) the ionization it produces (B) the scintillation light it produces (C) the electron - hole pairs it produces (D) the...
In the following circuit, the voltage across and the current through the 2 kS resistance are 500 S2 1kQ W + 20 V 10 V 30 V ,2 kg (A) 20 V, 10 mA (B) 20 V, 5 mA (C) 10 V, 10 mA (D) ...
The unit vector normal to the surface x' + y2 - z =1 at the point P(1,1,1) is (A) I+]-k (B) 2ĩ + ]-K (0) 1+2] -k (D) 21+27-K V3 3...
Let (P,9) and (P,Q) be two pairs of canonical variables. The transformation e=9ª cos(Bp) P=qª sin(Bp) is canonical for (A) a = 2, B =1/2 (B) a=2, B=2 (C) a =1, B=1 (D) 0=1/2, B=2...
The lifetime of an atomic state is 1 nanosecond. The natural line width of the spectral line in the emission spectrum of this state is of the order of (A) 10-1° eV (B) 10' eV (C) 1...
The degeneracy of an excited state of nitrogen atom having electronic configuration Is'2s'2p'3d' is (A) 6 (B) 10 (C) 15 (D) 150...
In the following circuit, Trl and Tr2 are identical transistors having VBE = 0.7 V. The current passing through the transistor Tr2 is S100 Tr2 Trl (A) 57 mA (B) 50 mA (C) 48 mА (D)...
The following Boolean expression can be simplified to Y=A\cdotB\cdotC\cdotD+Ã\cdotB\cdotC\cdotD+Ã\cdotB\cdotC\cdotD+Ã\cdotB\cdotC\cdotD+Ã\cdotB\cdotC\cdotD+A\cdotB\cdotC\cdotD (A) ...
Consider the following circuit. 1 kS 4 kg www ww +10 V Vin -10 V Which of the following correctly represents the output Vou corresponding to the input Vin? (A) (B) +SVL +5V +2V] +2...
Which of the following statements is TRUE for the function f (z) ? (A) f(z) is analytic everywhere in the complex plane (B) f(z) hasa zero at z = П (C) f(z) has a pole of order 2 a...
The density of states of electrons (including spin degeneracy) in the band is given by (A) L (B) L toyasin(ka) 2mya sin(ka) (C) L (D) L 2nyacos(ka) tyacos(ka)...
The value of a for which y, is orthogonal to v, is (A) 2 (B) 1 (C) -1 (D) -2...
Choose the most appropriate word from the options given below to complete the following sentence. If you are trying to make a strong impression on your audience, you cannot do so b...
Choose the most appropriate word(s) from the options given below to complete the following sentence. I contemplated Singapore for my vacation but decided against it. (A) to visit (...
If Log (P) = (1/2)Log (Q) = (1/3) Log (R), then which of the following options is TRUE? (A) P' = Q'R' (B) Q'= PR (C) Q'=R'P (D) R= P'Q'...
Which of the following options is the closest in the meaning to the word below: Inexplicable (A) Incomprehensible (B) Indelible (C) Inextricable (D) Infallible...
Choose the word from the options given below that is most nearly opposite in meaning to the given Amalgamate (A) merge (B) split (C) collect (D) separate...
A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can...
The variable cost (V) of manufacturing a product varies according to the equation V= 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces ...
Few school curricula include a unit on how to deal with bereavement and grief, and yet all students at some point in their lives suffer from losses through death and parting. Based...
A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is eplaced with 1 litre of water. Subsequently, I litre of the mixture is again repl...
Consider the following OP-AMP circuit. Vin + 5 V 4 k 1 k + - + 10 V - 10 V Vout Which one of the following correctly represents the output Vout corresponding to the input Vin? (A...
In the following circuit, for the output voltage to be Vo = ( - V1 + V2 /2), the ratio R1/R2 is V2 + - + VCC - VCC Vo R R V1 R2 R1 (A) 1/2 (B) 1 (C) 2 (D) 3...
In the following circuit, the voltage drop across the ideal diode in forward bias condition is 0.7 V. 24 Volt 12 k 6 k 3.3k The current passing through the diode is (A) 0.5 mA (...
Total binding energies of O15, O16 and O17 are 111.96 MeV, 127.62 MeV and 131.76 MeV, respectively. The energy gap between 1p1/2 and 1d5/2 neutron shells for the nuclei whose mass ...
Given B r F , where k j i B B ˆ ˆ ˆ 0 is a constant vector and r is the position vector. The value of C r d F , where C is a circle of unit radius cen...
The equilibrium vibration frequency for an oscillator is observed at 2990 cm-1. The ratio of the frequencies corresponding to the first and the fundamental spectral lines is 1.96. ...
The energy of the particle is (A) m k 2 5 2 2 (B) m k 4 3 2 2 (C) m k 2 2 2 (D) m k 2 2...
In the equilibrium condition, the separation between the positive and the negative charge centers is (A) 8.66 10-16 m (B) 2.60 10-15 m (C) 2.60 10-16 m (D) 8.66 10-15 m...
Choose the grammatically INCORRECT sentence:...
Which one of the following options is the closest in meaning to the word given below? Mitigate (A) Diminish (B) Divulge (C) Dedicate (D) Denote...
Choose the most appropriate alternative from th e options given below to complete the following sentence: Despite several --------- the mission succeeded in its attempt to resolve ...
The cost function for a product in a firm is gi ven by 5q2, where q is the amount of production. The firm can sell the product at a market price of 50 per unit. The number of units...
Choose the most appropriate alternative from the options given below to complete the following sentence: Suresh's dog is the one --------- was hurt in the stampede. (A) that (B) wh...
Which of the following assertions are CORRECT? P: Adding 7 to each entry in a list adds 7 to the mean of the list Q: Adding 7 to each entry in a list adds 7 to the standard deviati...
An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplie s 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a ...
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x - 0.1x2 where y is...
Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal interviews to collect and collate economic data. Requirements: High School -pass, must be ...
Given the sequence of terms, AD CG FK JP, the next term is (A) OV (B) OW (C) PV (D) PW END OF THE QUESTION PAPER Paper Question no. Key Paper Question no. Key PH 1A PH 41 B PH 2C P...
Interference fringes are seen at an observation plane z = 0, by the superposition of two plane waves Ak\vecԦrԦ) 1 and Ak\vecԦrԦ) 1, where A1 and A2 are real amplitudes. The conditi...
What should be the clock frequency of a 6-bit A/D converter so that its maximum conversion time is 32 μs? (A) 1 MHz (B) 2 MHz (C) 0.5 MHz (D) 4 MHz...
The number of distinct ways of placing four indistinguishable balls into five distinguishable boxes is ____________. 2013 PHYSICS - PH PH 7/13...
If AԦ and B\vecԦ are constant vectors, then (AԦB\vecԦrԦ) is (A) AԦB\vecԦ (B) AԦB\vecԦ (C) rԦ (D) Zero...
+ 1 2) is equal to [Given (n+1) = n (n) and (1/2) = √\pi] (A) 0! 2 √\piB) 20! 0! 2 √\piC) 20! 0! 2^2 √\piD) 0! 2^2 √\pi...
The relativistic form of Newton's second law of motion is...
The total energy of an ionic solid is given by an expression = ^2 4\pi0 + where is Madelung constant, r is the distance between the nearest neighbours in the crystal and B is a c...
A proton is confined to a cubic box, whose sides have length 10-12 m. What is the minimum kinetic energy of the proton? The mass of proton is 1.67 10-2 kg and Planck's constant is ...
For this circuit the frequency above which the gain will decrease by 20 dB per decade is (A) 15.9 kHz (B) 1.2 kHz (C) 5.6 kHz (D) 22.5 kHz...
A number is as much greater than 75 as it is smaller than 117. The number is: (A) 91 (B) 93 (C) 89 (D) 96...
The professor ordered to the students to go out of the class. I II III IV Which of the above underlined parts of the sentence is grammatically incorrect? (A) I (B) II (C) III (D) I...
Which of the following options is the closest in meaning to the word given below: Primeval (A) Modern (B) Historic (C) Primitive (D) Antique...
Friendship, no matter how _________it is, has its limitations....
Select the pair that best expresses a relationship similar to that expressed in the pair: Medicine: Health (A) Science: Experiment (B) Wealth: Peace (C) Education: Knowledge (D) Mo...
X and Y are two positive real numbers such that 6 and 8 . For which of the following values of ) the function ݂ܻwill give maximum value?...
If 7| =5 then the values of | is: (A) 2, 1/3 (B) 1/2, 3 (C) 3/2, 9 (D) 2/3, 9 2013 PHYSICS - PH PH 13/13...
Following table provides figures (in rupees) on annual expenditure of a firm for two years - 2010 and 2011. Category 2010 2011 Raw material 5200 6240 Power & fuel 7000 9450 Salary ...
A firm is selling its product at Rs. 60 per unit. The total cost of production is Rs. 100 and firm is earning total profit of Rs. 500. Later, the total co st increased by 30%. By w...
Abhishek is elder to Savar. Savar is younger to Anshul. Which of the given conclusions is logically valid and is inferred from the above statements?...
The unit vector perpendicular to the surface 32 2 2= + +z y x at the point ( )1 , 1 , 1is (A) 3 ˆˆ ˆ z y x− + (B) 3 ˆˆ ˆ z y x− − (C) 3 ˆˆ ˆ z y x+ − (D) 3 ˆˆ ˆ z y x+ +...
If the half -life of an elementary particle moving with speed 0.9 c in the laboratory frame is 810 5−× s, then the proper half-life is __________ × 10-8 s. (𝑐𝑐 = 3 × 108 𝑚𝑚/𝑠�...
An unpolarized light wave is incident from air on a glass surface at the Brewster angle. The angle between the reflected and the refracted wave is (A) 00 (B) 045 (C) 090 (D) 0120...
Two masses m and 3m are attached to the two ends of a massless spring with force constant K. If m = 100 g and K = 0.3 N/m, then the natural angular frequency of oscillation is ____...
The recoil momentum of an atom is Ap when it emits an infrared photon of wavelength 1500 nm, and it is Bp when it emits a photon of visible wavelength 500 nm. The ratio B A p p is ...
For a gas under isothermal conditions, its pressure P varies with volume V as 3 / 5−∝ V P . The bulk modulus B is proportional to (A) 2 / 1−V (B) 3 / 2−V (C) 5 / 3−V (D) 3 / 5−V...
Which one of the following high energy processes is allowed by conservation laws? (A) 0 0Λ + Λ → +p p (B) n p+ → +− 0π π (C) ee p nν+ + →− (D) γ µ+ →+ +e PH 1/10 PH (GATE 2014)...
The length element ds of an arc is given by, ( ) ( ) 2 122212 32 ) ( dx dxdx dx ds+ + = .The metric tensor ijg is (A) 1 3 3 2 (B) 12 3 2 32 (C...
The input given to an ideal OP-AMP integrator circuit is The correct output of the integrator circuit is (A) (B) (C) (D)...
A bead of mass m can slide without friction along a massless rod kept at 45 0 with the verti cal as shown in the figure. The rod is rotating about the vertical axis with a constant...
For Nickel , the number density is 8 × 1023 𝑎𝑎𝑎𝑎𝑎𝑎𝑚𝑚𝑠𝑠/𝑐𝑐𝑚𝑚3 and electronic configuration is 1s22s22p63s23p63d84s2. T he value of the saturation magnetization of Nick...
Given that the linear transformation of a generalized coordinate q and the corresponding momentum p, Q = q + 4ap P = q + 2p is canonical, the value of the constant a is ___________...
In an interference pattern formed by two coherent sources, the maximum and the minimum of the intensities are 9I0 and I0, respectively. The intensities of the individual waves are ...
ψ1 and ψ2 are two orthogonal states of a spin 2 1 system. It is given that + = 1 0 3 2 0 1 3 1 1ψ , where 0 1 and 1 0 represent...
The current gain of the transistor in the following circuit is \beta\beta𝑑𝑑𝑐𝑐 = 100. The value of collector current Ic is _______________ mA....
In order to measure a maximum of 1 V with a resolution of 1 mV using a n-bit A/D converter, working under the principle of ladder network, the minimum value of n is _____________ ....
In an inertial frame S, two events A and B take place at (ct, = 0, 7, = 0) and (ct = 0, 7g = 2ý), respectively. The times at which these events take place in a frame S' moving with...
vaine of ( - di slang sRis (А) Ф-Ф, (В) Ф -ф...
Question Type : MCO If f(x) = e-** and g (x) = xe-* , then (A) fandg are differentiable everywhere (B) fis differentiable everywhere but g is not (C) g is differentiable everywhere...
Consider w = f (z) = u(x, y) + iv(x, y) to be an analytic function in a domain D. Which one of the following options is NOT correct? (A) u(x, y) satisfies Laplace equation in D (B)...
The value of J? t2 8(3t-6)dt is (upto one decimal place)...
Which one of the following DOES NOT represent an exclusive OR operation for imputs A and B ? (A) (A + B)AB (C) (A + B)(A + B) (B) AB + BA (D) (A + B)AB...
Question Type : MCO Consider a complex function f(z) = 2(*+*)cos (2x) Which one of the following statements is correct? (A) f(z) has simple poles at z = 0 and z = - ½/ (B) Az) has ...
In the given circuit, the voltage across the source resistor is 1 V. The drain voltage (in V) is 25 V 5k2 2 M2 500 92...
A beam of X-ray of intensity lo is incident normally on a metal sheet of thickness 2 mm. The intensity of the transmitted beam is 0.0251. The linear absorption coefficient of the m...
The energy dependence of the density of states for a two dimensional non-relativistic electron gas is given by, g (E) = CE" , where C is constant. The value of n is...
Question Type : MCO Four forces are given below in Cartesian and spherical polar coordinates. F=Kexp(-7/R')f (ii) F, = K(xy-y°₴) (iv) F, = K(ф/r) where K is a constant. Identify th...
Consider a system of eight non-interacting, identical quantum particles of spin-3/2 in a one dimensional box of length L. The minimum excitation energy of the system, in units of 2...
Consider the circuit shown in the figure, where RC = 1. For an input signal Vi shown below, choose the correct V. from the options: R Vi o- 1 o Vo R$ 1 2 3 (A) (B) 2 -1 (C) Vo T 0....
In the simple current source shown in the figure, Qi and Q are identical transistors with current gain B = 100 and VE = 0.7 V 5k23 The current I. (in mA) is (upto two decimal place...
In a rigid-rotator of mass M, if the energy of the first excited state is 1 meV, then the fourth excited state energy (in meV) is _...
A particle of mass 0.01 kg falls freely in the earth's gravitational field with an initial velocity v (0) = 10 ms'. If the air exerts a frictional force of the form, f = -kv, then ...
Question Type : MCO In the given circuit, if the open loop gain A = 105 , the feedback configuration and the closed loop gain Af are Vio 0 Vo 9 kg 1 kn $ 1 (A) series-shunt, Af = 9...
A function (2) satisfies the ordinary diferential equation y° + - * = 0, where m = 0,1,2,3,.... Consider the four statements P, Q, R, S as given below. P: z'' and z*™ are linearly ...
A monochromatic plane wave (wavelength = 600 nm) E, expli(kz - ct)] is incident normally on a diffraction grating giving rise to a plane wave E, exp ilk, \cdotF- cot) in the first ...
The atomic masses of 53 Eu, 62Sm, }H and neutron are 151.921749, 151.919756, 1.007825 and 1.008665 in atomic mass units (amu), respectively. Using the above information, the Q-valu...
There are four electrons in the $3d$ shell of an isolated atom. The total magnetic moment of the atom in units of Bohr magneton is _______....
Which of the following is an analytic function of z everywhere in the complex plane? (A) z (B) (E*) (C) |7|" (D) VE...
In a Young's double slit experiment using light, the apparatus has two slits of unequal widths. When only slit-l is open, the maximum observed intensity on the screen is 4/. When o...
Two blocks are connected by a spring of spring constantk. One block has mass m and the other block has mass 2m. If the ratio k/m = 4 s-3 , the angular frequency of vibration w of t...
Consider the reaction 3Mn + è → LACr + X. The particle X is (A) Y (B) Ve (C) n (D) п...
A two-dimensional square rigid box of side L contains six non-interacting electrons at T = 0 K. The mass of the electron is m. The ground state energy of the system of electrons, i...
The direction of Üf for a scalar field f(x, y,z) = =x2-xy +=2? at the point P (1, 1,2) is (1) (-]-27) (B) (1+2k) (C) (-2k) (D) (+2Ê)...
A particle of mass m = 0.1 kg is initially at rest at origin. It starts moving with a uniform acceleration à =10î ms7 at t = O. The action S of the particle, in units of J-s, at t ...
In an inertial frame of reference S, an observer finds two events occurring at the same time at co- ordinates x, = 0 and Xz = d. A different inertial frame S' moves with velocity v...
Consider a system having three energy levels with energies O, 2e and 3&, with respective degeneracies of 2, 2 and 3. Four bosons of spin zero have to be accommodated in these level...
For the digital circuit given below, the output X is A. (A)A+B\cdotC (C) А\cdot(B+C) (B) A.(B+C) (D) A+(B\cdotC)...
For the transistor shown in the figure, assume VBE = 0.7 V and Pdc = 100. If Vin = 5V, Vout (in Volts) is _. (Give your answer upto one decimal place) 10 V > 3kг Vin owv 200 k S O ...
The state of a system is given by (4)=(41)+2182)+3183) where Ф,), (Ф2) and (Фs) form an orthonormal set. The probability of finding the system in the state |Ф2) is (Give your answe...
Light is incident from a medium of refractive index n = 1.5 onto vacuum. The smallest angle of incidence for which the light is not transmitted into vacuum is _ _degrees. (up to tw...
The best resolution that a 7 bit A/D convertor with 5 V full scale can achieve is to two decimal places). Correct: 1 Wrong : 0 mV. (up...
In the figure given below, the input to the primary of the transformer is a voltage varying sinusoidally with time. The resistor R is connected to the centre tap of the secondary. ...
The atomic mass and mass density of Sodium are 23 and 0.968 g cm', respectively. The number density of valence electrons is x1022 cm*. (Up to two decimal places.) (Avogadro number,...
(B) 3kg 9 - KB 2 (D) 6kB Correct: 1 Wrong : -0.33 the angian (te mo g's motive 10 = 4, a (4) let one orine following is TRUE? (A) Both the canonical momentum and equation of motion...
Two identical masses of 10 gm each are connected by a massless spring of spring constant 1 N/m. The non-zero angular eigenfrequency of the system is _rad/s. (up to two decimal plac...
The Poison bracket [x, xp, + yP, I is equal to (A) -x (B) y (C) 2Px (D) Py...
The contour integral O- de 1+2 evaluated along a contour going from -oo to too along the real axis and closed in the lower half-plane by a half circle is equal to _ _ (up to two de...
The Compton wavelength of a proton is _fm. (up to two decimal places). (mp =1.67x10-27 kg, h = 6.626x10-34Js, e = 1.602×10-19C, c= 3x108 ms~')...
Electromagnetic interactions are : (A) C conserving (B) C non-conserving but CP conserving (C) CP non-conserving but CPT conserving (D) CPT non-conserving...
The coefficient of elkx in the Fourier expansion of u(x) = Asin? (ax) for k = -20 is (A) A/4 (B) -A/4 (C) A/2 (D) -A/2...
A uniform volume charge density is placed inside a conductor (with resistivity 10-22m). The charge density becomes 1/(2.718) of its original value after time _ femto seconds. (up t...
The total energy of an inert-gas crystal is given by E(R) = - po (in eV), where R is the inter-atomic spacing in Angstroms. The equilibrium separation between the atoms is Angstrom...
Consider a metal with free electron density of 6x1022 cm-3 . The lowest frequency electromagnetic radiation to which this metal is transparent is 1.38x101 Hz. If this metal had a f...
An object travels along the x- direction with velocity c / 2 in a frame O. An observer in a frame O' sees the same object travelling with velocity c / 4. The relative velocity of O...
ite irise fare do is equal ra. _. (up to two decimal places)....
The imaginary part of an analytic complex function is v(x, y) = 2xy + 3y. The real part of the function is zero at the origin. The value of the real part of the function at 1 + i i...
A uniform solid cylinder is released on a horizontal surface with speed 5 m/s without any rotation (slipping without rolling). The cylinder eventually starts rolling without slippi...
Which one of the following gases of diatomic molecules is Raman, infrared, and NMR active? (A) 'H-'H (B) "C-160 (C) 'H-35Cl (D) 160-160...
Consider two particles and two non-degenerate quantum levels 1 and 2. Level 1 always contains a particle. Hence, what is the probability that level 2 also contains a particle for e...
A person weighs W, at Earth's north pole and We at the equator. Treating the Earth as a perfect sphere of radius 6400 km, the value 100xWp - We) / Wais _ _. (up to two decimal plac...
The geometric cross-section of two colliding protons at large energies is very well estimated by the product of the effective sizes of each particle. This is closest to (A) 10 b (B...
For the transistor amplifier circuit shown below with R1 = 10 kg, R2=10 kg, R3=1 ks, and B = 99. Neglecting the emitter diode resistance, the input impedance of the amplifier looki...
In spherical polar coordinates (r, 0, Ф), the unit vector Ô at (10, 7/4, n/2) is (A) K ((+) (C(-+) PH 1/12 GATE 2018 Physics...
The logic expression ABC + ABC + ABC + ABC can be simplified to (A) A XORC (B) A AND & (C) 0 (D) 1...
In a 2-to-1 multiplexer as shown below, the output X = Ao if C = 0, and X = A, if C = 1. A1 - Which one of the following is the correct implementation of this multiplexer? (A) (B) ...
A spaceship is travelling with a velocity of 0.7c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. À person in the space ...
An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance rj to that at rz(= 2 rj) from the wire is PH 4/12 GATE 2018 Physic...
If X is the dimensionality of a free electron gas, the energy (E) dependence of density of states is given by EX-Y, , where Y is...
- Q. 55 carry two marks each. Physics Given V1 = î - j and V2 = - 2i + 3j + 2k, which one of the following ½z makes (V,V2,Vz) a complete set for a three dimensional real linear vec...
An interstellar object has speed v at the point of its shortest distance R from a star of much larger mass M. Given v2 = 2 GM/R, the trajectory of the object is (A) circle (B) elli...
Three particles are to be distributed in four non-degenerate energy levels. The possible number of ways of distribution: (i) for distinguishable particles, and (ii) for identical B...
An n-channel FET having Gate-Source switch-off voltage VGs(OFF) = - 2 V is used to invert a 0 - 5 V square-wave signal as shown. The maximum allowed value of R would be kZ (up to t...
For the transformation Q =/2q e-1+2a cosp, P = JZqe-a-1 sinp (where a is a constant) to be canonical, the value of a is PH 9/12 GATE 2018 Physics...
Given d'f (x) _ , df(x) dx? - + f(x) = 0, and boundary conditions f (0) = 1 and f (1) = 0, the value of f (0.5) is two decimal places). _ (up to...
A uniform circular disc of mass m and radius R is rotating with angular speed w about an axis passing through its center and making an angle 0 = 30° with the axis of the disc. If t...
The relative magnetic permeability of a type-I super conductor is (a) 0 (b) 1 − (c) 2π (d) 1 4π GATE 2019...
For the following circuit, what is the magnitude of out V if in 1.5 V V = ? (a) 0.015V (b) 0.15V (c) 15V (d) 150V GATE 2019...
For a spin-1/2 particle, let $|\uparrow\rangle$ and $|\downarrow\rangle$ denote its spin up and spin down states, respectively. If $|a\rangle = \frac{1}{\sqrt{2}}(|\uparrow\downarr...
Consider a transformation from one set of generalized coordinate and momentum ( ,q p ) to another set ( , Q P ) denoted by, ; s r Q pq P q = = where s and r are constants. The tran...
The pole of the function ( ) cot f z z = at 0 z = is (a) a removablesingularity (b) an essential singularity (c) a simple pole (d) a second order pole GATE 2019...
Consider a three-dimensional crystal of N inert gas atoms. The total energy is given by ( ) 12 6 2 U R N p q R R σ σ = ∈ − , where 12.13, 14...
The energy-wavevector ( ) E k − dispersion relation for a particle in two dimensions is E Ck = , where C is a constant. If its density of states ( ) D E is proportional to p E then...
Let $|\psi_1\rangle = \begin{pmatrix} 1 \\ 0 \end{pmatrix}$ and $|\psi_2\rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix}$ represent two possible states of a two-level quantum system....
Official Question 38 from GATE PH 2019 Examination...
A solid cylinder of radius R has total charge Q distributed uniformly over its volume. It is rotating about its axis with angular speedω . The magnitude of the total magnetic momen...
Official Question 40 from GATE PH 2019 Examination...
A 3-bit analog-to-digital converter is designed to digitize analog signals ranging from 0 V to 10 V. For this converter, the binary output corresponding to an input of 6 V is...
Official Question 42 from GATE PH 2019 Examination...
For the following circuit, the correct logic values for the entries 2 X and 2Y in the truth table are (a) 1 and 0 (b) 0 and 0 (c) 0 and 1 (d) 1 and 1 GATE 2019...
For a given load resistance 4.7 L R = ohm, the power transfer efficiencies load total P P η = of a dc voltage source and a dc current source with internal resistances 1...
The ground state electronic configuration of the rare-earth ion ( 3 Nd + ) is [ ] 3 2 6 4 5 5 Pd f s p . Assuming LS coupling, the Lande g - factor of this ion is 8 11. The effecti...
Let θ be a variable in the range π θ π − ≤ < . Now consider a function ( ) 1 for 2 2 0 otherwise π π θ ψ θ − ≤ < = if its Fourier-series is written as ( ) im m m C e θ ψ θ...
Two spaceships A and B , each of the same rest length L , are moving in the same direction with speeds 4 5 c and 3 5 c , respectively, where c is the speed of light. As measured by...
Official Question 62 from GATE PH 2019 Examination...
Official Question 63 from GATE PH 2019 Examination...
Two events, one on the earth and the other one on the Sun, occur simultaneously in the earth’s frame. The time difference between the two events as seen by an observer in a spacesh...
Which one of the following is a solution of du(x) 2= ku(x), for k real? (A) (B) (0) (D) e kx sinkx coskx sinh x...
He is known for his unscrupulous ways. He always sheds_ tears to deceive people. fox's crocodile's crocodile fox Jofra Archer, the England fast bowler, is_ more fast faster less fa...
owd funding deals with mobilisation of funds for a project from a large number onle who would be willing to invest smaller amounts through web-based olatforms the project. (A) (B) ...
(A) (B) (C) (D) Funds raised through coerced contributions on web-based platforms. Funds raised through voluntary contributions on web-based platforms. P, Q. R and S are to be uniq...
Question 9 of Section Physics, GATE PH 2020....
Consider a diatomic molecule formed by identical atoms. If Ey and Ee represent the energy of the vibrational nuclear motion and electronic motion respectively, then in terms of the...
Question 14 of Section Physics, GATE PH 2020....
Question 17 of Section Physics, GATE PH 2020....
Let p be the momentum conjugate to the generalized coordinate q. If the transformation Q=V2q''' cos p P=Sa''' sin p is canonical, then m =...
Question 25 of Section Physics, GATE PH 2020....
Question 27 of Section Physics, GATE PH 2020....
Question 28 of Section Physics, GATE PH 2020....
R +12V Vin \cdotVout R -12V C (A) (B) (0) (D)...
maximum along Z' maximum along y' maximum along x' uniform over the sphere A charge q moving with uniform speed enters a cylindrical region in free space at t = 0 and exits the reg...
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 i...
Consider the circuit given in the figure. Let the forward voltage drop across each diode be 0.7 V. The current I (in mA) through the resistor is -+10.1 V 1 k5 > LAHA...
Question 44 of Section Physics, GATE PH 2020....
Question 45 of Section Physics, GATE PH 2020....
If x=$ a, sinkx, for -n ≤x≤t, the value of a, is _...
0, Let f(x) =<n, 0, x<- 1 2n <X< 2n 2n 2n <x....
Question 51 of Section Physics, GATE PH 2020....
Question 52 of Section Physics, GATE PH 2020....
Question 53 of Section Physics, GATE PH 2020....
Question 55 of Section Physics, GATE PH 2020....
(A) A matter wave is represented by the wave function Ф(x, y, z, t) = Aei (4x+3y+52-10mt) where A is a constant. The unit vector representing the direction of propagation of this m...
The above combination of logic gates represents the operation (A) OR (B) NAND (C) AND (D) NOR...
For the refractive index $n = n_r(\omega) + i n_{im}(\omega)$ of a material, which of the following statements are correct?...
Complex function $f(z) = z + |z - a|^2$ ($a$ is a real number) is...
Consider the complex function f(z) = z2 sin z (z - 𝜋)4 . At z = 𝜋 , which of the following options is(are) CORRECT?...
The complex function e-( 2 z-1) has __________...
Consider the function f(z) = 1 z2(z-2)3 of a complex variable z. The residues of the function at z = 0 and z = 2, respectively, are...
The wire loop shown in the figure carries a steady current I. Each straight section of the loop has length d. A part of the loop lies in xy plane and the other part is tilted at 30...
In the transistor circuit shown in the figure, VBE = 0.7 V and \betaDC = 400. The value of the base current in \muA (rounded off to one decimal place) is ___________...
Consider the set {1, x, x2}. An orthonormal basis in x ∈ [-1,1] is formed from these three terms , where the normalization of a function f(x) is defined via ∫ x2[f(x)]2dx = 1 1 -1 ...
A wheel of mass 4M and radius R is made of a thin uniform distribution of mass 3M at the rim and a point mass M at the center . The spokes of the wheel are massless. The center of ...
The function f(z) of complex variable z given below, f(z) = z2 - 5z + 4 z3 + 4z - z2 - 4 has singular points at z =...