GATE 2024 PH – Previous Year Questions with Solutions
All 65 questions of GATE 2024 PH with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – If '→' denotes increasing order of intensity, then the meaning of the words [smile → giggle → laugh] is analogous to [disapprove → → chide]. Which one…
- Question 2 – Find the odd one out in the set: 19, 37, 21, 17, 23, 29, 31, 11
- Question 3 – In the following series, identify the number that needs to be changed to form the Fibonacci series. 1, 1, 2, 3, 6, 8, 13, 21, ...
- Question 4 – The real variables x,y,z and constants p,q,r satisfy x/(pq-r2)=y/(qr-p2)=z/(rp-q2). Given nonzero denominators, px+qy+rz is
- Question 5 – Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land…
- Question 6 – In the given text, the blanks are numbered (i)−(iv). Select the best match for all the blanks. Prof. P (i) merely a man who narrated funny stories.…
- Question 7 – **Official result: marks to all candidates.** This question has no unique scored answer and is retained for reference. How many combinations of…
- Question 8 – The bar chart gives the batting averages of VK and RS for 11 calendar years from 2012 to 2022. Considering that 2015 and 2019 are world cup years,…
- Question 9 – A planar rectangular paper has two V-shaped pieces attached as shown below. This piece of paper is folded to make the following closed…
- Question 10 – **Official result: marks to all candidates.** This question has no unique scored answer and is retained for reference. Four equilateral triangles are…
- Question 11 – If F 1(Q,q)=Qq generates a canonical transformation from (p,q) to (P,Q), which relation is correct?
- Question 12 – An unpolarized plane wave in dielectric medium 1 of index n 1 strikes medium 2 of index n 2>n 1 at angle -1(n 2/n 1). Which statement is true?
- Question 13 – A particle in an infinite one-dimensional well has (x,t)=23e-iE 1t/ 1(x)+16ei/6e-iE 2t/ 2(x)+16ei/4e-iE 3t/ 3(x). The normalized 1, 2, 3 are the…
- Question 14 – If a thermodynamical system is adiabatically isolated and experiences a change in volume under an externally applied constant pressure, then the…
- Question 15 – The mean distance between atoms in HD is r, with hydrogen mass m H. The difference between the two lowest rotational energies in multiples of 2/(m…
- Question 16 – Crystal structures of two metals A and B are two-dimensional square lattices with same lattice constant a. Electrons in metals behave as free…
- Question 17 – For 235 92 U+n93 37Rb+141 55Cs+2n, neglect initial and final neutron momenta. The daughter kinetic-energy ratio KE(Rb)/KE(Cs) is
- Question 18 – The symbols C, D, Vin and V0 shown in the figure denote capacitor, ideal diode, input voltage and output voltage, respectively. Which one of the…
- Question 19 – Let Ne and Te, respectively, denote number and kinetic energy of electrons produced in a nuclear beta decay. Which one of the following distributions…
- Question 20 – An infinite cylinder of radius R has frozen-in magnetization M=ke-s z, with s the distance from its axis. There is no free current. With vacuum…
- Question 21 – Atomic numbers of V, Cr, Fe and Zn are 23, 24, 26 and 30, respectively. Which one of the following materials does NOT show an electron spin resonance…
- Question 22 – A particle has V(x)= for x0, V(x)=V 0 for a x b, and zero elsewhere, with b>a>0. For E<V 0, which schematic wavefunction is valid?
- Question 23 – Let ( p, q,t) be ensemble phase-space density and H( p, q) the Hamiltonian. With Poisson bracket \A,B\, d/dt=0 implies
- Question 24 – Consider the following circuit: Suppose the input signal P is and the input signal Q is Which one of the following output signals is correct?
- Question 25 – Two spacecraft fly apart along x with individual speeds 0.5c in an inertial frame. The speed of T with respect to S is
- Question 26 – Let P, Q, R be different nuclei. Which nuclear process is possible?
- Question 27 – The temperature dependence of the electrical conductivity (σ) of three intrinsic semiconductors A, B and C is shown in figure. Let EA, EB and EC be…
- Question 28 – Trial functions 1=e-Z(r 1+r 2) and 2=e-Z(r 1+r 2)(1+g r 1- r 2 ) estimate helium ground energy E 0. With variational parameters Z,g and corresponding…
- Question 29 – A particle has wavefunction e-(i x+) with real constants ,. In which potential is it moving?
- Question 30 – Consider I= V2(1/r)\,dV where r=x2+y2+z2. Which statement(s) is/are correct?
- Question 31 – The complex function e-2/(z-1) has
- Question 32 – The minimum number of basic logic gates to realize B(A+B)+A( B+A) is (in integer).
- Question 33 – Solid ammonia vapor pressure obeys P=23.03-3754/T, and liquid ammonia obeys P=19.49-3063/T, with T in kelvin. The triple-point temperature in K (two…
- Question 34 – E=k(x x+y y)/(x2+y2). Its flux through a sphere of radius R centered at the origin is n kR. The value of n (in integer) is
- Question 35 – A system has H= i=12Na iq i2+ i=12Nb ip i2, with positive constants. Its ensemble average is Nk BT. The integer is
- Question 36 – A two-nucleon bound state has binding energy B and rest energy mc2. The minimum photon energy to dissociate it is
- Question 37 – The spin–orbit Hamiltonian is H=-k L S. The splitting between 2p 3/2 and 2p 1/2 is
- Question 38 – For L=m x y-m 02xy with conjugate momenta p x,p y, the canonical equations are
- Question 39 – The X-ray diffraction pattern of a monatomic cubic crystal with rigid spherical atoms of radius 1.56 Å shows several Bragg reflections of which the…
- Question 40 – A parallel capacitor has potential zero at x = 0 and V 0 at x = d, filled by = 0(1+x/d). Neglect edges. The field is
- Question 41 – x+2x=F( t), with x(0)= x(0)=0. Which is correct?
- Question 42 – An atom is subjected to a weak uniform magnetic field B⃗ . The number of lines in its Zeeman spectrum for transition from n= 2, l= 1 to n= 1, l= 0 is
- Question 43 – Consider P=pmatrix1&2\\0&1pmatrix, Q=pmatrix1&0\\0&1pmatrix. Which statement(s) is/are true?
- Question 44 – An infinite one-dimensional lattice has spin-half ions at every site, pointing only along +z or −z. Denote entropies of paramagnetic, ferromagnetic…
- Question 45 – F=(2xz+3y2) y+4yz2 z. The path A → B → C → D → A is the unit square in z = 0. Which option(s) is/are true?
- Question 46 – Two charges +q are 2d apart. A grounded solid conducting sphere of radius a is midway between them. Assume a2 d2. Which statement(s) is/are true?
- Question 47 – V(x)=V 0+12m 02x2 for x > 0 and infinity for x ≤ 0. Figures P,Q,R,S specify offsets and frequencies. With E j(X) the j-th level of X, which…
- Question 48 – For a one-electron atom, H 0=p2/(2m)-V(r), with Coulomb V. Add H=12m2c2rdVdr L S. Which statement(s) is/are true?
- Question 49 – Decays of mesons and baryons can be categorized as weak, strong and electromagnetic decays depending upon the interactions involved in the processes.…
- Question 50 – The semiconductor shown carries 2 mA along +x. Majority carrier concentration is 12.51013 cm−3, with negligible minority carriers. In a constant +z…
- Question 51 – A and B are contravariant and covariant vectors; repeated indices are summed. Which expressions are tensors?
- Question 52 – The temperature dependence of magnetic susceptibility (Column I) and materials (Column II) are shown. Which option(s) is/are correct? Column I Column…
- Question 53 – Curves P and Q give X-ray intensity versus wavelength at different accelerating voltages for the same target. 1=0.25 Å, 2=0.5 Å, 3=1.0 Å, 4=2.25 Å.…
- Question 54 – Apart from the acoustic modes, 9 optical modes are identified from the measurements of phonon dispersions of a solid with chemical formula AnBm, where…
- Question 55 – An oscillating dipole d(t)=d 0( t) z is at the origin. For distant points in spherical coordinates, which intensity statements are true?
- Question 56 – The transforms are f()=(2)-1/2 f(x)ei xdx and f(x)=(2)-1/2 f()e-i xd. Define (f*g)(x)=(2)-1/2 f(y)g(x-y)dy, all integrals over the real line. Which…
- Question 57 – A material behaves as a superconductor below a critical temperature Tc and as a normal conductor above Tc. A magnetic field B⃗ = Bẑ is applied when T>…
- Question 58 – A typical biasing of a silicon transistor is shown in figure. The value of common-emitter current gain β for the transistor is 100. Ignore reverse…
- Question 59 – An ideal gas has Q=1N![V/(T)3]N, where is thermal de Broglie wavelength. Use N!=N N-N. For density N/V=2.51025 m−3, e/(k BT)(T)-310-25 is m−3 (one…
- Question 60 – L=m x2/2- x4 with positive lambda. At total energy E, T=a 0(E/)1/4dx(2/m)(E- x4). The integer a is
- Question 61 – A mass m in an infinite well of width a has perturbation V=h2/(40ma2) over 3a/4<x<a, as shown. The first-order shift of its fourth energy eigenstate…
- Question 62 – Three-dimensional noninteracting bosons have zero chemical potential and k2. Their low-temperature C V Tn/2. The integer n is
- Question 63 – Consider the operational amplifier circuit shown in figure. The output voltage V0 is V (in integer).
- Question 64 – An electron in a proton Coulomb field has = 100/3+ 210/3-5 320/3. Energy measured at t 1 is E 2. Total angular momentum is measured at t 2>t 1, and…
- Question 65 – According to the nuclear shell model, the absolute magnetic-moment difference between 15 8 O and 15 7 N in nuclear magnetons is a/3. The integer a is