GATE 2021 MT – Previous Year Questions with Solutions
All 65 questions of GATE 2021 MT with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Five persons P, Q, R, S, T sit in a row facing the same direction. P and T cannot sit at either end; P must not sit adjacent to S; R is second from…
- Question 2 – Consider: (i) The number of candidates who appear for the GATE examination is staggering. (ii) A number of candidates from my class are appearing for…
- Question 3 – Digital watch X beeps every 30 seconds and watch Y every 32 seconds. They beep together at 10 AM. The immediately next time they beep together is .
- Question 4 – If =2, =3, +=5, and =10, then (-)2= .
- Question 5 – Mr X’s front door faces east. He leaves through the back door directly opposite it, walks 50 m straight, turns right, then walks 50 m. His final…
- Question 6 – Statement 1: All entrepreneurs are wealthy. Statement 2: All wealthy are risk seekers. Conclusion I: All risk seekers are wealthy. Conclusion II: Only…
- Question 7 – A box contains 15 blue and 45 black balls. Two are selected randomly without replacement. The probability that the first is blue and the second black…
- Question 8 – The ratio of the area of the incircle to that of the circumcircle of an equilateral triangle is .
- Question 9 – A square sheet has side 1 unit. Fold along its main diagonal, then along the folded shape’s symmetry line, then again along its new symmetry line. The…
- Question 10 – “The world is going through the worst pandemic in the past hundred years. The air travel industry is facing a crisis, as the resulting quarantine…
- Question 11 – The eigenvalues of bmatrix1&0&-1\\0&1&0\\-1&0&1bmatrix are .
- Question 12 – Which is a homogeneous function of degree three?
- Question 13 – For vector field V(x,y,z) with components V x,V y,V z depending on x,y,z, its divergence is .
- Question 14 – Which diagram shows the centre-split defect in rolling?
- Question 15 – Single-crystal nickel-based superalloy turbine blades for aero-engines are manufactured using .
- Question 16 – Elements A and B have the same crystal structure. For a dilute solution of B in A, which is true? Here H mix is mixing enthalpy, a B activity and X B…
- Question 17 – For the uniaxial tensile stress–strain behaviour of polycrystalline aluminium, which statement is FALSE?
- Question 18 – Which statement about creep deformation is FALSE?
- Question 19 – Which element alloyed with iron is a ferrite stabilizer?
- Question 20 – Which is the correct decreasing sequence of quenching power for steel heat treatment?
- Question 21 – For a zero-order chemical reaction, which statement is FALSE?
- Question 22 – Which element oxidizes first in basic oxygen steelmaking?
- Question 23 – Which is a hydrometallurgical operation?
- Question 24 – The value of x02(5x)/2x is (nearest integer).
- Question 25 – Annealed-specimen grain size X has a symmetric distribution with mean =5 μm and standard deviation =0.5 μm. Given P(X+2)=0.98, the percentage with…
- Question 26 – Given E Ni2+/Ni=-0.25 V and F=96500 C/mol, the standard chemical potential Ni2+ at 298 K is J/mol (nearest integer).
- Question 27 – Copper melts at 1358 K with melting enthalpy 13400 J/mol. Its liquid-to-solid free-energy change at 1058 K is J/mol (nearest integer). Assume C…
- Question 28 – A body has stress tensor bmatrix50&0&0\\0&200&0\\0&0&100bmatrix MPa. For yielding under Tresca’s criterion, its uniaxial tensile yield stress must be…
- Question 29 – For homogeneous spherical-solid nucleation in liquid at fixed undercooling, a 20% rise in nucleus surface energy causes a % increase in critical…
- Question 30 – Iron’s room-temperature saturation magnetization is 1700 kA/m and lattice parameter 0.287 nm. Its per-atom magnetic moment is 10-23 A·m2 (one decimal…
- Question 31 – An FCC crystal’s first X-ray reflection is at Bragg angle =30. The second reflection has Bragg angle degrees (one decimal place).
- Question 32 – Steel containing 0.6 wt.% C is cooled slowly from 900 °C to room temperature. The proeutectoid ferrite fraction is (two decimal places). Given…
- Question 33 – Polyethylene’s degree of polymerization is 30000. Its average molecular weight is g/mol (nearest integer). Atomic weights of C and H are 12 and 1.
- Question 34 – Water flows over a finite plate. At distance x=x 1 from the leading edge, V x=0.5y-0.5y3. The boundary-layer thickness there is m (two decimal…
- Question 35 – A crystal’s vacancy concentration doubles when temperature increases from 27 °C to 127 °C. Vacancy-formation enthalpy is kJ/mol (two decimal places).…
- Question 36 – The minimum value of y=x2-2x+4 is .
- Question 37 – Match forming-process diagrams P–S in Column I to names in Column II. 1. Extrusion 2. Rolling 3. Deep drawing 4. Open-die forging
- Question 38 – Match nondestructive testing methods P–S with principles 1–4. P. Dye penetrant test Q. Radiography R. Eddy current test S. Ultrasonic inspection 1.…
- Question 39 – The number of degrees of freedom for M(s)+CO 2(g) MO(s)+CO(g) is .
- Question 40 – Which condition gives the binary A–B phase diagram shown? H mixsolid and H mixliquid denote solid and liquid mixing enthalpies.
- Question 41 – Without external stress, which statement about point-defect/dislocation interaction is FALSE?
- Question 42 – Single-crystal aluminium is in uniaxial tension along [112]. At applied stress 100 MPa and critical resolved shear stress 25 MPa, which slip system…
- Question 43 – The shown steady one-dimensional temperature distribution is across adjacent refractory blocks of unit cross-sectional area and conductivities k 1,k…
- Question 44 – Fully developed one-dimensional Newtonian flow in a horizontal pipe of radius R has v z=( P/L)(R2-r2)/(4). Here P=P 1-P 2, viscosity is , radial…
- Question 45 – Match terms to unit processes. P. Submerged entry nozzle Q. Electric heating R. Raceway zone S. Oxygen lancing 1. Ladle furnace 2. Continuous casting…
- Question 46 – A blast furnace uses hematite ore with 80% Fe 2O 3 and 20% gangue. Coke use is 600 kg per ton hot metal, with 85% C and 15% ash. Hot metal is 95.5% Fe…
- Question 47 – Use Newton–Raphson on f(x)=x- x with initial guess 0.5 radians. The root estimate after one iteration is (three decimal places).
- Question 48 – The work by F=2x i+3y j along a straight line from (0,0) to (1,2) is (nearest integer).
- Question 49 – A coin is tossed three times. Given more heads than tails, the probability of exactly one tail is (two decimal places).
- Question 50 – A 3000 W machine makes a continuous fillet weld at 6 mm/s. Heat-transfer factor is 0.6, melting factor 0.5, and unit energy for melting 6 J/mm3. The…
- Question 51 – Liquid iron is cast into a spherical sand mould of radius 6 cm and a cubical sand mould of edge 12 cm. The sphere solidifies in 60 minutes. The cube…
- Question 52 – True strain for 60% height reduction in forging is (two decimal places).
- Question 53 – For 2Cu(s)+SO 2(g) Cu 2S(s)+O 2(g) at 973 K, (p O 2/p SO 2)= (two decimal places). Given G=-100 kJ for 2Cu(s)+0.5S 2(g) Cu 2S(s) and G=292 kJ for SO…
- Question 54 – One mole of ideal gas at 10 atm and 300 K expands reversibly and adiabatically to 1 atm. Work done by the gas is J (nearest integer). Given R=8.314 J…
- Question 55 – The figure shows the entropy versus temperature plot of a reversible engine cycle. For T 1=200 K and T 2=600 K, its efficiency is % (two decimal…
- Question 56 – Two dislocation lines parallel to z lie in the x–z plane as shown. The glide force exerted by the edge dislocation on the screw dislocation is N…
- Question 57 – A shear stress 100 MPa bows a dislocation between precipitates spaced 0.2 μm. If spacing increases to 0.5 μm, the needed shear stress is MPa (nearest…
- Question 58 – A plate is in plane strain with zz=0, xx= yy0, and xy= xz= yz=0. For Poisson ratio 0.3, zz/ xx is (one decimal place).
- Question 59 – An infinite metal plate has a central through-thickness crack of full length 80/ mm. Its maximum mode-I applied stress is MPa (nearest integer).…
- Question 60 – An A–B alloy with 5 wt.% B solidifies without convection, with the shown hypothetical eutectic phase diagram. Under steady state, the critical…
- Question 61 – A thick steel plate with 0.1 wt.% C is carburized at 950 °C, keeping surface C at 1.1 wt.%. After 9 hours, the depth where C reaches 0.6 wt.% is mm…
- Question 62 – At 25 °C, iron corrodes in deaerated pH-3 acid with corrosion current density 4 μA/cm2. Its corrosion potential is V (two decimal places). Given…
- Question 63 – An interstitial atom just fits an octahedral void in BCC iron without distorting the structure. If iron’s atomic radius is 0.124 nm, the interstitial…
- Question 64 – Nickel oxidizes isothermally at 800 K for 400 s, gaining 2 mg/cm2. Its weight gain after 1600 s is mg/cm2 (nearest integer). Assume gain proportional…
- Question 65 – A solid sphere of radius 0.5 m is enclosed by a hollow sphere of radius 1 m. Radiation exchanges between the small sphere’s outer surface (1) and…