GATE 2024 MT – Previous Year Questions with Solutions
All 65 questions of GATE 2024 MT 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 [dry → arid → parched] is analogous to [diet → fast → ]. Which one of the…
- Question 2 – Two distinct nonzero real variables x,y satisfy (x+y)(x-y). The value of x/y
- Question 3 – Consider the following sample of numbers: 9, 18, 11, 14, 15, 17, 10, 69, 11, 13 The median of the sample is
- Question 4 – The numbers of ₹1, ₹5, and ₹10 coins a person has are in the ratio 5:3:13. What percentage of the total money is in ₹5 coins?
- Question 5 – For positive real p,q, (p2+q2)= p+ q+23. The value of (p4+q4)/(p2q2) is
- Question 6 – Select the best match for blanks (i)–(iv). Steve was advised to keep his head (i) before heading (ii) to bat; for, while he had a head (iii) batting,…
- Question 7 – A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A…
- Question 8 – A pie chart gives the macronutrient energy contributions to a 2,000 kcal diet: carbohydrates 35%, proteins 20%, unsaturated fat 20%, saturated fat…
- Question 9 – A rectangular paper of 20 cm × 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The…
- Question 10 – The least number of squares to be added in the figure to make AB a line of symmetry is
- Question 11 – Independent normally distributed variables X 1,X 2 have means 1, 2 and variances 1, 2. Their sum X=X 1+X 2 has mean and variance satisfying
- Question 12 – Which Taylor series represents [(1+x)/(1-x)] about the origin for real x <1?
- Question 13 – The figure shows normal distributions a,b,c. For distribution p, p is standard deviation and p is mean; all means are positive. Which deduction is…
- Question 14 – In an A–B solid solution, the activity and mole fraction of A are a A and X A. Its activity coefficient is
- Question 15 – Two different-metal rods, each of length L/2 and diameter d L, have constant conductivities k 1>k 2 and perfect contact (zero interface thermal…
- Question 16 – Match the laws in Column I with material properties in Column II. Column I: P. Hooke’s law Q. Fick’s law R. Fourier’s law S. Darcy’s law Column II: 1.…
- Question 17 – Wet high intensity magnetic separators (WHIMS) are used to concentrate
- Question 18 – Which one of the following reagents is NOT used in froth flotation process?
- Question 19 – Which reaction is Boudouard’s reaction? Phase labels (s), (l), and (g) denote solid, liquid, and gas.
- Question 20 – Which process is NOT related to extraction and refining of titanium from ilmenite ore?
- Question 21 – Which statement about industrial aluminium production from pure dry alumina by Hall–Héroult electrolytic reduction is correct?
- Question 22 – Which schematic shows the rate of solid nucleation from a pure liquid metal versus undercooling T=T m-T, where T m is freezing temperature and T is…
- Question 23 – Which crystal-structure change occurs when mild steel transforms from austenite to martensite?
- Question 24 – The figure shows a circular dislocation loop with fixed Burgers vector b (horizontal arrow). The dash-dot lines are horizontal and vertical diameters,…
- Question 25 – Match the concepts in Column I with phenomena in Column II. Column I: P. Peierls–Nabarro stress Q. Cottrell’s atmosphere R. Paris law S. Considère’s…
- Question 26 – Match the defects in Column I with manufacturing processes in Column II. Column I: P. Misrun Q. Earing R. Alligatoring S. Chevron cracking Column II:…
- Question 27 – Which one of the following processes is NOT involved in the sintering of a green compact of ceramic powders? Assume that sintering is performed…
- Question 28 – Which statements are correct for a real square matrix A? Here AT denotes transpose and A-1 inverse.
- Question 29 – Which of the following is/are criterion/criteria for equilibrium of an isolated system held at constant temperature and constant pressure?
- Question 30 – Which (h k l) reflections are allowed in an X-ray diffraction pattern of a crystal with an FCC lattice?
- Question 31 – The divergence of V=x2y i+y3z j+z4 k at (1,1,1) is (nearest integer).
- Question 32 – Two atoms have pair-interaction energy U=-1.6/r6+51.2/r12, where U is in eV and distance r in Å. Their equilibrium bond length is Å (nearest integer).
- Question 33 – A solid embryo contacts a perfectly flat mould wall as shown. Its wetting angle is degrees (one decimal place). Surface tensions are: liquid–mould…
- Question 34 – A single crystal has slip-plane normal at 60 and slip direction at 45 to the tensile axis. Its critical resolved shear stress is 2 MPa. The tensile…
- Question 35 – The force to extrude an aluminium rod from cross-sectional area 150 mm2 to 50 mm2 is N (nearest integer). The extrusion constant, accounting for flow…
- Question 36 – If bmatrix1&2\\8&1bmatrixbmatrixx\bmatrix=bmatrixx\bmatrix, where x,y are not both zero, the values of are
- Question 37 – If dy/dx=4xy and y(0)=1, then
- Question 38 – A slender cylindrical rod of conductivity k, length L, and diameter d L contacts an infinite liquid heat sink at its right end, as shown. At steady…
- Question 39 – Match dimensionless numbers in Column I with their transport-phenomena applications in Column II. Column I: P. Reynolds number Q. Schmidt number R.…
- Question 40 – In a cubic lattice, what is the ratio of interplanar spacings of the (100), (110) and (111) planes? (Round off to two decimal places)
- Question 41 – The constitutional undercooling condition for a hypothetical binary alloy of A with solute B during solidification is shown in the figure along with…
- Question 42 – A quenched steel is tempered for the same time at T 1<T 2<T 3, giving the shown microstructures. Black circles are cementite in ferrite; r 1, r 2, r 3…
- Question 43 – The initially stress-free isotropic metal cuboid shown has thermal expansion coefficient , Young’s modulus E, and Poisson ratio . Its dimensions along…
- Question 44 – Match the entries in Column I with stacking sequences of close-packed planes in Column II. Column I: P. FCC structure Q. Intrinsic stacking fault in…
- Question 45 – Which graph represents Griffith’s criterion for growth of a center crack in an infinitely large, brittle isotropic plate? SE is the magnitude of total…
- Question 46 – For slab rolling, assess the assertion [a] and reason [r]. [a]: Grooves parallel to the roll axes are made on roll surfaces to achieve large thickness…
- Question 47 – Which of the following statements is/are correct?
- Question 48 – A creep test of a pure polycrystalline metal is performed in tension and the creep strain rate is observed to decrease during the primary stage. The…
- Question 49 – Which of the following statements is/are correct for joining processes?
- Question 50 – Which of the following statements is/are correct for non-destructive testing?
- Question 51 – Experimental data are (x,y)=(1,8),(2,15),(3,19). A line y=mx+c is fitted by least squares. Its slope m is (one decimal place).
- Question 52 – The integral 01xe-x\,dx is (two decimal places).
- Question 53 – For element A, vacancy-formation enthalpy and entropy per vacancy are 0.5 eV and 3k B. Its equilibrium vacancy mole fraction at 500 K is 10-4 (two…
- Question 54 – A steel bar has ultimate tensile strength 1000 MPa and fully reversed fatigue limit 250 MPa. By the Goodman relation, its fatigue limit at tensile…
- Question 55 – During carburization at 950 °C, carbon concentration reaches 0.8 wt.% at depth 0.3 mm after one hour. The time to obtain the same concentration at 0.6…
- Question 56 – An ideal solution is made by mixing 10 g of A and 50 g of B at 673 K. Its molar free energy of mixing is kJ mol-1 (one decimal place). Given: R=8.314…
- Question 57 – At 298 K, the Cu2+ concentration needed to make the potential of pure copper 0.17 V is 10-6 gram-mol L-1 (two decimal places). Given: R=8.314 J mol-1…
- Question 58 – A nonporous spherical Fe 2O 3 particle of initial radius 510-2 m is topochemically reduced by H 2. The sharp reactant–product interface remains…
- Question 59 – A long cylindrical metal rod of radius r, length L r, and resistivity e carries current I in vacuum and loses heat only by radiation. Its steady…
- Question 60 – A 1000 kg sphalerite concentrate containing 60% ZnS is completely roasted with stoichiometric pure oxygen. The oxygen required is kg (one decimal…
- Question 61 – An 800 g A–B alloy containing 20 wt.% B is held at T 1 in the shown phase diagram. The mass of B dissolved in α is g (nearest integer).
- Question 62 – A mild-steel pipeline is cathodically protected using zinc at current density 10 mA m-2. Zinc required per square meter per year is g (nearest…
- Question 63 – A large rectangular component under fully reversed cyclic loading develops a dominant surface fatigue crack. Stress amplitude is A=100 MPa, material…
- Question 64 – A simple vertical casting gate has cross-sectional area 2 cm2 and sprue height 10 cm. The filling time for a 40 cm × 20 cm × 10 cm mould is s (one…
- Question 65 – Arc welding has actual heat input 200 J mm-3, current 200 A, voltage 20 V, weld cross-sectional area 2 mm2, and heat-transfer efficiency 0.9. Welding…