GATE 2024 PI – Previous Year Questions with Solutions
All 65 questions of GATE 2024 PI with answers and explanations. Read each question, then practise it by topic or as a full paper.
Practise this paper in The GATE Grind →
- Question 1 – If '→' denotes increasing order of intensity, then the meaning of the words [sick → infirm → moribund] is analogous to [silly → → daft]. Which one of…
- Question 2 – The 15 parts of the given figure are to be painted such that no two adjacent parts with shared boundaries (excluding corners) have the same color. The…
- Question 3 – How many 4-digit positive integers divisible by 3 can be formed using only the digits 1, 3, 4, 6, 7, such that no digit appears more than once in a…
- Question 4 – The sum of the following infinite series is 2 + 12 + 13 + 14 + 18 + 19 + 116 + 127 +
- Question 5 – In an election, the share of valid votes received by the four candidates A, B, C, and D is represented by the pie chart shown. The total number of…
- Question 6 – Thousands of years ago, some people began dairy farming. This coincided with a number of mutations in a particular gene that resulted in these people…
- Question 7 – The probability of a boy or a girl being born is 1/2. For a family having only three children, what is the probability of having two girls and one…
- Question 8 – Person 1 and Person 2 invest in three mutual funds A, B, and C. The amounts they invest in each of these mutual funds are given in the table. Mutual…
- Question 9 – Three different views of a dice are shown in the figure below. The piece of paper that can be folded to make this dice is
- Question 10 – Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes…
- Question 11 – Find the coefficient of z³ in the Taylor expansion of sin z around z = 0.
- Question 12 – F=(100x+100y) i+(-50x+200y) j. Evaluate C F d l along an anticlockwise circle of radius 2, with d l=dx i+dy j.
- Question 13 – A uniform Euler–Bernoulli cantilever has length L and flexural rigidity EI. Force F acts at 2L/3 from its fixed end as shown. Find free-end static…
- Question 14 – An electrically heated thin copper wire is covered with insulation thickness t. Under steady conditions heat loss per unit length is Q. Which…
- Question 15 – A cube of side a and cylinder of radius r and length 4r, of the same material and sand-casting process, have equal solidification times under…
- Question 16 – Match deep-drawing defects P: orange peel; Q: flange wrinkling; R: tearing at the bottom corner; S: earing at top edge, with causes 1: no blank-holder…
- Question 17 – Which pure metal is HCP at room temperature?
- Question 18 – For simple indexing with a dividing head on a horizontal mill, select crank movement that creates 12 equal disc divisions.
- Question 19 – The shown four-department layout is input to CRAFT. Which pair cannot be exchanged?
- Question 20 – Which concept is NOT closely related to interchangeability in product design?
- Question 21 – Which therblig does not advance work and can be eliminated through motion economy?
- Question 22 – With many work-sampling observations, which distribution estimates required sample size?
- Question 23 – Which is NOT an assumption of linear programming?
- Question 24 – In a single-server Markovian queue, Poisson arrivals imply what interarrival-time distribution?
- Question 25 – Which forecasting method needs the least historical data?
- Question 26 – Which statement is NOT true about Total Productive Maintenance (TPM)?
- Question 27 – f(x,y)=u(x,y)+iv(x,y) is analytic, with real x,y,u,v. Which ONE OR MORE equations hold?
- Question 28 – For mild steel under uniaxial tension, which ONE OR MORE statements are true?
- Question 29 – Which ONE OR MORE statements about friction stir welding are true?
- Question 30 – Which ONE OR MORE are supply-chain decision areas?
- Question 31 – A continuous variable has density f(x) = K/4 on 0 ≤ x ≤ 1, and zero otherwise. Find K (integer).
- Question 32 – x1(x2-2ax+b)/(x-1)=8. Find a − b (integer).
- Question 33 – In the shown square truss ABCD of side a, diagonal AC is an inextensible string and other members are rigid. Find the maximum F for static equilibrium…
- Question 34 – An offset slider–crank is shown, with crank l, connecting rod 3l and offset l. For l = 10 cm, find slider stroke (one decimal cm).
- Question 35 – A 100 mm diameter blank is cut from 2 mm sheet. Radial punch–die clearance is 6% of sheet thickness. Find punch diameter (two decimal mm).
- Question 36 – A=pmatrixa&b\&-apmatrix. If A² = I, which equation is true?
- Question 37 – In the equilibrium iron–carbon diagram, eutectoid temperature and composition are 727°C and 0.77 wt% C. A 1.2 wt% C steel cools from 1000°C to room…
- Question 38 – Match polymer processes P: extrusion; Q: injection molding; R: blow molding; S: compression molding, with applications 1: complex close-tolerance…
- Question 39 – Plastic deformation begins in plane stress at principal stresses 200 and 100 MPa. Under von Mises yielding, find uniaxial tensile yield strength (one…
- Question 40 – Match three-DOF robot configurations P: Cartesian; Q: cylindrical; R: spherical; S: articulated, with joint types 1: one prismatic and two rotary; 2:…
- Question 41 – Activities A,B,C have no predecessors; D follows A,B; E follows B,C; F follows A,B. Find the minimum dummy activities for an activity-on-arrow…
- Question 42 – Maximize Z=6x 1+5x 2 subject to R₁: 2x 1+5x 240; R₂: 2x 1+x 222; R₃: x 1+x 213; and x₁,x₂ ≥ 0. The optimum is (9,4). Which resource shadow prices are…
- Question 43 – Which ONE OR MORE items are required to make the shown eccentric hole in a disc on a lathe?
- Question 44 – For an acceptance-sampling plan, which ONE OR MORE statements are true?
- Question 45 – Seven mixed cards numbered 1–7 are in a box. One is drawn randomly and known to be odd. Find the conditional probability that it exceeds four (integer…
- Question 46 – x(t)+4x(t)=e-t for t ≥ 0, with x(0) = x′(0) = 0. Find x(π/8) to three decimals.
- Question 47 – At x = 0,1,2,3,4, tabulated y values are 1,3,6,9,12. Use the trapezoidal rule for 04y(x)dx (one decimal).
- Question 48 – A pump draws pond water. A 5.05 cm hose connects at its outlet 1.02 m below surface level. Just after the pump, gauge pressure is 50 kPa and mass flow…
- Question 49 – An air-standard Otto cycle starts compression at 200 kPa and 26.85°C. Constant-volume heat addition is 1.02 MJ/kg and efficiency is 50%. Assume ideal…
- Question 50 – A metal cylindrical air vessel has mean radius 1 m and wall thickness 4 mm. Allowable normal and shear stresses in its cylindrical portion are 100 and…
- Question 51 – A flat belt on a pulley of radius 20 cm transmits 6.283 kW at 600 rpm, with friction coefficient 0.3. Torque and tightening force F are shown. Find…
- Question 52 – Mild-steel butt joints are arc welded at 85% heat-transfer efficiency, ignoring other losses. First weld: 30 V,180 A,6 mm/s. Second uses identical…
- Question 53 – A cold-rolling pass reduces a plate to 3 mm using 400 mm diameter rolls at 300 rpm. Roll elastic deflection is negligible, bite angle 10°, and neutral…
- Question 54 – A sand-mold sprue has height h₂ = 200 mm and flow 106 mm³/s. Liquid height above point 2 is h c = 25 mm. Areas at 2,3 are A₂,A₃; points 1,3 are…
- Question 55 – Turn a 160 mm diameter,190 mm long workpiece at cutting speed 80π m/min and feed 0.2 mm/rev. Approach and overrun are 5 mm each. Find machining time…
- Question 56 – A CNC tool travels anticlockwise from A = (0,0) to B = (10,10) on the shown quarter-circle centered at C = (0,10), all mm. P has X coordinate 6 mm. X…
- Question 57 – A single-start metric thread has calculated pitch 1.4 mm from a two-wire pitch-diameter measurement. Find best-wire diameter (two decimal mm).
- Question 58 – Orthogonal turning uses cutting speed 2 m/s, feed 0.2 mm/rev and depth 2 mm. Specific cutting energy is 2 J/mm³. Ignore feed-force power. Find main…
- Question 59 – ECM removes copper at constant rate 2 cm³/min. Find current (one decimal A), using melting point 1085°C, density 9 g/cm³, atomic weight 63 g/mol,…
- Question 60 – A repairable machine operates 2400 hours in a year and breaks down eight times. Mean repair time including waiting is 20 hours. If it were reduced to…
- Question 61 – A packaging worker rated 120% takes an observed average nine minutes. Allowances are 10% of standard time. Find standard time (integer minutes).
- Question 62 – Three series assembly stations S₁,S₂,S₃ take 6,4,T minutes per toy. Steady-state line efficiency is 75%. Find maximum T (integer minutes).
- Question 63 – Machines A,B are bought together. A: price ₹20000, life ten years, salvage ₹5000. B: price ₹15000, life twenty years, salvage ₹5000. With…
- Question 64 – An item uses classical EOQ. Ordering cost per order rises 20% and demand rate also rises 20%. By what percentage does time between orders increase…
- Question 65 – Jobs A,B,C,D,E are ready at t = 0 and take 9,6,4,5,8 days respectively on one machine. Under SPT, find average flow time (one decimal days).