GATE 2026 PI – Previous Year Questions with Solutions
All 65 questions of GATE 2026 PI with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – “The shopkeeper sells lemons.” In this sentence, “lemons” is the .
- Question 2 – The figure is supposed to show three non-overlapping shapes: one oval and two triangles. Which figure P,Q,R,S fits the missing portion marked ? and…
- Question 3 – At how many points do y=x2 and y=-x2-2x-1 intersect in the real (x,y) plane?
- Question 4 – “If Anish had scored hundred runs in today’s match, he would have been made the captain of his team. He would have then become the youngest captain in…
- Question 5 – Which figure P,Q,R,S correctly shows figure (I) rotated 45° clockwise?
- Question 6 – Match Column I: (i) Lonely; (ii) Literal; (iii) Lousy; (iv) Lethal, with Column II: (p) Verbatim; (q) Solitary; (r) Deadly; (s) Terrible.
- Question 7 – PQ is a diameter of the circle centered at O. R,S lie on the circle and ∠ROS = 80°. PR and QS extended meet at T as shown. Find ∠RTS.
- Question 8 – Using the relationship between each polygon and its enclosed number, find X.
- Question 9 – Seven bulbs are arranged in a line as shown. All state changes in each step use states at the end of the previous step: an OFF bulb with exactly one…
- Question 10 – Positive integers P,Q satisfy P2=Q2+13. Find PQ.
- Question 11 – Which step is NOT part of product concept selection?
- Question 12 – Which statement about brazing filler material is FALSE?
- Question 13 – A 6 kW arc-welding source joins two similar metals. Total energy loss is 50%, weld cross-sectional area is 10 mm² and specific melting energy is 15…
- Question 14 – Which option gives ALL constraints defining the feasible region shown? The figure is not to scale.
- Question 15 – Using numerical integration, which option most closely approximates 01e-x2dx?
- Question 16 – Find the possible value(s) of 1/in, where i=-1 and n is an even positive integer.
- Question 17 – Match instruments P: sine bar; Q: profilometer; R: vernier calliper; S: ring GO gauge, with applications 1: milled planar-surface roughness; 2:…
- Question 18 – A plain-carbon steel of eutectoid composition is heat treated from austenitizing temperature to obtain ONLY bainite. Which heat treatment is used?
- Question 19 – An iron–carbon alloy at room temperature contains pro-eutectoid ferrite formed above the eutectoid temperature, and pearlite formed below it. Which…
- Question 20 – A student connects a shaft to a rotating machine-element hub using a tapered sunk key that prevents relative axial motion. Which key is most likely…
- Question 21 – The ratio of hydrostatic stress to volumetric strain is called .
- Question 22 – In the weighted graph, edge weights are distances. Let d be the shortest distance from A to E and p the number of paths attaining d. Find d/p.
- Question 23 – Which is NOT an assumption of the economic order quantity (EOQ) model?
- Question 24 – Painting takes six days in a construction project, with total float = free float = 0. Which statement is true?
- Question 25 – Which ONE OR MORE tube cross-sections can be produced by true centrifugal casting? Sections are perpendicular to the rotation axis; drawings are not…
- Question 26 – Match defects P: centerburst; Q: earing; R: zipper cracks; S: cold shut, with processes 1: deep drawing; 2: rolling; 3: extrusion; 4: closed-die…
- Question 27 – Which ONE OR MORE are established geometric-model data-transfer formats in CAD?
- Question 28 – Which ONE OR MORE values can be a correlation coefficient?
- Question 29 – Which ONE OR MORE processes of the Carnot cycle shown are isentropic? Figure is not to scale.
- Question 30 – A 50 mm square is blanked from a 2 mm strip of shear strength 200 MPa. Neglect clearance and friction. Find minimum force for a single operation, in…
- Question 31 – A box contains five coated and ten otherwise identical uncoated cutting inserts, randomly mixed. An operator takes four simultaneously for a…
- Question 32 – A customer invests ₹2,00,000 now for payouts of ₹1,00,000 yearly for three consecutive years. Discount rate is 15% per year. Find investment NPV (₹,…
- Question 33 – The modified Taylor law is VTnfm=constant, where speed V is m/s, life T is minutes, feed f is mm/rev, n = 0.25 and m = 0.5. Two conditions have equal…
- Question 34 – Evaluate C(2x\,dx+2y\,dy+2z\,dz), where C is a semicircle in z = 0 starting at (0,0,0) and ending at (1,0,0). Give an integer.
- Question 35 – A toy-car plant has monthly demands: September 8000; October 6500; November 10500; December 9500 units. It can use ONLY in-house production,…
- Question 36 – The figure gives polymer-extrusion product sections P,Q and available die openings 1–4. Which mapping most likely matches products to dies? Sections…
- Question 37 – Gas-atomized iron powder has tap density 3.26 g/cm³ and apparent density 2.66 g/cm³. Solid iron density is 7.85 g/cm³. Which is closest to its degree…
- Question 38 – Match the matrices P,Q,R,S to properties 1: singular; 2: triangular; 3: symmetric; 4: trace-free. P=pmatrix-30&17&5\\17&0&-12\\5&-12&4pmatrix,…
- Question 39 – Sheet-metal drawing is feasible if reduction ratio < 0.5 and thickness/diameter ratio > 1%. A 2 mm sheet is drawn with a 100 mm punch using various…
- Question 40 – A student determines flatness and parallelism of a part’s top surface from the shown cross-section, uniform in Z. Which statement is correct?
- Question 41 – The failure-rate function is r(t)=f(t)/(1-F(t)), where f is the failure-time density and F(t)=1-e-atb, a > 0, b > 0. Find r(t).
- Question 42 – Match processes P: laser beam machining; Q: abrasive waterjet machining; R: ion beam machining; S: mechanical milling, with dominant removal…
- Question 43 – A vertical glass tube of diameter 2.5 mm is immersed in a fluid with zero contact angle, surface tension 0.1 N/m, density 1000 kg/m³ and g = 10 m/s².…
- Question 44 – An M/M/1 queue has arrival rate three customers per minute and steady-state mean number n in the system. Utilization is below one. Find mean time in…
- Question 45 – A 10 cm steel cube is sand cast using a cylindrical side riser of diameter d and height h. Assume no shared cooling surface between casting and riser;…
- Question 46 – A 200 mm wide, 23 mm thick strip must be rolled to 20 mm in one pass with 200 mm diameter rolls. Available lubricants P,Q,R,S have friction…
- Question 47 – The source prints the minimum-energy orthogonal-machining relation =C-/2+/2, with φ shear angle, α rake angle and β friction angle. Which ONE OR MORE…
- Question 48 – Which ONE OR MORE homogeneous robotic transformations involve a rotation through θ about the Y-axis?
- Question 49 – For the ideal OC curve shown, p₀ is acceptable quality level (AQL) and p₁ is lot tolerance percent defective (LTPD). Which ONE OR MORE statements are…
- Question 50 – The two-hand operation chart shown describes nut-and-bolt assembly by a left-handed operator. Which ONE OR MORE statements are correct?
- Question 51 – Which ONE OR MORE work materials are NOT commonly machined with diamond cutting tools?
- Question 52 – A CNC machine mills a straight slot in one pass from (0,0) to (180,180) in the XY plane, coordinates in mm. Actual Y velocity is 5% below intended,…
- Question 53 – In laser machining, t m=[( m- 0)k2H]2, with diffusivity α, melting temperature θ m, conductivity k and absorbed heat flux H. A uniform 1 kW beam of…
- Question 54 – A 2D stylus profilometer measures a 0.8 mm surface profile. The graph uses vertical magnification 10000 and horizontal magnification 100. Areas…
- Question 55 – A homogeneous isotropic linear-elastic cylindrical component of diameter 10 mm is under uniform uniaxial tension. A 14 kN force reduces its diameter…
- Question 56 – A custom 20-tooth full-depth spur pinion has pressure angle 20°, width b = 10m and transmitted torque 95 N·m. Safe bending stress is 180 MPa and form…
- Question 57 – A product has fixed cost ₹3,00,000 and variable cost ₹150/unit. Selling 5000 units produces profit equal to 20% of sales revenue. Find break-even…
- Question 58 – Two oil plants must meet demands of two markets. Costs per litre are C₁₁ = 250, C₁₂ = 280, C₂₁ = 150, C₂₂ = 180; plant capacities K₁ = 500 and K₂ =…
- Question 59 – A central server processes one program at a time. Four programs are ready at 10:00 am. Programs 1,2,3,4 take 60,40,90,100 minutes, with same-day due…
- Question 60 – dy/dt=2y and y(0) = 2. Find y(1), rounded to two decimals.
- Question 61 – Soldering-defect count per semiconductor device is Poisson with p(x)=e-x/x! and mean three. Find the probability a randomly chosen device has at least…
- Question 62 – A job has elements A,B, each observed three times. A times are 20,25,21 s with 105% rating; B times are 19,17,18 s with 90% rating. Add 20%…
- Question 63 – All sizes are mm. Hole limits are 22+0.018 +0.010 and shaft limits are 22+0.075 +0.004. Find clearance magnitude when shaft is at minimum material…
- Question 64 – A steady-state assembly line performs cutting, welding, polishing in sequence. Three workers are assigned exclusively one to each task. Task times per…
- Question 65 – In the composite filament-winding process shown, a 700 mm mandrel rotates at 6 rev/min. Find axial slider speed v c (m/s, two decimals) for a 45°…