GATE 2023 PI – Previous Year Questions with Solutions
All 65 questions of GATE 2023 PI with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – “You are delaying the completion of the task. Send contributions at the earliest.”
- Question 2 – References : : : Guidelines : Implement (By word meaning)
- Question 3 – PQRS is a parallelogram with PS = 7 cm, PT = 4 cm, and PV = 5 cm, as shown. PT and PV are perpendicular to QR and RS, respectively. What is RS in cm?…
- Question 4 – In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics. When he was younger, he was also a poet. He did not win any…
- Question 5 – A line of symmetry divides a figure into two parts that are mirror images about that line. The figure consists of 16 unit squares, three already…
- Question 6 – Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world,…
- Question 7 – To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2. If the total cost of…
- Question 8 – The World Bank has declared that it does not plan to offer new financing to Sri Lanka, which is battling its worst economic crisis in decades, until…
- Question 9 – The coefficient of x4 in (x-1)3(x-2)3 is .
- Question 10 – Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without…
- Question 11 – Given A=pmatrix1&-1&4\\3&2&-1\\2&1&-1pmatrix and B=(B ij) 33, B is the skew-symmetric matrix of A. Find B₁₃.
- Question 12 – Which differential equation is nonlinear?
- Question 13 – For 0<x1, (1+x)/x=1+bx+cx2+. Find b and c, respectively.
- Question 14 – Three unbiased coins are tossed. Given that at least two outcomes are tails, find the probability that all three are tails.
- Question 15 – Two infinite plane parallel black surfaces exchange thermal radiation. A black radiation shield is inserted midway between them. Find the ratio of…
- Question 16 – An alumina grinding wheel has ANSI designation 51 A 36 K 5 V 23. What does K indicate?
- Question 17 – The directrix and generatrix of a machining operation are shown. Which surface is produced?
- Question 18 – In an NC machine, what is the function of an interpolator?
- Question 19 – Which machining process essentially requires vacuum in the machining zone?
- Question 20 – Which forecasting method is qualitative?
- Question 21 – Find the homogeneous transformation matrix translating point P from (10,15) to (15,25), using column vectors.
- Question 22 – A copper rod 200 mm in diameter and 400 mm long is extruded to diameter 100 mm. Find the extrusion ratio.
- Question 23 – The surface-texture symbol is shown, with all values in µm. Find the difference between maximum and minimum surface roughness Rₐ.
- Question 24 – A thin cylinder has length L, diameter d, wall thickness t, Young’s modulus E and Poisson ratio μ. Find its change in length under internal pressure…
- Question 25 – Creep of mild steel at elevated temperature involves which behavior?
- Question 26 – What is the minimum number of control points required to generate a quadratic B-spline curve?
- Question 27 – Use Euler’s method for dy/dx=x3y-4, y(0) = 1, with step 0.1. Find y(0.1) to two decimals.
- Question 28 – A solid circular flywheel disk is 0.025 m thick, has density 7800 kg/m³ and central mass moment of inertia 4.36 kg·m². Find its radius in m to two…
- Question 29 – Standard time per machine job is 10 min. Five machines are each available 300 hours/month with average utilization 80%. Find maximum monthly…
- Question 30 – P travels from X to Y by aircraft: monetary worth of travel time and comfort ₹8000, ticket cost ₹4000. Q travels by train: worth ₹2000, cost ₹2000.…
- Question 31 – A wooden cube of side 0.1 m and specific gravity 0.75 is held submerged by a massless rigid wire in the shown oil–water pool. Oil SG = 0.7; oil depth…
- Question 32 – Steam steadily enters a turbine at h₁ = 3200 kJ/kg and exits wet at 0.1 bar. Heat loss is 100 kJ/kg and work output 1000 kJ/kg; neglect…
- Question 33 – Thirty samples of size 100 contain 420 total nonconformities. Find the lower control limit of the control chart for number of nonconformities, to two…
- Question 34 – Resistance spot welding uses current 4500 A for 0.2 s. Effective interface resistance is 400 × 10⁻⁶ Ω and thermal efficiency is 50%. Find heat used to…
- Question 35 – A metal rod has initial diameter 14 mm. After a tensile test its fractured-end diameter is 12 mm. Find ductility as percentage reduction in area, to…
- Question 36 – z(x,y)=ex-2y, x(t)=et, y(t)=e-t, with all variables real. Find dz/dt.
- Question 37 – Two cards are drawn successively without replacement from a standard 52-card deck. Find the probability that their suits differ.
- Question 38 – Match P: collet; Q: dividing head; R: lead screw, with 1: indexing; 2: thread cutting; 3: holding the tool in place.
- Question 39 – A massless beam is fixed at one end and supported by a roller at the other. A downward force P acts at its midpoint, as shown. Find the roller…
- Question 40 – Six jobs require drilling followed by reaming. Processing times (drilling, reaming), in minutes, are 1:(30,45), 2:(30,15), 3:(60,40), 4:(20,25),…
- Question 41 – Match room-temperature materials P: Si; Q: Fe; R: Al; S: Zn, with crystal structures 1: FCC; 2: HCP; 3: diamond cubic; 4: BCC.
- Question 42 – Match recording methods P: outline process chart; Q: string diagram; R: multiple activity chart; S: two-handed process chart, with applications 1:…
- Question 43 – Match products P: beverage can; Q: seamless pipe; R: connecting rod; S: bearing steel balls, with processes 1: forging; 2: skew rolling; 3: extrusion;…
- Question 44 – The dual of an LPP is: minimize w=4w 1+6w 2+5w 3-w 4, subject to pmatrix1&0&1&0\\0&0&1&-1pmatrixpmatrixw 1\ 2\ 3\ 4pmatrixpmatrix3\\-2pmatrix, w i0.…
- Question 45 – Choose a facility location using weighted scores (higher is better). Factor weights are raw materials 0.4, skilled labor 0.3, infrastructure 0.2 and…
- Question 46 – According to the Fe–C phase diagram, which microstructure occurs in plain carbon steel with 0.4 wt% carbon at room temperature?
- Question 47 – Which is the most appropriate process for manufacturing a plastic chair?
- Question 48 – Apply Newton–Raphson to x5-15=0, starting at x₀ = 1. Find the first approximation x₁ to two decimals.
- Question 49 – For A=pmatrix4&2\\3&3pmatrix, find the eigenvalue associated with eigenvector pmatrix2\\-3pmatrix (integer).
- Question 50 – A work-sampling study with 100 observations found 25% worker idle time. Find the number of observations required for ±10% accuracy at 95.45%…
- Question 51 – Product P has annual demand 2500 units, ordering cost ₹60/order and annual holding cost ₹30/unit. Q has demand 3600, ordering cost ₹80 and holding…
- Question 52 – The shown system has seven components with reliabilities R A = 0.96, R B = 0.92, R C = 0.94, R D = 0.89, R E = 0.95, R F = 0.88 and R G = 0.90. Find…
- Question 53 – Project activities A–J have durations (days) A:8, B:10, C:8, D:7, E:16, F:15, G:18, H:14, I:9, J:4. Predecessors are A:–, B:–, C:–, D:A, E:A, F:B,D,…
- Question 54 – A system has 10 essential components, each with exponential failure rate 0.04 per 4000 hours. Find system mean time to failure in hours (integer).
- Question 55 – A CNC waterjet cuts the shortest straight slot from (2,1) to (10,10) in the XY plane, coordinates in mm. Feed rate is 1.5 mm/s. Find machining time in…
- Question 56 – In orthogonal cutting with rake angle 0°, cutting force is twice thrust force. Find coefficient of friction to one decimal.
- Question 57 – A cubical casting initially has side 100 mm. Volumetric solidification shrinkage and subsequent solid contraction are each 10%; shape is retained on…
- Question 58 – Straight turning uses feed rate 100 mm/min, spindle speed 1600 rpm and ASA tool signature 8–8–5–5–7–25–0. Find geometric peak-to-valley surface…
- Question 59 – An arc weld is made at 25 V, 200 A and speed 2 mm/s. Heat used for melting is 80% of generated heat; unit melting energy is 10 J/mm³. Find volume of…
- Question 60 – Water flows in a 0.02 m diameter pipe at Reynolds number 1000. The pipe is heated externally at uniform heat flux; steady flow and heat transfer are…
- Question 61 – In an ideal air-standard Brayton cycle, compressor inlet is 100 kPa and 300 K. Thermal efficiency is 50%; heat addition is 1000 kJ/kg. Air has…
- Question 62 – A key of width and height 6 mm fixes a gear to a shaft of diameter 20 mm. Power is 10 kW at 600 rpm; allowable key shear stress is 80 N/mm². Neglect…
- Question 63 – A cylindrical casting has diameter 10 cm and mass 12.56 kg. Material density is 7.85 × 10⁻³ kg/cm³. Chvorinov exponent n = 2 and solidification time…
- Question 64 – A spur-gear pair transmits 20 kW at pitch-line velocity 10 m/s. Driving-gear diameter is 0.5 m. Find tangential force between driver and driven gear…
- Question 65 – Products P and Q sell in a 10:1 ratio. Fixed cost is ₹140000. Selling prices are ₹10/unit for P and ₹40/unit for Q; variable costs are ₹5 and ₹20/unit…