GATE 2022 PI – Previous Year Questions with Solutions
All 65 questions of GATE 2022 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 – Inhaling the smoke from a burning could you quickly.
- Question 2 – A sphere of radius r cm is packed in a cubical box. What is the minimum box volume in cm³?
- Question 3 – P and Q fill a tank in 10 and 6 minutes respectively. R drains 34 litres/min. All operate at constant rates. With all three operating, a full tank…
- Question 4 – Six persons P,Q,R,S,T,U sit around a circular table facing the center. P sits next to S and T; Q is diametrically opposite P; the shortest S–R…
- Question 5 – The top view shows a building with several rooms and initially closed doors. Find the minimum number of doors that must be opened to travel from P to…
- Question 6 – Rice, a versatile and inexpensive carbohydrate source, is a critical dietary component worldwide. Climate change and extreme weather threaten its…
- Question 7 – Each shown disk has eight equally likely outcomes 1–8. Two arrows are spun independently. Find the probability that the resulting numbers sum to 8.
- Question 8 – Given 3p-q<4 and 3q-p<12, which expression follows?
- Question 9 – Statements: some engineers are writers; no writer is an actor; all actors are engineers. Conclusions: I some writers are engineers; II all engineers…
- Question 10 – Which set of pieces shown can form a square with a single round hole near its center, without overlapping?
- Question 11 – For vectors a,b,c, find ( a b) c.
- Question 12 – Numerically integrate y = 2x+5 from x = 1 to 3 using ordinates at x = 1,2,3. Which statement is true?
- Question 13 – Which metal has FCC structure?
- Question 14 – An isotropic material has shear modulus G. What is the maximum possible Young’s modulus?
- Question 15 – Match casting methods P: continuous; Q: investment; R: centrifugal, with products 1: thin intricate components; 2: hollow axisymmetric parts such as…
- Question 16 – In injection blow molding of plastic beverage bottles, blowing is accomplished using what medium?
- Question 17 – In electrical-discharge machining with discharge voltage V b, spark energy is proportional to which expression?
- Question 18 – Match CNC codes P:G91; Q:M02; R:G32; S:M05, with 1:end of program; 2:incremental coordinates; 3:spindle stop; 4:thread cutting in turning.
- Question 19 – Which control chart tracks the number of defects in a welded joint?
- Question 20 – Which statement about concurrent engineering is true?
- Question 21 – Match the shown therblig symbols P,Q,R,S with meanings 1: rest to overcome fatigue; 2: avoidable delay; 3: inspect; 4: search.
- Question 22 – Match layouts P:process; Q:product; R:fixed position, with production types 1:job; 2:batch; 3:mass.
- Question 23 – A=pmatrix3\\2pmatrixpmatrix1&4pmatrix. Find det(A), rounded to nearest integer.
- Question 24 – Find the order of (dy/dx)2+5\,dy/dx+4y=5x3 (integer).
- Question 25 – A lot has ten spur gears, one defective. Three are drawn randomly without replacement. Find the probability all three are nondefective, to two…
- Question 26 – The shown slider–crank rotates at 60 rpm. Crank radius is 30 mm and connecting-rod length 120 mm. Find average piston speed over one crank revolution…
- Question 27 – Water of kinematic viscosity 1 × 10⁻⁶ m²/s flows through an 8 mm horizontal circular pipe. Flow is fully developed and laminar, with maximum axial…
- Question 28 – Yield begins at principal stresses 100,100,200 MPa. Find uniaxial yield stress according to von Mises, nearest integer MPa.
- Question 29 – Orthogonal machining uses a zero-rake single-point tool. Chip-compression ratio is 1.25. Find shear angle in degrees to one decimal.
- Question 30 – A lathe cuts a single-start 2 mm pitch thread using a single-start lead screw of pitch 4 mm. Find lead-screw revolutions per workpiece revolution to…
- Question 31 – Absolute surface deviations from a datum line are 10,15,12,10,13,12,20,25 µm. Find RMS roughness in µm to one decimal.
- Question 32 – A machine has two motors but needs only one to function. Their reliabilities are 0.90 and 0.70. Find machine reliability to two decimals.
- Question 33 – Bank interarrival times are exponential, with eight arrivals per hour. Find the probability of no arrival during 15 minutes, to two decimals.
- Question 34 – A ₹65000 machine has salvage value ₹5000. Straight-line annual depreciation is ₹10000. Find useful life in years (integer).
- Question 35 – Activities A–G have expected durations 4,5,4,1,7,6,8 minutes and variances 1,1,1,0,4,1,4 respectively. The critical path is B,E,G. Find…
- Question 36 – When a matrix is squared, which statement is correct?
- Question 37 – Find the general solution of 4y-4y+y=0, with arbitrary constants c₁,c₂.
- Question 38 – A normally distributed parameter was surveyed with n = 1000, giving confidence interval [500,700], mean 600. What sample size gives [550,650] at the…
- Question 39 – Eutectoid steel initially fully austenitic at 750°C cools to 35°C. Match P:water quench; Q:oil quench; R:air cool; S:furnace cool, with 1:coarse…
- Question 40 – In the shown three-member truss, AC = BC. A 10 kN force acts leftward at B parallel to AC. Find member BC force.
- Question 41 – Match powder-metallurgy steps P:atomization; Q:sintering; R:compaction; S:infiltration, with descriptions 1:press blended powder into die shapes;…
- Question 42 – An assembly has hole size 25.000 mm with upper/lower deviations +0.002/−0.001 mm and shaft size 25.000 mm with deviations +0.001/−0.003 mm. Identify…
- Question 43 – Four products P,Q,R,S each have batch size 2 × 10⁷. Defective counts are 60,71,80,55 respectively. Which statement is true?
- Question 44 – Match P:product synthesis; Q:product simplification; R:product analysis; S:product standardization, with 1:convert conceptual design into an…
- Question 45 – Evaluate x1(x3-3x+2)/(x3-x2-x+1) to one decimal.
- Question 46 – A thick cylinder has inner/outer diameters 20/40 mm and internal pressure 100 MPa. Taking tensile stress positive, find radial plus hoop stress at…
- Question 47 – A solid circular shaft transmits 10 kW at 1440 rpm. Material shear yield stress is 150 MPa and safety factor 2. Find static-strength diameter in mm to…
- Question 48 – Air initially at 15°C, 1 bar is heated irreversibly to 303°C, 2 bar. Treat it as calorically perfect, R = 287 J/(kg·K), γ = 1.4. Find entropy change…
- Question 49 – Hot working occurs at homologous temperature 0.8. The metal melts at 800°C. Find working temperature in °C, nearest integer.
- Question 50 – A 30 mm diameter, 40 mm high cylinder is open-die forged between platens. Assume perfect plasticity, flow stress 300 MPa. Find ideal load at 30%…
- Question 51 – Steady GTAW uses 18 V and 160 A. Arc creation loses 40% of input power; workpiece convection/radiation lose 800 W. Find effective power melting the…
- Question 52 – Turning a 20 mm steel bar with an HSS tool gives life 10 min at 400 rpm and 40 min at 200 rpm. Find tool life at 300 rpm, nearest integer minute.
- Question 53 – Two tools turn at feed 0.2 mm/rev. Tool 1 has zero nose radius, side cutting-edge angle 20° and end cutting-edge angle 10°. Tool 2 has nose radius 0.5…
- Question 54 – ECM obeys dy/dt=/y-f, where gap y is in mm, time t in minutes and feed f in mm/min. Given λ = 6 × 10⁻³ cm²/min, find feed maintaining gap 0.1 mm, to…
- Question 55 – A positioning table is driven by a 4 mm pitch lead screw. An 80-tooth gear on a stepper-motor shaft drives a 20-tooth lead-screw gear. Motor step…
- Question 56 – Two spherical steel balls of diameters 3 and 4 cm are placed in a cylindrical cavity as shown. The bigger ball is above the smaller one. Cavity depth…
- Question 57 – Five samples of 80 mobile screens have defective counts 4,10,5,6,5. Find the p-chart upper control limit using ±3σ, as fraction defective to two…
- Question 58 – A factory uses 100 bulbs and individually replaces failures at ₹300 each. Cumulative failure probabilities at 1,2,3,4,5 months are…
- Question 59 – A company procures 384 parts annually. Annual holding cost is ₹30/part; ordering cost is ₹1000/order. Find EOQ (integer).
- Question 60 – Observed machining-cycle times 42,43,44,45,46 minutes have frequencies 1,2,3,2,1 respectively. Worker rating is 110%. Find standard time with 10%…
- Question 61 – A component passes sequentially through five workstations with cycle times 85,55,90,65,70 seconds. Find steady-state mass-production output per hour…
- Question 62 – Vaccine supplies at W1,W2 are 200,150; hospital demands H1,H2,H3 are 100,150,125. Unit transport costs for W1 are (5,7,3), for W2 (4,6,7) rupees. Find…
- Question 63 – Maximize z=20x 1+6x 2+Px 3, with C₁: 8x 1+2x 2+3x 3250; C₂: 4x 1+3x 2150; C₃: 2x 1+x 350; x ≥ 0. Optimal x = (0,50,50) and dual y = (0,2,8). Find P to…
- Question 64 – A plant produces 24 electric cars/day. Setup cost is ₹19476 million, variable cost ₹0.6 million/car and selling price ₹1.5 million/car. Find days to…
- Question 65 – Weekly oxygen-cylinder demand is forecast using exponential smoothing, α = 0.2. Actual demands in weeks 1–4 are 375,412,592,439; forecast for week 3…