GATE 2021 PI – Previous Year Questions with Solutions
All 65 questions of GATE 2021 PI with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – A city currently has population 1102500, increasing at 5% per annum. What was its population two years ago?
- Question 2 – Positive integers p,q satisfy p/q+q/p=3. Find p2/q2+q2/p2.
- Question 3 – Find the least number of squares to add to the shown arrangement so P–Q becomes a line of symmetry.
- Question 4 – Nostalgia is to anticipation as is to . Choose the analogous relation.
- Question 5 – Which sentences are grammatically correct? (i) I woke up from sleep. (ii) I woked up from sleep. (iii) I was woken up from sleep. (iv) I was wokened…
- Question 6 – Statements: all purple are green; all black are green. Conclusions: I some black are purple; II no black is purple. Which option is logically correct?
- Question 7 – Computers are ubiquitous and improve efficiency from agriculture to space exploration. Artificial intelligence enables computers to learn given enough…
- Question 8 – A square sheet of side 1 unit is cut along its main diagonal. One resulting triangle is revolved about a short edge to form a solid cone. Find cone…
- Question 9 – The bar chart shows minutes X and Y exercise each day of a week. On how many days does one student exercise at least 10% longer than the other?
- Question 10 – Corners are cut from an equilateral triangle to produce the shown regular convex hexagon. Find hexagon area/original triangle area.
- Question 11 – A product has exponential time to failure with constant failure rate 0.00006 per hour. Find reliability after 4000 operating hours.
- Question 12 – Under concurrent engineering, at what stage are all product life-cycle elements from conception to disposal considered?
- Question 13 – For a single-sampling attribute plan with acceptance number zero and sample size at most ten, which form describes the operating-characteristic curve?
- Question 14 – Which computerized layout-design technique is an improvement heuristic?
- Question 15 – Which is NOT a measure of forecast error?
- Question 16 – Pearlite in eutectoid steel consists of alternating layers of α-ferrite and which phase?
- Question 17 – Which defect is NOT associated with welding?
- Question 18 – Match components P:aluminium-alloy IC-engine piston; Q:low-carbon steel oil pan; R:tungsten-carbide cutting insert; S:plastic bottle, with processes…
- Question 19 – Doubling cutting speed reduces turning-tool life to one-eighth. Find exponent n in Taylor’s law VTn=C.
- Question 20 – Which mechanism does NOT transform rotary motion to translation in machine tools?
- Question 21 – Match features P:surface-plate flatness error; Q:cam profile; R:machine-tool slideway alignment error; S:screw-thread pitch and angle errors, with…
- Question 22 – A die-sinking EDM has pulse frequency 10 kHz and off-time 40 µs. Find duty factor.
- Question 23 – A 0.3 m cantilever carries UDL C = 10 kN/m over its full length, as shown. Flexural rigidity is 5000 N·m². Neglect self-weight. Find curvature…
- Question 24 – A circular rod of length 2 m has flexural rigidity 2000 N·m² and pinned ends, under axial compression P as shown. Find elastic critical buckling load…
- Question 25 – Two equal-length steel cylindrical parts are press-fitted as shown. E = 200 GPa, ν = 0.33, radial interference δ = 0.05 mm, interface radius R = 25 mm…
- Question 26 – Which dimensionless number is the ratio of inertial to viscous force?
- Question 27 – A capillary tube of 3 mm inner diameter is inserted into fluid of density 900 kg/m³, surface tension 0.1 N/m and contact angle 30°. Find capillary…
- Question 28 – Steel has uniaxial tensile and compressive yield strength 700 MPa. Under pure shear its ordered principal stresses are σ₁ = σ, σ₂ = 0, σ₃ = −σ. Find σ…
- Question 29 – A mild-steel tensile specimen of gauge length 50 mm and diameter 10 mm is extended at 4 mm/min, first from 50 to 55 mm and then 55 to 60 mm. Neglect…
- Question 30 – An M30 bolt requires pretension F i = 350 kN. Torque coefficient K = 0.2. Find tightening torque in N·m (integer).
- Question 31 – A 150 mm wide polyamide flat belt transmits 15 kW. Driving-pulley pitch diameter is 150 mm and speed 200 rpm. Find tight-side minus slack-side tension…
- Question 32 – A refrigerator removes heat at 300 kJ/min to maintain its inside at 2°C. Input power is 2 kW. Find COP to one decimal.
- Question 33 – An ideal Otto cycle receives 800 kJ/kg during constant-volume heat addition and rejects 381 kJ/kg during constant-volume cooling. Find thermal…
- Question 34 – For real x,y and i=-1, (3i+1)x+(4i+4)y+5=0. Find x to one decimal.
- Question 35 – Find the minimum of f(x,y,z)=x2+5y2+5z2-4x+40y-40z+300 (integer).
- Question 36 – Four independent out-of-control rules are used simultaneously. Their Type-I error probabilities are 0.005,0.02,0.03,0.05. Find overall Type-I error…
- Question 37 – An in-control process has estimated standard deviation 2 mm and specifications 120 ± 8 mm. Its mean shifts to 118 mm. Find C p and C pk, respectively.
- Question 38 – Identical independent components form a parallel system of reliability 0.97. Each component reliability is 0.68. Find the number of components; round…
- Question 39 – Choose a retail site by weighted factors. Weights are community income 0.4, demand growth 0.1, proximity to existing store 0.3 and public transport…
- Question 40 – In classical EOQ, Q is optimal order quantity and C is minimum annual ordering-plus-holding cost. If quantity is incorrectly set to Q′ = 2Q, find…
- Question 41 – A=pmatrix8&3\\2&7pmatrix has eigenvalues 5 and 10. For constant α and 2×2 identity I, find eigenvalues of B = A+αI.
- Question 42 – Products P,Q earn unit profits 4,5. Per-unit resource uses (P,Q) and availability are manpower (1,1):10; R1 (1,2):18; R2 (2,1):18. Find maximum…
- Question 43 – An NC tool moves along a circular arc from (20,20) to (10,10), centered at (20,10). Which printed command performs the intended operation?
- Question 44 – A hole is 30 mm with upper/lower deviations +0.040/0.000 mm. Its mating shaft has minimum clearance 0.01 mm and tolerance 0.03 mm. Find maximum…
- Question 45 – GO and NO GO snap gauges are specified for a shaft 36.000 mm with deviations +0.070/+0.010 mm. Gauge tolerance is 5% of the stated “hole tolerance”.…
- Question 46 – A circular tank of diameter 4 m holds water to depth 3 m. Assuming almost steady flow and no losses, find time to empty through a 5 cm diameter…
- Question 47 – A discrete random variable has P(X=x)=1/2x, x = 1,2,… . Find E[X] (integer).
- Question 48 – Airport security-screening time is exponential with mean 15 min. A passenger must clear within 15 min to catch a flight. Find probability of missing…
- Question 49 – Four jobs A,B,C,D are available on day 1 for a single CNC machine. Processing times (days) are 8,5,7,9 and due days 14,10,12,19 respectively. Using…
- Question 50 – Five observed spot-welding times are 40,35,45,37,43 seconds. Standard time is 45 s and allowance is 9 s. Find operator performance rating in percent…
- Question 51 – A machine initially costs ₹1000000 and has salvage ₹50000 after ten years. Using straight-line depreciation, find book value at end of year 7 in…
- Question 52 – Activities and (duration in days; predecessors) are A:(2;–), B:(3;–), C:(2;A), D:(4;A,B), E:(4;C), F:(3;C), G:(X;D,E), H:(2;F,G). Project duration is…
- Question 53 – A wire is drawn from 5 mm to 4 mm diameter through a conical die at pulling speed 5 m/s. Neglect friction/redundant work. Drawing stress is…
- Question 54 – An arc-welding DC source has linear characteristic with open-circuit voltage 60 V and short-circuit current 600 A. Melting energy is 10 J/mm³;…
- Question 55 – A sand-cast disk is 50 mm thick and 1.0 m in diameter. Chvorinov’s equation is t=B(V/A)2. Thickness and diameter are both halved to 25 mm and 0.5 m…
- Question 56 – Orthogonal machining of mild steel uses rake 15°, uncut chip thickness 0.9 mm and chip thickness 1.8 mm. Find shear angle in degrees to one decimal.
- Question 57 – A shaper removes the top layer of a 750 × 300 mm plate in one depth of cut, with 750 mm along tool travel. Approach and overtravel are 25 mm each;…
- Question 58 – A fiber laser cuts 3 mm steel at 2 kW. Initial temperature 30°C; melting point 1530°C; absorptivity 50%; density 8000 kg/m³; specific heat 500…
- Question 59 – The shown open-loop NC drive has a 1.8° stepper, gear reduction 4:1 (four motor turns per lead-screw turn), and single-start 4 mm pitch screw. For…
- Question 60 – A 30 kg smooth rigid sphere rests on two frictionless rigid inclines, left at 60° and right at 30° to horizontal, as shown. Use g = 9.81 m/s². Find…
- Question 61 – The shown rigid members AB,BC,CA form an equilateral truss, with pin A and frictionless roller C. A downward 10 kN force acts at B. Neglect member…
- Question 62 – Fluid of dynamic viscosity 1 Pa·s and density 1000 kg/m³ flows at 0.2 litre/s through a 1 cm circular pipe. Assuming fully developed flow, find…
- Question 63 – At x = 0,1,…,10, y(x) values are 5,3,0,−5,−10,−6,0,5,11,18,30. Use the trapezoidal rule for 010y(x)dx, to one decimal.
- Question 64 – A sphere has radius 1 m, centered at the origin, and thermal conductivity K = 50 W/(m·K). Its temperature field is T=100-70x+51y-80z-10x2-20y2-20z2.…
- Question 65 – A 3.5 mm sheet is plane-strain rolled in a two-high mill. Both rolls have diameter 500 mm and speed 200 rpm. Friction coefficient is 0.08; roll…