GATE 2025 PI – Previous Year Questions with Solutions
All 65 questions of GATE 2025 PI with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Courage : Bravery :: Yearning : Select the most appropriate option to complete the analogy.
- Question 2 – We tennis in the lawn when it suddenly started to rain. Select the most appropriate option to complete the above sentence.
- Question 3 – A 4 × 4 digital image has pixel intensities (U) as shown in the figure. The number of pixels with U 4 is: 0 1 0 2 --- --- --- --- 4 7 3 3 5 5 4 4 6 7…
- Question 4 – In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options…
- Question 5 – A rectangle has a length L and a width W, where L > W. If the width, W, is increased by 10%, which one of the following statements is correct for all…
- Question 6 – Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk. Column-I Column-II --- --- P. This house is in a mess. 1.…
- Question 7 – Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical…
- Question 8 – A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius r cm as shown in the figure. The side of the dodecagon is d cm. All…
- Question 9 – If a real variable x satisfies 3x2 = 27 9x, then the value of 2x2(2x)2 is:
- Question 10 – The number of patients per shift (X) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹ 1000(X - 0.2),…
- Question 11 – Find the eigenvalues of A=pmatrix0&-1\\1&0pmatrix.
- Question 12 – For orthogonal Cartesian unit vectors i,j,k, find the curl of -2y i+x j.
- Question 13 – If F(s) is the Laplace transform of f(t), find the transform of ebtf(t) for real constant b.
- Question 14 – Which differential equation is linear?
- Question 15 – A bag has five red, seven green and three blue balls. Two balls are drawn randomly one after another. Find the probability that the second is red.
- Question 16 – In which welding process is an exit hole common?
- Question 17 – An aircraft has two engines, each of reliability R. It crashes only if both stop. Find reliability against a crash.
- Question 18 – What is the proper sequence of product design?
- Question 19 – A worker is idle in x of n work-sampling observations. Find the standard deviation of estimated mean idle proportion.
- Question 20 – The atomic packing factor of a body-centered cubic crystal is closest to .
- Question 21 – Which statement about injection molding a polymer composite is FALSE?
- Question 22 – An 8 mm through-hole is needed in 30 mm mild-steel plate. Which process best combines high dimensional accuracy with short processing time?
- Question 23 – Which casting defect can result when molten metal is supplied through two gates?
- Question 24 – Match CNC types P: turning center (lathe); Q: vertical machining center, with minimum-axis counts i: 3; ii: 2; iii: 4.
- Question 25 – A simply supported beam AB of span L has an applied moment M at C, distance a from A, as shown. Find the magnitude of reaction at A.
- Question 26 – Relate hoop stress σ₁ and longitudinal stress σ₂ in a closed thin cylindrical pressure vessel.
- Question 27 – A starting simplex tableau maximizes z=6x 1+4x 2. Rows list [x₁,x₂,S₁,S₂,S₃,S₄ RHS]: S₁: [6,3,1,0,0,0 36]; S₂: [2,1,0,1,0,0 40]; S₃: [−1,3,0,0,1,0 2];…
- Question 28 – Heat addition in an ideal Diesel cycle is .
- Question 29 – Principal stresses are 300,250,100 MPa. Yielding is just beginning. Find yield strength according to Tresca (integer MPa).
- Question 30 – In orthogonal straight turning, feed is 0.1 mm/rev and cut depth is 0.5 mm. ASA side cutting-edge angle is 0°. Find chip width (one decimal mm).
- Question 31 – A lathe has a single-start lead screw of 6 mm pitch. It cuts a double-start thread of 3 mm pitch while the spindle runs at 400 rpm. Find lead-screw…
- Question 32 – A toy company can make batteries with annual fixed cost ₹2,00,000 and variable cost ₹70/unit, or buy at ₹90/unit. Find annual demand at the…
- Question 33 – Annual demand is 2000 bulbs, ordering cost ₹300/order and annual holding cost ₹30/bulb. Find EOQ (integer bulbs).
- Question 34 – Fifteen gearbox features are critical to quality. Of 40000 gearboxes produced last quarter, 1500 defects occurred in these features. Find DPMO…
- Question 35 – Hole dimensions are 30+0.04 -0.02 mm and shaft dimensions 30+0.06 +0.03 mm. Find maximum possible clearance (two decimal mm).
- Question 36 – Solve dy/dx+y=ex with y(0) = 0.
- Question 37 – Which function is analytic in z = x + iy, with i=-1?
- Question 38 – Match processes P: EDM; Q: LBM; R: CHM; S: WJM, with features 1: undercutting causes dimensional error; 2: cutting edible items; 3: deep square blind…
- Question 39 – Match grinding terms P: loading; Q: glazing; R: dressing; S: truing, with definitions 1: regenerate sharpness; 2: chips fill spaces between grits; 3:…
- Question 40 – A CNC vertical mill cuts a straight XY slot from P = (10,5) mm, shown in the figure. Slot slope dy/dx = 1.25 and X feed is 120 mm/min. Find the cutter…
- Question 41 – The project network shows activities A–H and durations in days. Find its critical path.
- Question 42 – Which ONE OR MORE are benefits of product standardization?
- Question 43 – Simpson’s 1/3 rule with four equal subintervals gives 13(x2-2x)dx=n/3. Find integer n.
- Question 44 – Find the rate of change of f=x2+2y2+z at (1,1,1) in the direction 3 i+4 k (integer).
- Question 45 – A perfectly plastic wire has flow stress 300 MPa. During ideal frictionless drawing, back tension is zero and front tension is 200 MPa. Find…
- Question 46 – A cold-rolling process without front/back tensions requires minimum friction coefficient 0.04. Assume large rolls. If draft doubles and roll diameters…
- Question 47 – For DC arc welding, voltage V (V) and arc length l (cm) satisfy V = 30 + 30l. Open-circuit voltage is 80 V. Find maximum possible arc length (two…
- Question 48 – A worker receives 30 minutes personal allowance during an eight-hour shift. Normal product time is five minutes. Find standard time (integer seconds).
- Question 49 – Six indivisible tasks occur sequentially in a single-line layout, taking 37,8,19,34,36,17 minutes. Find the number of stations needed to minimize…
- Question 50 – Drill a 10 mm through-hole in 30 mm mild-steel plate at 600 rpm and feed 0.3 mm/rev. Approach and breakthrough distances are 3 mm each. Find drilling…
- Question 51 – The iron–carbon eutectoid occurs at 723°C and 0.83 wt% C. Ferrite has 0.022 wt% C and cementite 6.67 wt% C. A 0.7 wt% C steel is cooled from 950°C…
- Question 52 – Orthogonal cutting uses rake angle 10°, cutting force 900 N and thrust force 275 N. Find rake-face friction coefficient (two decimals).
- Question 53 – An 80 mm cube casting undergoes volumetric solidification shrinkage 4.5% and solid contraction 2%. Assume uniform cooling in every direction. Find the…
- Question 54 – Casting solidification starts at 10:00 am. Centerline metal starts solidifying at 10:03 and finishes at 10:10. Casting is completely solid when the…
- Question 55 – A 200 mm link OA rotates counterclockwise at constant angular velocity 100 rad/s. At the shown position it makes 30° with +X. Find absolute X…
- Question 56 – A 1000 N force acts at A of the bracket fixed at B as shown. Find moment magnitude about B (one decimal N·m).
- Question 57 – A plate is attached to a channel with three identical carbon-steel bolts as shown. Permissible shear yield strength is 400 N/mm². The plate carries 12…
- Question 58 – Marketing expenditure x and annual profit y over three years are (3,22),(4,27),(6,36), in common units. Use linear regression to estimate year-four…
- Question 59 – Plants P₁,P₂,P₃ supply 6,1,9 thousand litres; centers D₁,D₂,D₃ demand 7,5,4 thousand litres. Transport costs (hundreds of ₹) are P₁: [2,3,11]; P₂:…
- Question 60 – Annual demand is 5000 units, ordering cost ₹400/order and annual holding rate 30% of unit price. All-units prices are ₹10 for Q < 1200, ₹8 for 1200 ≤…
- Question 61 – A vernier’s zero lies between main divisions 20 and 21; its fourth division coincides with a main division. Five vernier divisions equal four main…
- Question 62 – A broach produces key slots of mean size 10.56 mm and standard deviation 0.05 mm. For sample size five, find the X-bar chart upper control limit (two…
- Question 63 – A machine costs ₹70000. End-of-year resale values for years 1–5 are ₹40000,30000,25000,22000,20000; annual maintenance costs are…
- Question 64 – Water flows steadily, fully developed and laminar through a smooth circular pipe of diameter 10 cm and length 10 m. Pressure drop is 0.2 Pa; kinematic…
- Question 65 – A 20 cm wall has left face held at 25°C and right face exposed to 50°C air. There is no internal heat generation; k = 100 W/(m·K) and right-side…