GATE Chemical Engineering
PYQ Archive

GATE 2026, Q1

"He often _____ the numbers. False claims are not going to help. Honesty _____ trust", said the manager. Choose the option with the correct order of words to fill the blanks.

The correct answer is A, exaggerates; engenders.

GATE 2026 official key: (A). "Exaggerates" fits inflating the numbers; "engenders" (= creates) fits "Honesty engenders trust".

GATE 2026, Q2

In the sequence of tiles shown below, the missing tile indicated by the question mark should be:

The correct answer is B, Option B.

GATE 2026 official key: (B).

GATE 2026, Q3

A school has 100 students distributed among 1st to 10th standards. Based on this, which one of the following statements is always correct?

The correct answer is A, There are at least 10 students who belong to the same standard..

GATE 2026 official key: (A). By the pigeonhole principle, 100 students across 10 standards forces at least one standard to have ⌈100/10⌉ = 10 or more students.

GATE 2026, Q4

How many 3-digit numbers can be formed using three distinct single digit prime numbers?

The correct answer is B, 24.

GATE 2026 official key: (B). The single-digit primes are 2, 3, 5, 7 (4 digits); arranging 3 distinct digits from these 4 gives ⁴P₃ = 4×3×2 = 24 numbers.

GATE 2026, Q5

In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like neither Mathematics nor English. The number of students in the group is ____

The correct answer is C, 24.

GATE 2026 official key: (C). By inclusion-exclusion, Math ∪ English = 10+12−4 = 18; adding the 6 who like neither gives 18+6 = 24.

GATE 2026, Q6

Charity : P :: Retaliation : Q. Choose the appropriate pair of words P and Q that fit the analogy.

The correct answer is D, P = Magnanimous; Q = Vindictive.

GATE 2026 official key: (D). Charity reflects magnanimity (generosity); retaliation reflects vindictiveness (seeking revenge).

GATE 2026, Q7

A paper shown in Panel I is folded along the dashed lines to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

The correct answer is A, Only (i) can correspond to the unfolded cube in Panel I..

GATE 2026 official key: (A). Tracing the fold lines, only cube (i)'s face pattern is consistent with the shaded regions in Panel I.

GATE 2026, Q8

Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. All corners are to be colored such that any two corners connected by an edge must be of different colors. The minimum number of colors required to achieve this is ________

The correct answer is D, 2.

GATE 2026 official key: (D). The cube's vertex-edge graph is bipartite (3-regular, no odd cycles), so 2 colors suffice.

GATE 2026, Q9

Four hills H1, H2, H3, and H4 are present in an area. (i) Neither H2 nor H3 is the easternmost hill. (ii) Neither H2 nor H3 is the westernmost hill. (iii) Neither the easternmost hill nor the westernmost hill is the southernmost hill. (iv) Two hills are located to the west of H2. (v) The southernmost hill has at least two hills to its east. The southernmost hill is ________.

The correct answer is C, H3.

GATE 2026 official key: (C). Working through conditions (i)-(v) together pins down H3 as the only hill consistent with all constraints as the southernmost.

GATE 2026, Q10

Circle C1 with center O1 and radius r1 touches the square VWXY at points P and Q, while circle C2 with center O2 and radius r2 touches the square VWXY at points R and S. The two circles touch each other at T. Given r1 = 1 cm and VY = VW = 4 cm, r2 = _____ cm.

The correct answer is C, 7 − 4√2.

GATE 2026 official key: (C). Solving the tangency conditions (O1O2 = r1+r2, each center offset r from its two adjacent sides) with r1 = 1 cm gives r2 = 7 − 4√2 cm.

GATE 2025, Q1

Is there any good show _______ television tonight? Select the most appropriate option to complete the above sentence.

The correct answer is D, on.

GATE 2025 official key: (D). The idiom is "on television", "on" is the correct preposition for a broadcast medium.

GATE 2025, Q2

As the police officer was found guilty of embezzlement, he was _______ dismissed from the service in accordance with the Service Rules. Select the most appropriate option to complete the above sentence.

The correct answer is D, summarily.

GATE 2025 official key: (D). "Summarily dismissed" = dismissed immediately, without the usual formalities, the standard collocation for disciplinary termination.

GATE 2025, Q4

A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting and soldering the wire. If the wire is 12 m long, what is the minimum number of cuts required to construct the wire frame of the cube?

The correct answer is A, 3.

GATE 2025 official key: (A). A cube has 12 edges of total length 12 m, matching the wire exactly (no waste). The wire can be bent into an Eulerian-type path covering all 12 edges using just 3 cuts to create the needed separate segments/loops that, when soldered at the joints, form the complete wire frame.

GATE 2025, Q5

The figures I, II and III are parts of a sequence, each showing a circle with a shaded sector of increasing angular size. Which one of the following options comes next in the sequence at IV?

The correct answer is B, Option B.

GATE 2025 official key: (B), based on the visual progression shown across panels I–III of the official figure.

GATE 2025, Q6

"Why do they pull down and do away with crooked streets, I wonder, which are my delight, and hurt no man living? Every day the wealthier nations are pulling down one or another in their capitals and their great towns: they do not know why they do it; neither do I. It ought to be enough, surely, to drive the great broad ways which commerce needs and which are the life-channels of a modern city, without destroying all history and all the humanity in between: the islands of the past." (From Hilaire Belloc's "The Crooked Streets") Based only on the information provided in the above passage, which one of the following statements is true?

The correct answer is B, The wealthier nations are pulling down the crooked streets in their capitals..

GATE 2025 official key: (B). The passage states wealthy nations are "pulling down one or another [crooked street] in their capitals and their great towns," directly supporting (B); the other options misread or invert the passage's claims.

GATE 2025, Q7

Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant, he notices that the hour and minute hands on the wall clock are exactly coinciding. After about an hour, when he leaves the restaurant, he notices that the clock hands are again exactly coinciding. How much time (in minutes) did Rohit spend at the restaurant?

The correct answer is C, 65 5/11.

GATE 2025 official key: (C). Clock hands coincide every 12/11 hours = 65 5/11 minutes, so consecutive coincidences are always 65 5/11 minutes apart.

GATE 2025, Q8

A color model is shown in the figure with color codes: Yellow (Y), Magenta (M), Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K). Which one of the following options displays the color codes that are consistent with the color model?

The correct answer is A, Diagram A.

GATE 2025 official key: (A), matching the standard CMYK/RGB overlap color model shown in the official figure.

GATE 2025, Q9

A circle with center at (x, y) = (0.5, 0) and radius = 0.5 intersects with another circle with center at (x, y) = (1, 1) and radius = 1 at two points. One of the points of intersection (x, y) is:

The correct answer is B, (0.2, 0.4).

GATE 2025 official key: (B). Distance from (0.5,0.4)... checking (0.2,0.4): distance to (0.5,0)=√(0.09+0.16)=√0.25=0.5 ✓ (matches radius 0.5); distance to (1,1)=√(0.64+0.36)=√1=1 ✓ (matches radius 1). Both circle equations are satisfied.

GATE 2025, Q10

An object is said to have an n-fold rotational symmetry if the object, rotated by an angle of 2π/n, is identical to the original. Which one of the following objects exhibits 4-fold rotational symmetry about an axis perpendicular to the plane of the screen?

The correct answer is B, Shape B.

GATE 2025 official key: (B), the shape that maps onto itself under four successive 90° rotations in the official figure.

GATE 2024, Q1

If → denotes increasing order of intensity, then the meaning of the words [simmer → seethe → smolder] is analogous to [break → raze → ________]. Which one of the given options is appropriate to fill the blank?

The correct answer is B, obliterate.

GATE 2024 official key: (B). The first triad increases in intensity; by analogy [break → raze → obliterate] continues to intensify (a fissure/fracture is milder than a break, which is milder than razing, which is milder than obliterating).

GATE 2024, Q2

In a locality, the houses are numbered in the following way: the house-numbers on one side of a road are consecutive odd integers starting from 301, while the house-numbers on the other side are consecutive even numbers starting from 302. The total number of houses is the same on both sides. If the difference of the sum of the house-numbers between the two sides is 27, then the number of houses on each side of the road is

The correct answer is A, 27.

GATE 2024 official key: (A). For n houses per side, the i-th pair is (299+2i, 300+2i), a difference of 1 per pair, so the total difference of sums is n. Setting n = 27 satisfies the given difference of 27.

GATE 2024, Q3

For positive integers m and n, with m/n ≠ 1, (m/n)^(m/n) = m^(m/n − 1). Then,

The correct answer is A, nᵐ = mⁿ.

GATE 2024 official key: (A). Manipulating the given identity and equating exponents of the resulting power relation leads to mᵐ = nⁿ.

GATE 2024, Q4

Which one of the given options is a possible value of x in the following sequence? 3, 7, 15, x, 63, 127, 255

The correct answer is D, 31.

GATE 2024 official key: (D). Each term is 2ⁿ−1: 3=2²−1, 7=2³−1, 15=2⁴−1, x=2⁵−1=31, 63=2⁶−1, 127=2⁷−1, 255=2⁸−1.

GATE 2024, Q5

On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?

The correct answer is C, 50.

GATE 2024 official key: (C). The minute and second hands coincide every 60/59 minutes after 12:00:00. Counting crossing times t_k = 60k/59 strictly between the 5-minute and 55-minute marks gives k = 5,…,54, i.e., 50 crossings.

GATE 2024, Q6

In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks. "From the ancient Athenian arena to the modern Olympic stadiums, athletics (i) the potential for a spectacle. The crowd (ii) with bated breath as the Olympian artist twists his body, stretching the javelin behind him. Twelve strides in, he begins to cross-step. Six cross-steps (iii) in an abrupt stop on his left foot. As his body (iv) like a door turning on a hinge, the javelin is launched skyward at a precise angle."

The correct answer is D, (i) holds, (ii) waits, (iii) culminate, (iv) pivots.

GATE 2024 official key: (D). Subject-verb agreement: "athletics holds" (treated as singular), "the crowd waits" (singular collective noun), "six cross-steps culminate" (plural), "his body pivots" (singular).

GATE 2024, Q7

Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions of the people. How many unique seating arrangements are possible such that each person is sitting next to their twin?

The correct answer is A, 12.

GATE 2024 official key: (A). Treating each twin-pair as a block that must occupy two adjacent chairs and counting the distinct relative circular arrangements of the three blocks (with the remaining empty chairs distributed among the gaps) gives 12 unique arrangements.

GATE 2024, Q8

The chart shows the Electricity Generation (MWh, left axis, bars) and Installed Capacity (MW, right axis, ✕ marks) of four power generation technologies T1, T2, T3, and T4 over 1000 hours. From the figure: T1 generates 4000 MWh at 20 MW capacity; T2 generates 6000 MWh at 30 MW capacity; T3 generates 3000 MWh at 15 MW capacity; T4 generates 8000 MWh at 40 MW capacity. The Capacity Factor of a technology = Electricity Generation (MWh) / [Installed Capacity (MW) × 1000 h]. Which one of the given technologies has the highest Capacity Factor?

The correct answer is A, T1.

GATE 2024 official key: (A). Capacity factors: T1 = 4000/(20×1000) = 0.50; T2 = 6000/(30×1000) = 0.30; T3 = 3000/(15×1000) = 0.467; T4 = 8000/(40×1000) = 0.30. T1 has the highest at 0.50.

GATE 2024, Q9

In the 4×4 array shown, each cell of the first three columns has either a cross (X) or a number, as per the given rule: the number in a cell represents the count of crosses among its immediate neighboring cells (left, right, top, bottom, diagonals). The grid (rows 1–4, columns 1–3) reads: Row1: 1, 1, 2; Row2: 2, X, 3; Row3: 2, X, 4; Row4: 1, 2, X. As per this rule, the maximum number of crosses possible in the empty (4th) column is

The correct answer is C, 2.

GATE 2024 official key: (C). Let column-4 cells be a,b,c,d (rows 1–4). The constraints from cells (1,3)=2, (2,3)=3, (3,3)=4 (counting already-known crosses at (2,2),(3,2),(4,3)) reduce to: a+b=1, c=0, b+d=1. Maximizing a+b+c+d gives a=1,b=0,c=0,d=1, i.e., 2 crosses.

GATE 2024, Q10

During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the ratio of the Earth-Sun and Earth-Moon distances is closest to

The correct answer is B, 382.

GATE 2024 official key: (B). With the right angle at the Moon, Earth-Sun/Earth-Moon = 1/cos(89.85°) = 1/sin(0.15°) ≈ 1/0.002618 ≈ 382.

GATE 2026, Q17

An irreversible chemical reaction occurs on a porous catalyst. All the pores are of same size. In strong pore diffusion regime, the observed activation energy is 120 kJ mol⁻¹. The activation energy of diffusion is 10 kJ mol⁻¹. Assuming Arrhenius temperature dependency for both reaction and diffusion, which one of the following is the true activation energy (in kJ mol⁻¹) of the reaction?

The correct answer is D, 230.

GATE 2026 official key: (D). In the strong pore-diffusion regime, E_observed = (E_true + E_diffusion)/2, so E_true = 2(120) − 10 = 230 kJ/mol.

GATE 2026, Q19

For an irreversible reaction containing inerts in the feed, single-pass conversion in a reactor is 70%. Which one of the following statements is CORRECT?

The correct answer is C, Recycle increases the overall conversion..

GATE 2026 official key: (C). Recycling unreacted feed lets it react further on later passes, raising overall conversion above the single-pass value (a purge is still needed to bleed off inerts).

GATE 2026, Q31

Consider a homogeneous gas phase reaction, A + 2B → 2C + 3D, occurring at constant temperature and pressure in a varying volume batch reactor. The vessel is initially charged with 50 moles of A and 150 moles of B. The gases behave ideally. For complete conversion of A, the ratio of the final volume to the initial volume is ______ (rounded off to one decimal place).

The correct answer is 1.4 to 1.6.

GATE 2026 official key: 1.4 to 1.6. Initial total = 200 mol. Complete A conversion consumes 100 mol B (50 mol B left), forms 100 mol C and 150 mol D. Final total = 50+100+150 = 300 mol. At constant T,P, V_f/V_i = n_f/n_i = 300/200 = 1.5.

GATE 2026, Q42

Consider the following homogeneous isothermal liquid-phase parallel reactions carried out in three reactor configurations (having identical volumes and same operating temperatures), as shown in the figure. A + B → D Rate of formation of D: 𝑟𝐷 = 𝑘1𝐶𝐴𝐶𝐵 A + B → U Rate of formation of U: 𝑟𝑈 = 𝑘2𝐶𝐴^2𝐶𝐵 where D is the desired product and U is the undesired product. The inlet concentrations of A and B are the same in all three configurations (𝐶𝐴0 = 𝐶𝐵0 = 1 mol L −1 ). The total molar feed flow rate of A (𝐹𝐴0) and that of B (𝐹𝐵0) are the same in all three configurations (𝐹𝐴0 = 𝐹𝐵0 = 10 mol min−1 ). In configuration I, 𝐹𝐴0 is equally distributed among all the inlets. Similarly, in configuration III, 𝐹𝐵0 is equally distributed among all the inlets. Assuming plug flow behavior, at steady state, which one of the following statements is CORRECT?

The correct answer is B, Configuration I gives the highest selectivity of the desired product..

GATE 2026 official key: (B). Since rU = k2CA²CB grows faster with CA than rD = k1CACB, keeping CA low favors D. Configuration I distributes A across multiple inlets, keeping CA low throughout, giving the highest selectivity to D.

GATE 2026, Q43

The reaction rate constants of two reactions follow Arrhenius' law. The activation energies of Reaction 1 and Reaction 2 are E1 and E2, respectively and E1 < E2. Assuming same value for the frequency factor for both the reactions, which one of the following statements is CORRECT?

The correct answer is D, Reaction 2 is more temperature sensitive than Reaction 1 at all temperatures..

GATE 2026 official key: (D). d(ln k)/dT = Ea/(RT²), so the larger activation energy (E2 > E1) makes Reaction 2's rate constant more sensitive to temperature at every T.

GATE 2026, Q55

A first-order homogeneous liquid-phase reaction (A→B) occurs in an adiabatic, ideal mixed flow reactor at steady state. Feed flow rate is 4 L min⁻¹, reactor volume 20 L. At the reactor temperature of 500 K, k = 1 min⁻¹, and heat of reaction is −20 kcal mol⁻¹. The feed and reaction-mixture heat capacity is 0.3 kcal mol⁻¹ K⁻¹. The inlet feed temperature (in K) is _________ (rounded off to one decimal place).

The correct answer is 443 to 446.

GATE 2026 official key: 443.0 to 446.0. τ = 20/4 = 5 min; X = kτ/(1+kτ) = 5/6 = 0.833. Adiabatic balance: T − T0 = X(−ΔHrxn)/Cp = 0.833×20/0.3 ≈ 55.6 K, so T0 = 500 − 55.6 ≈ 444.4 K.

GATE 2026, Q56

A first-order homogeneous liquid-phase reaction (A→B) occurs in a non-ideal isothermal reactor at steady state. The RTD variance from a pulse tracer experiment is 4 min². Feed flow rate is 5 L min⁻¹, reactor volume 25 L, and k = 0.4 min⁻¹. Based on the tanks-in-series model, the conversion (in %) is _______ (rounded off to one decimal place).

The correct answer is 82 to 82.6.

GATE 2026 official key: 82.0 to 82.6. τ = 25/5 = 5 min; N = τ²/σ² = 25/4 = 6.25. X = 1 − 1/(1+kτ/N)^N = 1 − 1/(1.32)^6.25 ≈ 82.4%.

GATE 2026, Q57

A feed containing 10 mol% propylene, 15 mol% ammonia, and rest air (80 mol% N2, 20 mol% O2) is charged into a reactor to produce acrylonitrile: 2 C3H6 + 2 NH3 + 3 O2 → 2 C3H3N + 6 H2O. If the conversion of the limiting reactant is 30%, the composition of C3H3N (in mol%) in the product stream is ___________ (rounded off to two decimal places).

The correct answer is 2.9 to 3.

GATE 2026 official key: 2.90 to 3.00. Basis 100 mol feed: C3H6=10 (limiting, tied with O2). Reacted: C3H6=3, NH3=3, O2=4.5; formed: C3H3N=3, H2O=9. New total = 100−10.5+12 = 101.5 mol. Mol% C3H3N = 3/101.5 ≈ 2.96%.

GATE 2026, Q64

Cyclohexane (C6H12) is produced from benzene (C6H6) and hydrogen (H2): C6H6 + 3H2 → C6H12. Overall and single-pass conversions are 90% and 25%, respectively. The recycle stream contains 25 mol% C6H6 and 75 mol% H2. If the fresh feed contains 25% excess H2, at steady state, the ratio of the molar flow rate of recycle stream to that of the fresh feed is _________ (rounded off to one decimal place).

The correct answer is 2.1 to 2.3.

GATE 2026 official key: 2.1 to 2.3. Basis fresh feed=100 mol (21.05 C6H6, 78.95 H2, 25% excess H2). Reactor C6H6 reacted = 0.25×(21.05+0.25R) = 0.9×21.05 gives R ≈ 218.9, so R/F ≈ 2.19.

GATE 2025, Q20

Choose the CORRECT ordering of the diameter d of the different types of pores in a solid catalyst.

The correct answer is D, d(Micro-pore) < d(Meso-pore) < d(Macro-pore).

GATE 2025 official key: (D). By IUPAC convention, micropores (<2 nm) are smallest, followed by mesopores (2–50 nm), followed by macropores (>50 nm).

GATE 2025, Q23

Choose the CORRECT statement that describes the dependence of the variance (σ²_θ) of the residence time distribution (RTD) with respect to the number of tanks (N) in the Tanks-in-Series model of non-ideal reactors.

The correct answer is D, σ²_θ monotonically decreases with N.

GATE 2025 official key: (D). σ²_θ = 1/N for the Tanks-in-Series model, so variance decreases monotonically as N increases (approaching plug flow as N→∞).

GATE 2025, Q29

Choose the option that correctly matches the items in Group 1 with those in Group 2. Group 1: (P) Coking, (Q) Poisoning, (R) Sintering. Group 2: (I) Prolonged exposure of catalyst to high temperature, (II) Deposition of carbonaceous material on catalyst surface, (III) Irreversible chemisorption of molecules on active sites of catalyst.

The correct answer is B, (P)→(II), (Q)→(III), (R)→(I).

GATE 2025 official key: (B). Coking = carbon deposition (II); Poisoning = irreversible chemisorption on active sites (III); Sintering = prolonged high-temperature exposure causing loss of active surface area (I).

GATE 2025, Q31

Consider an enzymatic reaction that follows Michaelis-Menten kinetics. Let K_m, S, and V_max denote the Michaelis constant, substrate concentration, and maximum reaction rate, respectively. Which of the following statements is/are TRUE?

The correct answers are A. For S ≪ K_m, the reaction is apparent first-order in S.; B. For S ≫ K_m, the reaction rate is nearly independent of S.; D. K_m is independent of the total enzyme concentration..

GATE 2025 official key: (A, B, D). v = V_max·S/(K_m+S): for S≪K_m, v≈(V_max/K_m)S (first order); for S≫K_m, v≈V_max (zero order, independent of S); at S=K_m, v=V_max/2 (not V_max, making C false); K_m is an intrinsic kinetic constant independent of enzyme loading.

GATE 2025, Q35

The residence-time distribution (RTD) function of a reactor (in min⁻¹) is E(t) = 1 − 2t for t ≤ 0.5 min, and E(t) = 0 for t > 0.5 min. The mean residence time of the reactor is ____ min (rounded off to 2 decimal places).

The correct answer is 0.04 to 0.18.

GATE 2025 official key: 0.04 to 0.05 OR 0.16 to 0.18 min (dual acceptable range due to the form of E(t) admitting two consistent readings of the mean, t̄ = ∫t·E(t)dt).

GATE 2025, Q42

A zero-order gas phase reaction A → B with rate (−r_A) = k = 100 mol/(L·min) is carried out in a mixed flow reactor of volume 1 L. Pure A is fed to the reactor at a rate of 1 mol/min. At time t=0, the outlet flow is stopped while the inlet flow rate and reactor temperature remain unchanged. Assume that the reactor was operating under steady state before the flow was stopped (t<0). The rate of consumption of A, −dC_A/dt, in mol/(L·min), at t=1 min is

The correct answer is D, 99.0.

GATE 2025 official key: (D). With the outlet closed, the reactor concentration decays exponentially toward the sustainable zero-order regime; evaluating the resulting consumption rate at t=1 min gives ≈99.0 mol/(L·min), per the official solution.

GATE 2025, Q58

The reaction A → products, with reaction rate (−r_A) = k(C_A)³, occurs in an isothermal PFR operating at steady state. As shown in the figure, the conversion reaches X₁ = 0.3 at axial position 1 (length l₁ from the inlet) and X₂ = 0.6 at axial position 2 (a further length l₂ downstream). The value of l₁/l₂ is ____ (rounded off to 2 decimal places).

The correct answer is 0.22 to 0.27.

GATE 2025 official key: 0.22 to 0.27. For third-order kinetics, l ∝ ∫dX/(1−X)³ = ½[1/(1−X)² − 1]. l₁ (0→0.3) ∝ ½[1/0.7²−1] = 0.520; l₂ (0.3→0.6) ∝ ½[1/0.4²−1/0.7²] = 2.105. l₁/l₂ ≈ 0.520/2.105 ≈ 0.25.

GATE 2025, Q59

The catalytic gas phase reaction A → products is carried out in an isothermal batch reactor of 10 L volume using 0.1 kg of a solid catalyst. The reaction is first-order with (−r_A) = k′·a(t)·C_A, where k′ = 1 L/(kg catalyst·h) and C_A is the concentration of A in mol/L. The catalyst activity a(t) undergoes first-order decay with rate constant k_d = 0.01 per hour and a(0) = 1. The reactant conversion after 1 day of operation is ____ (rounded off to 2 decimal places).

The correct answer is 0.17 to 0.21.

GATE 2025 official key: 0.17 to 0.21. ln(C_A/C_A0) = −(k′w/V)∫₀²⁴e^(−k_d t)dt = −0.01×100×(1−e^(−0.24)) ≈ −0.213, giving X = 1−e^(−0.213) ≈ 0.19.

GATE 2025, Q64

Consider the flowsheet shown in the figure for manufacturing C via the reaction A + B → C in an isothermal CSTR. Pure A and pure B are fed, along with a recycle stream of R kmol/h. The split in the separator is perfect so that the recycle stream contains only A and B (no C) and the product stream is pure C. Let x_i denote the mole fraction of species i (i = A, B, C) in the CSTR, which is operated in excess B with x_B/x_A = 4. The reaction is first-order in A with the reaction rate (−r_A) = k_x·x_A, where k_x = 5.0 kmol/(m³·h). The reactor volume V in m³ is to be optimized to minimize the cost objective J = V + 0.25R, where R is the recycle rate in kmol/h. For a product rate P = 100 kmol/h, the optimum value of V is ____ m³ (rounded off to the nearest integer). Given: d/dz[z/(1−z)] = 1/(1−z)².

The correct answer is 150.

GATE 2025 official key: 150. Minimizing J = V + 0.25R with the mole-balance constraint linking V, R and the fixed product rate P via the given derivative identity yields an optimum reactor volume of 150 m³.

GATE 2024, Q20

The rate of a reaction A → B is 0.2 mol/(m³·s) at a particular concentration C_A1. The rate constant of the reaction at a given temperature is 0.1 m³/(mol·s). If the reactant concentration is increased to 10·C_A1 at the same temperature, the reaction rate, in mol/(m³·s), is

The correct answer is A, 20.

GATE 2024 official key: (A). Rate = k·C_A² (second order). From initial: 0.2 = 0.1·C_A1² ⇒ C_A1 = √2. New rate = 0.1·(10√2)² = 0.1·200 = 20 mol/(m³·s).

GATE 2024, Q21

Two parallel first-order liquid phase reactions A →(k₁) B and A →(k₂) C are carried out in a well-mixed isothermal batch reactor. The initial concentration of A in the reactor is 1 kmol/m³, while that of B and C is zero. After 2 hours, the concentration of A reduces to half its initial value, and the concentration of B is twice that of C. The rate constants k₁ and k₂, in h⁻¹, are, respectively

The correct answer is B, 0.23, 0.12.

GATE 2024 official key: (B). C_A/C_A0 = e^(−(k1+k2)t): 0.5 = e^(−2(k1+k2)) ⇒ k1+k2 = ln2/2 ≈ 0.3466/h. Since C_B/C_C = k1/k2 = 2, k1 = 2k2 ⇒ 3k2 = 0.3466 ⇒ k2 ≈ 0.116, k1 ≈ 0.231, matching (0.23, 0.12).

GATE 2024, Q31

Consider the reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g) in a continuous flow reactor under steady-state conditions. The component flow rates at the reactor inlet are F°_N2 = 100 mol/s, F°_H2 = 300 mol/s, F°_inert = 1 mol/s. If the fractional conversion of H₂ is 0.60, the outlet flow rate of N₂, in mol/s, rounded off to the nearest integer, is _________

The correct answer is 40.

GATE 2024 official key: 40. H₂ reacted = 0.60×300 = 180 mol/s; by stoichiometry (1 N₂ : 3 H₂), N₂ reacted = 180/3 = 60 mol/s; N₂ outlet = 100 − 60 = 40 mol/s.

GATE 2024, Q44

A first-order heterogeneous reaction A → B is carried out using a porous spherical catalyst. Assume isothermal conditions, and that intraphase diffusion controls the reaction rate. At a bulk A concentration of 0.3 mol/L, the observed reaction rate in a 3 mm diameter catalyst particle is 0.2 mol/(s·L catalyst volume). At a bulk A concentration of 0.1 mol/L, the observed reaction rate, in mol/(s·L catalyst volume), in a 6 mm diameter catalyst particle, is

The correct answer is B, 0.033.

GATE 2024 official key: (B). For strong intraparticle diffusion limitation, the effectiveness factor η ∝ 1/d_p, so the observed rate ∝ C_Ab/d_p. Rate₂ = Rate₁×(C_Ab2/C_Ab1)×(d_p1/d_p2) = 0.2×(0.1/0.3)×(3/6) ≈ 0.033 mol/(s·L).

GATE 2024, Q45

A first-order liquid phase reaction A → B is carried out in two isothermal plug flow reactors (PFRs) of volume 1 m³ each, connected in series. The feed flow rate and concentration of A to the first reactor are 10 m³/h and 1 kmol/m³, respectively. At steady-state, the concentration of A at the exit of the second reactor is 0.2 kmol/m³. If the two PFRs are replaced by two equal-volume continuously stirred tank reactors (CSTRs) to achieve the same overall steady-state conversion, the volume of each CSTR, in m³, is

The correct answer is A, 1.54.

GATE 2024 official key: (A). PFR: 0.2 = exp(−k×0.2) ⇒ k ≈ 8.047/h. For 2 equal CSTRs: 1/0.2 = (1+kτ)² ⇒ 1+kτ = √5 ⇒ τ ≈ 0.1536 h ⇒ V = τ×F = 0.1536×10 ≈ 1.54 m³.

GATE 2024, Q46

The residence time distribution, E, for a non-ideal flow reactor is given in the figure. A first-order liquid phase reaction with a rate constant 0.2 min⁻¹ is carried out in the reactor. For an inlet reactant concentration of 2 mol/L, the reactant concentration (in mol/L) in the exit stream is

The correct answer is A, 0.905.

GATE 2024 official key: (A). Using the segregation model, C_exit = C₀∫E(t)e^(−kt)dt = 2×0.5×∫₃⁵e^(−0.2t)dt = 1×5×(e^(−0.6)−e^(−1.0)) ≈ 0.905 mol/L.

GATE 2024, Q54

Consider the process shown in the figure for manufacturing B via the reaction 2A → B. The feed to the process is 90 mol% A and a close-boiling inert component I, mixed with a recycle stream of unreacted A and I from the separator overhead (recycle-to-purge ratio 10), which is also split off as a purge stream (x_B=0 in both). At a particular steady-state: B product rate is 100 kmol/h (pure B), single-pass conversion of A in the reactor is 50%, and the recycle-to-purge stream flow ratio is 10. The flow rate of A in the purge stream, in kmol/h, rounded off to 1 decimal place, is _____

The correct answer is 18.1 to 18.3.

GATE 2024 official key: 18.1 to 18.3. With B=100=0.25×A_reactor,in ⇒ A_reactor,in=400 kmol/h (from 2A→B, 50% single-pass conversion). Overall balances on A and inert (fresh feed F: x_A=0.9, x_I=0.1) combined with the recycle/purge split (ratio 10, i.e., 11×purge = total light stream leaving separator) give A in purge = (0.5×400)/11 ≈ 18.2 kmol/h.

GATE 2024, Q62

A chemostat with cell recycle is shown in the figure. The feed flow rate and culture volume are F = 75 L/h and V = 200 L, respectively. The glucose concentration in the feed C_S0 = 15 g/L. Assume Monod kinetics with specific cell growth rate μ_g = (1/C_C)·(dC_C/dt)=(μ_m·C_S)/(K_S+C_S), where μ_m = 0.25 h⁻¹ and K_S = 1 g/L. The recycle ratio is α = 0.5 and the cell concentration factor is β = 2.0. Assume maintenance and death rates to be zero, input feed to be sterile (C_C0=0), and steady-state operation. The glucose concentration in the recycle stream, C_S1, in g/L, rounded off to 1 decimal place, is _________

The correct answer is 2.9 to 3.1.

GATE 2024 official key: 2.9 to 3.1. Cell balance around the chemostat gives μ = F[(1+α)−αβ]/V = 75×0.5/200 = 0.1875 h⁻¹. Solving Monod: 0.1875 = 0.25·C_S1/(1+C_S1) ⇒ C_S1 = 3.0 g/L.

GATE 2026, Q21

A two-dimensional temperature profile is given as T = 2x² + 3xy + y². If î and ĵ are the unit vectors along x and y directions, respectively, which one of the following is the directional derivative of T at the location x = 2, y = 2?

The correct answer is B, 14î + 10ĵ.

GATE 2026 official key: (B). ∇T = (4x+3y)î + (3x+2y)ĵ; at (2,2) this is (8+6)î + (6+4)ĵ = 14î + 10ĵ.

GATE 2026, Q22

Which one of the following is the value of lim (x→0) (eˣ − x − 1) / (cos x − 1)?

The correct answer is A, −1.

GATE 2026 official key: (A). This is a 0/0 form, so expand via Taylor series near x=0: eˣ−x−1 ≈ x²/2 and cos x−1 ≈ −x²/2, so the limit is (x²/2)/(−x²/2) = −1 (equivalently, apply L'Hôpital's rule twice).

GATE 2026, Q23

Which one of the following is the pair of eigenvalues of the matrix [[−3, 4], [4, 3]]?

The correct answer is B, −5, 5.

GATE 2026 official key: (B). The matrix is symmetric, so eigenvalues are real: det([[−3−λ,4],[4,3−λ]]) = λ² − 25 = 0 → λ = ±5 (check: trace = 0 = −5+5 ✓, det = −25 = −5×5 ✓).

GATE 2026, Q34

An experiment is performed by rolling an unbiased die once. Event A: the outcome is a prime number. Event B: the outcome is an odd number less than 4. The conditional probability of A given B, denoted by P(A|B), is ______ (rounded off to one decimal place).

The correct answer is 0.5.

GATE 2026 official key: 0.5. For equally likely outcomes, P(A|B) = |A∩B|/|B|. Here A={2,3,5} (primes) and B={1,3} (odd, <4), so A∩B={3}, giving P(A|B) = 1/2 = 0.5.

GATE 2026, Q40

Consider z1 = r1(cos θ1 + i sin θ1), z2 = r2(cos θ2 + i sin θ2), where r1, r2 are real numbers, 0 ≤ θ1 ≤ π/2, 0 ≤ θ2 ≤ π/2, and i = √−1. If |z1 + z2| = |z1| + |z2|, which one of the following conditions is necessarily CORRECT?

The correct answer is D, θ1 = θ2.

GATE 2026 official key: (D). Equality in |z1+z2| = |z1|+|z2| holds only when z1 and z2 point in the same direction, i.e. θ1 = θ2.

GATE 2026, Q41

Consider the following curve in polar coordinates: r = 2 − 2 sin θ. Which one of the following is the area enclosed by the curve for 0 ≤ θ ≤ 2π?

The correct answer is D, 6π.

GATE 2026 official key: (D). Area enclosed by a polar curve is A = ½∫₀^{2π} r² dθ. With r=2(1−sinθ), r²=4(1−2sinθ+sin²θ); since ∫sinθdθ=0 and ∫sin²θdθ=π over a full period, A = 2(2π−0+π) = 6π.

GATE 2026, Q62

Consider the differential equation x²(d²y/dx²) + 3x(dy/dx) − 3y = 0, with y = 3 and dy/dx = −5 at x = 1. The value of y at x = 2 is ______ (rounded off to two decimal places).

The correct answer is 2.24 to 2.26.

GATE 2026 official key: 2.24 to 2.26. Trial y=x^m gives m²+2m−3=0, so m=1,−3: y=C1x+C2x⁻³. Using the initial conditions, C1=1, C2=2, so y(2) = 2 + 2/8 = 2.25.

GATE 2026, Q63

The data (x,y) = (1,2), (2,6), (3,7), (4,10) are fitted to y = mx using the method of least squares. The value of m is ______ (rounded off to one decimal place).

The correct answer is 2.49 to 2.51.

GATE 2026 official key: 2.49 to 2.51. Fitting y=mx through the origin by least squares minimizes Σ(y−mx)², giving m = Σxy/Σx² = (2+12+21+40)/(1+4+9+16) = 75/30 = 2.5.

GATE 2025, Q3

The sum of the following infinite series is: 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + ⋯

The correct answer is C, e − 1.

GATE 2025 official key: (C). Since e = 1 + 1/1! + 1/2! + 1/3! + ⋯, the given series (which omits the leading 1) sums to e − 1.

GATE 2025, Q12

Consider a Cartesian coordinate system defined over a 3-dimensional vector space with orthogonal unit basis vectors î, ĵ and k̂. Let vector u = √2 î + (1/√2) ĵ + k̂, and vector v = (1/√2) î + √2 ĵ − k̂. The inner product of these vectors (u·v) is:

The correct answer is B, 1.

GATE 2025 official key: (B). The dot product is the sum of componentwise products: u·v = (√2)(1/√2) + (1/√2)(√2) + (1)(−1) = 1 + 1 − 1 = 1.

GATE 2025, Q13

Consider two complex numbers z₁ = 1 − i and z₂ = i. The argument of z₁z₂ is

The correct answer is B, π/4.

GATE 2025 official key: (B). z₁z₂ = (1−i)(i) = i − i² = i + 1 = 1 + i, whose argument is arctan(1/1) = π/4.

GATE 2025, Q14

A box contains 3 identical green balls and 7 identical blue balls. Two balls are randomly drawn without replacement from the box. The probability of drawing 1 green and 1 blue ball is

The correct answer is D, (³C₁ × ⁷C₁) / ¹⁰C₂.

GATE 2025 official key: (D). Order doesn't matter, so use combinations: favorable ways = ³C₁ (1 of 3 green) × ⁷C₁ (1 of 7 blue), over ¹⁰C₂ total ways to pick any 2 of 10 balls. P = (3×7)/45 = 21/45 = 7/15.

GATE 2025, Q36

Consider a Cartesian coordinate system with orthogonal unit basis vectors î, ĵ defined over a domain: x, y ∈ [0,1]. Choose the condition for which the divergence of the vector field u = ax î − by ĵ is zero.

The correct answer is A, a − b = 0.

GATE 2025 official key: (A). ∇·u = ∂(ax)/∂x + ∂(−by)/∂y = a − b. This vanishes only when a = b, i.e., a − b = 0.

GATE 2025, Q37

A probability distribution function is given as f(x) = 1/a for x ∈ (0, a), and 0 otherwise, where a is a positive constant. For a function g(x) = x², the expectation of g(x) is

The correct answer is A, a²/3.

GATE 2025 official key: (A). For continuous X, E[g(X)] = ∫g(x)f(x)dx (law of the unconscious statistician). With f(x)=1/a on (0,a): E[X²] = ∫₀ᵃ x²·(1/a)dx = (1/a)(a³/3) = a²/3.

GATE 2025, Q44

Consider the differential equation dy/dx + y/x = 0. Choose the CORRECT option(s) for the solution y.

The correct answers are B. y = c/x; c is a constant; D. y = 0.

GATE 2025 official key: (B, D). Separating variables, dy/y = −dx/x ⇒ ln y = −ln x + const ⇒ y = c/x, which includes the trivial solution y = 0 as the c = 0 case.

GATE 2025, Q45

Consider the matrix A = [[2, 3], [1, 2]]. The eigenvalues of the matrix are 0.27 and ____ (rounded off to 2 decimal places).

The correct answer is 3.68 to 3.78.

GATE 2025 official key: 3.68 to 3.78. The trace equals the sum of eigenvalues: tr(A) = 2+2 = 4, so the second eigenvalue = 4 − 0.27 = 3.73.

GATE 2024, Q11

The first non-zero term in the Taylor series expansion of (1 − x) − e^(−x) about x = 0 is

The correct answer is D, −x²/2.

GATE 2024 official key: (D). (1−x) − e^(−x) = (1−x) − (1 − x + x²/2 − x³/6 + ⋯) = −x²/2 + x³/6 − ⋯, so the constant and linear terms cancel, leaving −x²/2 as the first non-zero term.

GATE 2024, Q12

Consider the normal probability distribution function f(x) = [4/√(2π)]·e^(−8(x+3)²). If μ and σ are the mean and standard deviation of f(x) respectively, then the ordered pair (μ, σ) is

The correct answer is B, (−3, 1/4).

GATE 2024 official key: (B). Matching f(x) to 1/(σ√(2π))·e^(−(x−μ)²/(2σ²)): 1/σ = 4 ⇒ σ = 1/4, and 1/(2σ²) = 8 is consistent with σ = 1/4; (x−μ)² = (x+3)² ⇒ μ = −3.

GATE 2024, Q13

If z₁ = −1 + i and z₂ = 2i, where i = √−1, then Arg(z₁ ÷ z₂) is

The correct answer is B, π/4.

GATE 2024 official key: (B). Dividing complex numbers subtracts arguments: Arg(z₁÷z₂) = Arg(z₁) − Arg(z₂). In polar form z₁=−1+i is √2∠135° and z₂=2i is 2∠90°, so Arg(z₁/z₂) = 135°−90° = 45° = π/4.

GATE 2024, Q26

Consider a linear homogeneous system of equations Ax = 0, where A is an n×n matrix, x is an n×1 vector and 0 is an n×1 null vector. Let r be the rank of A. For a non-trivial solution to exist, which of the following conditions is/are satisfied?

The correct answers are A. Determinant of A = 0; C. r < n.

GATE 2024 official key: (A, C). A non-trivial solution exists iff A is singular, i.e., det(A) = 0, which is equivalent to rank(A) < n.

GATE 2024, Q30

Consider a matrix A = [[−5, a], [−2, −2]], where a is a constant. If the eigenvalues of A are −1 and −6, then the value of a, rounded off to the nearest integer, is ____________

The correct answer is -2.

GATE 2024 official key: −2. det(A) = (−5)(−2) − a(−2) = 10 + 2a must equal the product of eigenvalues (−1)(−6) = 6, so 10 + 2a = 6 ⇒ a = −2.

GATE 2024, Q47

Let r and θ be the polar coordinates defined by x = r cos θ and y = r sin θ. The area of the cardioid r = a(1 − cos θ), 0 ≤ θ ≤ 2π, is

The correct answer is A, 3πa²/2.

GATE 2024 official key: (A). The area enclosed by the cardioid r=a(1−cosθ) is a standard result: Area = (1/2)∫₀^(2π) r² dθ = 3πa²/2.

GATE 2024, Q51

Consider the line integral ∫_C F(r)·dr, with F(r) = x î + y ĵ + z k̂, where î, ĵ and k̂ are unit vectors in the (x,y,z) Cartesian coordinate system. The path C is given by r(t) = cos(t) î + sin(t) ĵ + t k̂, where 0 ≤ t ≤ π. The value of the integral, rounded off to 2 decimal places, is _________

The correct answer is 4.91 to 4.95.

GATE 2024 official key: 4.91 to 4.95. F·dr = d[½(x²+y²+z²)], a conservative field, so the integral = ½[(x²+y²+z²)]₀^π = ½[(1+π²)−1] = π²/2 ≈ 4.93.

GATE 2024, Q52

Consider the ordinary differential equation x²(d²y/dx²) − x(dy/dx) − 3y = 0, with the boundary conditions y(x=1) = 2 and y(x=2) = 17/2. The solution y(x) at x = 3/2, rounded off to 2 decimal places, is ___________

The correct answer is 4 to 4.08.

GATE 2024 official key: 4.00 to 4.08. This Cauchy-Euler equation has solutions y=x^m with m²−2m−3=0 ⇒ m=3,−1, so y=C1x³+C2/x. BCs give C1=C2=1, so y(x)=x³+1/x. At x=1.5: y=3.375+0.667≈4.04.

GATE 2024, Q53

Consider the function f(x,y,z) = x⁴ + 2y³ + z². The directional derivative of the function at the point P(−1, 1, −1) along (î+ĵ), where î and ĵ are unit vectors in the x and y directions, respectively, rounded off to 2 decimal places, is _______

The correct answer is 1.39 to 1.43.

GATE 2024 official key: 1.39 to 1.43. ∇f=(4x³,6y²,2z); at (−1,1,−1): (−4,6,−2). Normalizing (î+ĵ) to (1,1,0)/√2, directional derivative = (−4+6+0)/√2 = 2/√2 = √2 ≈ 1.41.

GATE 2026, Q15

Consider a closed system of one mole of an ideal gas undergoing a polytropic process. The process follows PVⁿ = constant, where P is the pressure, V is the volume and n is a constant. If the process is isobaric, which one of the following is the value of n?

The correct answer is A, 0.

GATE 2026 official key: (A). For PVⁿ = constant, an isobaric (constant-P) process requires n = 0, since P·V⁰ = P = constant.

GATE 2026, Q16

According to the phase rule, which one of the following is the number of degrees of freedom for pure water at its triple point?

The correct answer is B, 0.

GATE 2026 official key: (B). F = C − P + 2 = 1 − 3 + 2 = 0 at the triple point (solid + liquid + vapor of one component).

GATE 2026, Q27

Which of the following statements regarding the heat of reaction is/are CORRECT?

The correct answers are A. For endothermic reaction, it is positive.; B. For exothermic reaction, it is negative.; D. It is the enthalpy change for a process in which stoichiometric quantities of reactants, at a temperature and pressure, react completely in a single reaction to form products at the same temperature and pressure..

GATE 2026 official key: (A, B, D). By convention ΔH_rxn > 0 for endothermic (A) and < 0 for exothermic (B, making C false); (D) is the standard definition of heat of reaction.

GATE 2026, Q36

K value is defined as the ratio of mole fraction of a component in the vapor phase to that in the liquid phase. K values at 293 K: at 1100 kPa propane=1.8, iso-butane=0.85; at 1200 kPa propane=1.6, iso-butane=0.75; at 1300 kPa propane=1.4, iso-butane=0.65; at 1400 kPa propane=1.25, iso-butane=0.5; at 1500 kPa propane=1.1, iso-butane=0.45. Which one of the following is closest to the bubble point pressure (in kPa) of an equimolar mixture of propane and iso-butane at 293 K?

The correct answer is C, 1310.

GATE 2026 official key: (C). At the bubble point, Σ(zᵢKᵢ) = 1 for the equimolar mixture; interpolating the K-value table, this is satisfied closest to 1310 kPa.

GATE 2026, Q54

Methanol is formed by the gas phase reaction CO (g) + 2H2 (g) ⇌ CH3OH (g). The standard Gibbs free energies of formation at 298 K for CO and CH3OH are −137 kJ mol⁻¹ and −162 kJ mol⁻¹, respectively (R = 8.314 J mol⁻¹ K⁻¹). The equilibrium constant for the reaction at 298 K is _____ × 10⁴ (rounded off to one decimal place).

The correct answer is 2.3 to 2.5.

GATE 2026 official key: 2.3 to 2.5. ΔG°rxn = −162 − (−137) − 0 = −25 kJ/mol (H2 is an element). K = exp(25000/(8.314×298)) ≈ 2.4×10⁴.

GATE 2026, Q58

A gas mixture of 50 wt% argon and 50 wt% helium flows through a horizontal tube at 1 kg s⁻¹ and is heated from 300 K to 400 K at 1 bar (ideal gas, negligible KE/PE changes). Specific enthalpies (kJ kg⁻¹): Argon 348→400, Helium 1574→2092. At steady state, the heat input required (in kW) is ___________ (rounded off to the nearest integer).

The correct answer is 285.

GATE 2026 official key: 285. Steady-flow energy balance (negligible KE/PE): Q = Σ ṁᵢΔhᵢ. With 0.5 kg/s each of argon and helium: Q = 0.5×(400−348) + 0.5×(2092−1574) = 26 + 259 = 285 kW.

GATE 2025, Q15

The number of independent intensive variables that need to be specified to determine the thermodynamic state of a ternary mixture at vapor-liquid-liquid equilibrium is

The correct answer is C, 2.

GATE 2025 official key: (C). Gibbs phase rule: F = C − P + 2 = 3 − 3 + 2 = 2 (ternary mixture, C=3; three coexisting phases, P=3).

GATE 2025, Q16

The boundary of a system does not allow exchange of either mass or energy (in the form of heat and/or work) with the surroundings. The system is termed

The correct answer is A, Isolated.

GATE 2025 official key: (A). An isolated system exchanges neither mass nor energy with its surroundings, closed systems allow energy exchange, adiabatic systems allow work/mass but not heat, and open systems allow both.

GATE 2025, Q32

The following data is given for a ternary ABC gas mixture at 12 MPa and 308 K: mole fractions y_A=0.55, y_B=0.20, y_C=0.25; fugacity coefficients φ_A=0.75, φ_B=0.80, φ_C=0.95. The fugacity of the gas mixture is _____ MPa (rounded off to 3 decimal places).

The correct answer is 9.651 to 9.692.

GATE 2025 official key: 9.651 to 9.692. Mixture fugacity ≈ P·Σ(yᵢφᵢ) = 12×(0.55×0.75 + 0.20×0.80 + 0.25×0.95) ≈ 12×0.81 ≈ 9.7 MPa, within the official range.

GATE 2025, Q33

Ideal nonreacting gases A and B are contained inside a perfectly insulated chamber, separated by a thin partition, as shown in the figure. T_A = T_B = 273 K, P_A = P_B = 1 atm, V_B = 22.4 L, and V_A = 3V_B. The partition is removed, and the two gases mix until final equilibrium is reached. The change in total entropy for the process is ____ J/K (rounded off to 1 decimal place). Given: universal gas constant R = 8.314 J/(mol·K).

The correct answer is 18.5 to 18.9.

GATE 2025 official key: 18.5 to 18.9 J/K. V_B = 22.4 L at 273 K, 1 atm ⇒ n_B = 1 mol; V_A = 3V_B ⇒ n_A = 3 mol. Total n = 4 mol, y_A = 0.75, y_B = 0.25. ΔS_mix = −R(n_Aln y_A + n_Bln y_B) = −8.314×(3ln0.75 + 1×ln0.25) ≈ 18.7 J/K.

GATE 2025, Q48

An ideal monoatomic gas is contained inside a cylinder-piston assembly connected to a Hookean spring, as shown in the figure. The piston is frictionless and massless, with cross-sectional area 100 cm² and a stopper 5 cm away. Ambient pressure is 1 bar. Initial gas conditions: V_initial = 2 L, T_initial = 300 K. The spring constant is 10 kN/m and is initially unstretched. The gas is expanded reversibly by adding 362.5 J of heat, until the piston presses against the stoppers at the final equilibrium state. Neglecting heat loss to the surroundings, the final equilibrium temperature of the gas is ____ K (rounded off to the nearest integer). Given: for a monoatomic ideal gas, C_v = (3/2)R, where R = 8.314 J/(mol·K).

The correct answer is 595 to 605.

GATE 2025 official key: 595 to 605 K. ΔV = Area×stroke = 0.01 m²×0.05 m = 0.0005 m³. Force balance gives P(x) = P_amb + kx/A, so work done by gas W = P_amb·ΔV + ½k·x² = 100000×0.0005 + 0.5×10000×0.05² = 50 + 12.5 = 62.5 J. Energy balance: ΔU = Q − W = 362.5 − 62.5 = 300 J. Since n = P₁V₁/(RT₁) and nR = P₁V₁/T₁ = 100000×0.002/300 = 0.667 J/K, ΔU = n·(3/2)R·ΔT = (3/2)×0.667×ΔT = 300 ⇒ ΔT = 300 K, so T_final = 300+300 = 600 K.

GATE 2025, Q61

Methanol is produced by the reversible, gas-phase hydrogenation of carbon monoxide as CO + 2H₂ ⇌ CH₃OH. CO and H₂ are charged to a reactor and the reaction proceeds to equilibrium at 453 K and 2 atm. The reaction equilibrium constant, which depends only on the temperature, is 1.68 at the reaction conditions. The mole fraction of H₂ in the product is 0.4. Assuming ideal gas behaviour, the mole fraction of methanol in the product is ____ (rounded off to 2 decimal places).

The correct answer is 0.28 to 0.34.

GATE 2025 official key: 0.28 to 0.34. K_p = y_MeOH/(y_CO·y_H2²·P²) ⇒ 1.68 = y_MeOH/(y_CO×0.16×4), so y_MeOH ≈ 1.075·y_CO. With y_CO+0.4+y_MeOH=1, solving gives y_CO≈0.289 and y_MeOH≈0.311.

GATE 2024, Q18

Consider a vapour-liquid mixture of components A and B that obeys Raoult's law. The vapour pressure of A is half that of B. The vapour phase concentrations of A and B are 3 mol/m³ and 6 mol/m³, respectively. At equilibrium, the ratio of the liquid phase concentration of A to that of B is

The correct answer is A, 1.0.

GATE 2024 official key: (A). y_A=1/3, y_B=2/3. Raoult's law: x_A/x_B = (y_A/y_B)×(P_B*/P_A*) = (1/2)×2 = 1.0.

GATE 2024, Q32

Consider a binary mixture of components A and B at temperature T and pressure P. Let V̄_A and V̄_B be the partial molar volumes of A and B, respectively. At a certain mole fraction of A, x_A, (∂V̄_A/∂x_A)_{T,P} = 22 cm³/mol and (∂V̄_B/∂x_A)_{T,P} = −18 cm³/mol. The value of x_A, rounded off to 2 decimal places, is ________

The correct answer is 0.44 to 0.46.

GATE 2024 official key: 0.44 to 0.46. Gibbs-Duhem: x_A(∂V̄_A/∂x_A) + x_B(∂V̄_B/∂x_A) = 0 ⇒ 22x_A − 18(1−x_A) = 0 ⇒ 40x_A = 18 ⇒ x_A = 0.45.

GATE 2024, Q55

Methane combusts with air in a furnace as CH₄ + 2O₂ → CO₂ + 2H₂O. The heat of reaction ΔH_rxn = −880 kJ per mol CH₄ and is assumed constant. The furnace is well-insulated and no other side reactions occur. All components behave as ideal gases with a constant molar heat capacity of 44 J/(mol·°C). Air is 20 mol% O₂ and 80 mol% N₂. The air-fuel mixture enters the furnace at 50°C. The methane conversion X varies with the air-to-methane mole ratio, r, as X = 1 − 0.1e^(−2(r−rs)) with 0.9rs ≤ r ≤ 1.1rs, where rs is the stoichiometric air-to-methane mole ratio. For r = 1.05rs, the exit flue gas temperature in °C, rounded off to 1 decimal place, is ______

The correct answer is 1719 to 1730.

GATE 2024 official key: 1719.0 to 1730.0. rs = 2/0.2 = 10 (mol air/mol CH4). At r=10.5: X = 1−0.1e⁻¹ ≈ 0.9632. Basis 1 mol CH4: total moles = 1+10.5=11.5, unchanged by reaction (3→3 mol). Heat released = 0.9632×880,000 ≈ 847,600 J. Energy balance: 11.5×44×(Tf−323) = 847600 ⇒ Tf ≈ 1998.3 K ≈ 1725.3°C.

GATE 2024, Q56

An isolated system consists of two perfectly sealed cuboidal compartments A and B separated by a movable rigid wall of cross-sectional area 0.1 m², as shown in the figure. Initially, the movable wall is held in place by latches L1 and L2 such that the volume of compartment A is 0.1 m³. Compartment A contains a monoatomic ideal gas at 5 bar and 400 K. Compartment B is perfectly evacuated and contains a massless Hookean spring of force constant 0.3 N/m at its equilibrium length (stored elastic energy is zero). The latches L1 and L2 are released, the wall moves to the right by 0.2 m, where it is held at the new position by latches L3 and L4. Assume all walls and latches are massless. The final equilibrium temperature, in K, of the gas in compartment A, rounded off to 1 decimal place, is _________

The correct answer is 396.6 to 397.

GATE 2024 official key: 396.6 to 397.0 K. Applying an energy balance to the isolated system (accounting for the free/irreversible nature of the expansion against the near-negligible spring resistance and the vacuum in compartment B) gives a final gas temperature of ≈396.8 K, per the official solution.

GATE 2024, Q57

Ethylene obeys the truncated virial equation-of-state PV/RT = 1 + BP/RT, where P is the pressure, V is the molar volume, T is the absolute temperature and B is the second virial coefficient. The universal gas constant R = 83.14 bar·cm³/(mol·K). At 340 K, the slope of the compressibility factor vs. pressure curve is −3.538×10⁻³ bar⁻¹. Let G^R denote the molar residual Gibbs free energy. At these conditions, the value of dG^R/dP at constant temperature, in cm³/mol, rounded off to 1 decimal place, is ___________

The correct answer is -101 to -99.

GATE 2024 official key: −101.0 to −99.0. Since Z=1+(B/RT)P, dZ/dP=B/RT=−3.538×10⁻³ ⇒ B=−3.538×10⁻³×83.14×340≈−100.0 cm³/mol. For this EOS, G^R=BP (constant B), so dG^R/dP=B≈−100.0 cm³/mol.

GATE 2024, Q61

Heat is available at a rate of 2 kW from a thermal reservoir at 400 K. A two-stage process harnesses this heat to produce power. Stages 1 and 2 reject heat at 360 K and 300 K, respectively. Stage 2 is driven by the heat rejected by Stage 1. If the overall process efficiency is 50% of the corresponding Carnot efficiency, the power delivered by the process, in kW, rounded off to 2 decimal places, is ______

The correct answer is 0.24 to 0.26.

GATE 2024 official key: 0.24 to 0.26. Overall Carnot efficiency (400 K to 300 K) = 1−300/400 = 0.25. Actual efficiency = 0.5×0.25 = 0.125. Power = 0.125×2 = 0.25 kW.

GATE 2026, Q20

A binary mixture of butane and butadiene is to be separated in an extractive distillation using furfural. Furfural lowers the activity of butadiene more than it does for butane. Match the component labels (X, Y, Z) in the distillation sequence shown with the chemical species (Butane, Butadiene, Furfural).

The correct answer is A, P-1, Q-2, R-3.

GATE 2026 official key: (A). Furfural (Z) suppresses butadiene's volatility more than butane's, so butane leaves overhead as X and butadiene as Y: P-1, Q-2, R-3.

GATE 2026, Q33

Consider a non-reactive binary mixture of two ideal gases A and B in an isothermal horizontal closed tube. Due to the concentration difference at the two ends of the tube, equimolal counterdiffusion occurs along the axial direction. No concentration gradients exist in the radial direction. The profile for partial pressure of component A (pA) as a function of axial distance z is shown in the figure. The partial pressure of component B (pB) approaches zero at z = 0.8 m. At a location z = z1 the partial pressures of the components A and B are equal. The value of z1 (in m) is _____ (rounded off to two decimal places).

The correct answer is 0.27 to 0.29.

GATE 2026 official key: 0.27 to 0.29. pA rises linearly from ≈0.65 bar at z=0 to ≈2.6 bar at z=0.8 m (total pressure). Setting pA(z1) = P_total/2 = 1.3 bar and solving along the line gives z1 ≈ 0.28 m.

GATE 2026, Q38

Vapor pressure of water: 284 K → 1.28 kPa, 289 K → 1.80 kPa, 294 K → 2.50 kPa, 299 K → 3.40 kPa, 310 K → 6.40 kPa. An air and water vapor mixture at 100 kPa with a relative humidity of 20% has a dry-bulb temperature of 310 K. Assume latent heat of vaporization for water is 44 kJ mol⁻¹ and specific heat capacity of the air and water vapor mixture is 0.035 kJ mol⁻¹ K⁻¹. Which one of the following is closest to its wet-bulb temperature (in K)?

The correct answer is B, 294.

GATE 2026 official key: (B). Balancing the latent-heat driving force against the sensible-heat cooling with the given vapor-pressure data gives a wet-bulb temperature of about 294 K.

GATE 2026, Q39

A volatile organic compound (VOC) is to be adsorbed from air onto a bed of activated carbon. The equilibrium capacity of activated carbon at the feed conditions is 0.4 grams VOC per gram of activated carbon. The column contains 4 grams of activated carbon per cm² of cross-section. The feed rate into the adsorber column is 0.2 g VOC cm⁻² h⁻¹. Breakthrough time is defined as the time at which the exit concentration (c) reaches 0.05 c₀, where c₀ is the feed concentration. The breakthrough time is 2.1 h. The area under the c/c₀ curve between the initial and breakthrough times is 0.1 h. Which one of the following is the fraction of unused bed at breakthrough?

The correct answer is D, 0.75.

GATE 2026 official key: (D). Using the breakthrough-curve method with the given area (0.1 h) and breakthrough time (2.1 h), the fraction of unused bed works out to about 0.75.

GATE 2026, Q48

A gas stream with 2.01 mol % ammonia is to be scrubbed in a counter-current isothermal packed bed absorber using pure water to reduce its concentration to 0.01 mol %. Assume that dilute conditions apply, operating line is linear and the mass transfer coefficients are constant throughout the column. The liquid and the gas flows inside the absorber (in kmol m⁻² h⁻¹) are 1000 and 200, respectively. The equilibrium relationship is y = 0.9 x, where, y is the mole-fraction of ammonia in the gas phase and x is that in the liquid. Under these conditions, the height of overall gas transfer unit (HtOG) is 0.8 m and the number of overall gas transfer units (NtOG) is given by the following integral. N_tOG = ∫ [from y1 to y2] dy / (y - y*) The integration is performed between the two ends of the column, and y* is the equilibrium mole fraction in the gas phase, corresponding to the composition of the liquid at corresponding location. Which one of the following is the minimum length of the packing (in m) necessary to achieve the desired scrubbing?

The correct answer is B, 5.0.

GATE 2026 official key: (B). Integrating the driving force yields NtOG ≈ 6.23; multiplying by HtOG (0.8 m) gives the packed height: 6.23 × 0.8 ≈ 4.98 m, which rounds to 5.0 m.

GATE 2026, Q61

The flooding velocity curves for two different structured packings (P and Q) are shown. The ratio of mass velocities of liquid (Gx) to gas (Gy) is 1.27; liquid density 1200 kg m⁻³, gas density 1.2 kg m⁻³. For both packings, the allowable superficial vapor velocity is 60% of flooding velocity. The ratio of allowable mass velocity of vapor in packing P to that in packing Q is _____________ (rounded off to one decimal place).

The correct answer is 1.4 to 1.6.

GATE 2026 official key: 1.4 to 1.6. Reading u0,F off each curve at the given abscissa and taking 60% of flooding velocity for both packings, the ratio of allowable Gy (since ρy is common to both) works out to about 1.5.

GATE 2025, Q21

Schmidt number is defined as

The correct answer is B, Momentum Diffusivity / Mass Diffusivity.

GATE 2025 official key: (B). Sc = ν/D_AB = momentum diffusivity / mass diffusivity. (Compare: Pr = ν/α is momentum/thermal, Le = α/D is thermal/mass.)

GATE 2025, Q22

If k is the mass transfer coefficient and D_v is the molecular diffusivity, which one of the following statements is NOT CORRECT with respect to mass transfer theories?

The correct answer is B, For Penetration theory, k ∝ D_v^(1/3).

GATE 2025 official key: (B). Higbie's penetration theory actually gives k ∝ D_v^(1/2), not D_v^(1/3), making this statement the incorrect one.

GATE 2025, Q40

500 mg of a dry adsorbent is added to a beaker containing 100 mL solution of concentration 100 mg phenol/(L solution). The adsorbent is separated out after 5 h of rigorous mixing. If the residual concentration in the solution after separating the adsorbent is 30 mg phenol/(L solution), the amount of phenol adsorbed (in mg per gram of dry adsorbent) is

The correct answer is B, 14.

GATE 2025 official key: (B). Phenol adsorbed = (100−30) mg/L × 0.1 L = 7 mg, over 0.5 g adsorbent = 7/0.5 = 14 mg/g.

GATE 2025, Q47

Consider moist air with absolute humidity of 0.02 (kg moisture)/(kg dry air) at 1 bar pressure. The vapour pressure of water is given by the equation ln(P_sat) = 12 − 4000/(T−40), where P_sat is in bar and T is in K. The molecular weight of water and dry air are 18 kg/kmol and 29 kg/kmol, respectively. The dew temperature of the moist air is _____ °C (rounded off to the nearest integer).

The correct answer is 23 to 27.

GATE 2025 official key: 23 to 27°C. From humidity, p_w = 0.02×29/(18+0.02×29) ≈ 0.0312 bar. Solving ln(0.0312) = 12 − 4000/(T−40) gives T ≈ 298.6 K ≈ 25.6°C, within range.

GATE 2025, Q55

Gas containing 0.8 mol% component A is to be scrubbed with pure water in a packed bed column to reduce the concentration of A to 0.1 mol% in the exit gas. The inlet gas and water flow rates are 0.1 kmol/s and 3.0 kmol/s, respectively. For the dilute system, both the operating and equilibrium curves are considered linear. If the slope of the equilibrium line is 24, the number of transfer units, based on the gas side, N_OG is ____ (rounded off to 1 decimal place).

The correct answer is 4.2 to 4.6.

GATE 2025 official key: 4.2 to 4.6. With mG/L = 24×0.1/3 = 0.8, the Colburn equation gives N_OG = [1/(1−0.8)]·ln[(1−0.8)(0.008/0.001)+0.8] = 5×ln(2.4) ≈ 4.38.

GATE 2025, Q56

Solute A is absorbed from a gas into water in a packed bed operating at steady state. The absorber operating pressure and temperature are 1 atm and 300 K, respectively. At the gas-liquid interface y_i = 1.5x_i, where y_i and x_i are the interfacial gas and liquid mole fractions of A, respectively. At a particular location in the absorber, the mole fractions of A in the bulk gas and in the bulk water are 0.02 and 0.002, respectively. If the ratio of the local individual mass transfer coefficients for the transport of A on the gas-side (k_y) to that on the water-side (k_x), k_y/k_x = 2, then y_i equals ____ (rounded off to 3 decimal places).

The correct answer is 0.014 to 0.017.

GATE 2025 official key: 0.014 to 0.017. The tie-line slope from bulk to interface is −k_x/k_y = −0.5: (0.02−y_i)/(0.002−x_i) = −0.5, combined with y_i = 1.5x_i, gives x_i ≈ 0.0105 and y_i ≈ 0.0158.

GATE 2024, Q17

Consider the steady, uni-directional diffusion of a binary mixture of A and B across a vertical slab of dimensions 0.2 m × 0.1 m × 0.02 m as shown in the figure, with diffusion occurring along the x-direction across the 0.02 m thickness (cross-sectional area 0.2 m × 0.1 m). The total molar concentration of A and B is constant at 100 mol/m³. The mole fraction of A on the left and right faces of the slab are maintained at 0.8 and 0.2, respectively. If the binary diffusion coefficient D_AB = 1 × 10⁻⁵ m²/s, the molar flow rate of A in mol/s, along the horizontal x direction, is

The correct answer is A, 6 × 10⁻⁴.

GATE 2024 official key: (A). N_A = D_AB·C·(x_A1−x_A2)/L × Area = (1×10⁻⁵)(100)(0.6)/(0.02) × (0.2×0.1) = 0.03 × 0.02 = 6×10⁻⁴ mol/s.

GATE 2024, Q24

Which one of the given statements is correct with reference to gas-liquid contactors for mass transfer applications?

The correct answer is B, Tray towers are preferred over packed towers for systems requiring frequent cleaning..

GATE 2024 official key: (B). Trays are more accessible for inspection and cleaning than packing, so they are preferred when frequent cleaning is required. Packed towers generally handle foaming systems better; flooding occurs above the loading region (not below); and flooding can occur in any counter-current contactor.

GATE 2024, Q40

A gas stream containing 95 mol% CO₂ and 5 mol% ethanol is to be scrubbed with pure water in a counter-current, isothermal absorption column to remove ethanol. The desired composition of ethanol in the exit gas stream is 0.5 mol%. The equilibrium mole fraction of ethanol in the gas phase, y*, is related to that in the liquid phase, x, as y* = 2x. Assume CO₂ is insoluble in water and neglect evaporation of water. If the water flow rate is twice the minimum, the mole fraction of ethanol in the spent water is

The correct answer is B, 0.0126.

GATE 2024 official key: (B). In mole-ratio terms, Y_in=0.05/0.95=0.0526, Y_out=0.005/0.995=0.00503. At minimum water rate, exit liquid equilibrates with inlet gas: X_max=Y_in/2=0.0263, giving (L/Gs)_min≈1.809. At L/Gs=2×1.809=3.618, X_out=(Y_in−Y_out)/(L/Gs)≈0.01316, so x_out=X_out/(1+X_out)≈0.0126.

GATE 2024, Q41

Sulfur dioxide (SO₂) gas diffuses through a stagnant air-film of thickness 2 mm at 1 bar and 30°C. The diffusion coefficient of SO₂ in air is 1×10⁻⁵ m²/s. The SO₂ partial pressures at the opposite sides of the film are 0.15 bar and 0.05 bar. The universal gas constant is 8.314 J/(mol·K). Assuming ideal gas behavior, the steady-state flux of SO₂ in mol/(m²·s) through the air-film is

The correct answer is B, 0.022.

GATE 2024 official key: (B). Diffusion of A through stagnant B: N_A = [D·P/(RTδ)]·ln[(P−p_A2)/(P−p_A1)] = [(1e-5)(1e5)/(8.314×303×0.002)]×ln(95000/85000) ≈ 0.1985×0.1112 ≈ 0.022 mol/(m²·s).

GATE 2026, Q28

In which of the following condition(s), Bernoulli's equation is applicable?

The correct answers are A. incompressible flow; B. inviscid flow; D. flow along a streamline.

GATE 2026 official key: (A, B, D). The classical Bernoulli equation requires incompressible, inviscid flow evaluated along a streamline; it strictly applies to steady flow, so unsteady flow (C) is not a valid condition.

GATE 2026, Q32

Water is discharged from vertical side of a tank through a circular orifice of diameter 2 cm under laminar flow conditions. The water surface in the tank is maintained at constant level above the center of the orifice. If the fluid jet has a diameter of 1.6 cm at its vena contracta, then the coefficient of contraction is ________________ (rounded off to two decimal places).

The correct answer is 0.63 to 0.65.

GATE 2026 official key: 0.63 to 0.65. Coefficient of contraction Cc = A_jet/A_orifice = (d_jet/d_orifice)² since both cross-sections are circular; Cc = (1.6/2)² = 0.64.

GATE 2026, Q37

Consider a flow with the following velocity field: V = (x + y) î + (y + z) ĵ + (z + x) k̂, where î, ĵ and k̂ are the unit vectors in the x, y and z directions, respectively. Which one of the following is CORRECT?

The correct answer is C, The flow is compressible and rotational..

GATE 2026 official key: (C). Incompressible requires ∇·V=0 and irrotational requires ∇×V=0. Here ∇·V = ∂(x+y)/∂x + ∂(y+z)/∂y + ∂(z+x)/∂z = 1+1+1 = 3 ≠ 0 (compressible), and ∇×V = (−1,−1,−1) ≠ 0 (rotational).

GATE 2026, Q59

A cylindrical capillary glass tube, open at both ends, is vertically inserted in a pool of water; the water level in the tube rises 7 cm relative to the level outside. Surface tension of water is 0.07 N m⁻¹, contact angle 0°, density 1000 kg m⁻³, g = 10 m s⁻². The diameter of the capillary tube (in μm) is __________ (rounded off to the nearest integer).

The correct answer is 400.

GATE 2026 official key: 400. Capillary rise: h = 4γcosθ/(ρgd); with θ=0° (cosθ=1), solve for d = 4γ/(ρgh) = 4×0.07/(1000×10×0.07) = 0.0004 m = 400 μm.

GATE 2026, Q60

Consider steady, laminar flow of an incompressible fluid with zero pressure gradient over a thin horizontal flat plate of length 2 m, free stream velocity 1 m s⁻¹. A boundary layer thickness of 1 mm is observed at 0.25 m from the leading edge. At 1 m from the leading edge, the boundary layer thickness (in mm) is _________ (rounded off to the nearest integer).

The correct answer is 2.

GATE 2026 official key: 2. For a laminar boundary layer, δ ∝ √x, so δ(1 m) = δ(0.25 m) × √(1/0.25) = 1 mm × 2 = 2 mm.

GATE 2026, Q65

The velocity profile for fully developed laminar flow of an incompressible Newtonian fluid through a horizontal infinitely wide slit of gap 0.01 m is u(y) = 7.5 − 3×10⁵y², where y is measured from the center of the slit. The average velocity of the fluid (in m s⁻¹) is ____________ (rounded off to the nearest integer).

The correct answer is 5.

GATE 2026 official key: 5. Averaging u(y) over y ∈ [−0.005, 0.005]: u_avg = (1/0.01)×[7.5×0.01 − 3×10⁵×(2×0.005³/3)] = 0.05/0.01 = 5 m/s.

GATE 2025, Q18

The sum of the components of the force due to pressure and shear at the solid-fluid boundary of a solid body in the direction normal to the flow is

The correct answer is C, Lift.

GATE 2025 official key: (C). The force component parallel to the flow direction is drag; the component normal to the flow direction is lift.

GATE 2025, Q19

Choose the CORRECT option for pathlines, streaklines and streamlines for a STEADY flow field.

The correct answer is A, All three lines are identical.

GATE 2025 official key: (A). In steady flow, the velocity field doesn't change with time, so pathlines, streaklines, and streamlines all coincide.

GATE 2025, Q43

For a steady state, fully developed laminar flow of a Newtonian fluid through a cylindrical pipe at a constant volumetric flow rate, which of the following statements regarding the pressure drop across the pipe (ΔP) is/are TRUE?

The correct answers are A. ΔP increases with fluid viscosity; B. ΔP increases with pipe length.

GATE 2025 official key: (A, B). By the Hagen-Poiseuille equation, ΔP = 8μLQ/(πR⁴): ΔP increases with viscosity μ (A) and length L (B), and decreases (not increases) with pipe diameter, so (C) and (D) are false.

GATE 2025, Q50

An adiabatic pump of efficiency 40% is used to increase the water pressure from 200 kPa to 600 kPa. The flow rate of water is 600 L/min. The specific heat of water is 4.2 kJ/(kg·°C). Assuming water is incompressible with a density of 1000 kg/m³, the maximum temperature rise of water across the pump is ____ °C (rounded off to 3 decimal places).

The correct answer is 0.139 to 0.145.

GATE 2025 official key: 0.139 to 0.145°C. Ideal (reversible) work = ΔP/ρ = 400,000/1000 = 400 J/kg. Actual work = 400/0.4 = 1000 J/kg; the loss (1000−400=600 J/kg) appears as a temperature rise: ΔT = 600/4200 ≈ 0.143°C.

GATE 2024, Q15

An infinitely long cylindrical water filament of radius r is surrounded by air. Assume water and air to be static. The pressure outside the filament is P_out and the pressure inside is P_in. If γ is the surface tension of the water-air interface, then P_in − P_out is

The correct answer is C, γ/r.

GATE 2024 official key: (C). Young-Laplace: ΔP = γ(1/R₁ + 1/R₂). For a cylinder, R₁ = r and R₂ = ∞, giving ΔP = γ/r. (For a sphere it would be 2γ/r; for a soap bubble, 4γ/r.)

GATE 2024, Q16

The velocity field in an incompressible flow is v = αxy î + v_y ĵ + β k̂, where î, ĵ, k̂ are unit vectors in the (x,y,z) Cartesian coordinate system. Given that α and β are constants, and v_y = 0 at y = 0, the correct expression for v_y is

The correct answer is B, −αy²/2.

GATE 2024 official key: (B). Continuity: ∂(αxy)/∂x + ∂v_y/∂y + ∂β/∂z = 0 ⇒ αy + ∂v_y/∂y = 0. Integrating: v_y = −αy²/2 + C; at y=0, C=0, so v_y = −αy²/2.

GATE 2024, Q33

Consider the steady, uni-directional, fully-developed, pressure-driven laminar flow of an incompressible Newtonian fluid through a circular pipe of inner radius 5.0 cm. The magnitude of shear stress at the inner wall of the pipe is 0.1 N/m². At a radial distance of 1.0 cm from the pipe axis, the magnitude of the shear stress, in N/m², rounded off to 3 decimal places, is ______

The correct answer is 0.019 to 0.021.

GATE 2024 official key: 0.019 to 0.021. For laminar pipe flow, shear stress varies linearly with radius: τ(r) = τ_wall·(r/R) = 0.1×(1/5) = 0.02 N/m².

GATE 2024, Q36

Consider a steady, fully-developed, uni-directional laminar flow of an incompressible Newtonian fluid (viscosity μ) between two infinitely long horizontal plates separated by a distance 2H, as shown in the figure. The flow is driven by the combined action of a pressure gradient and the motion of the bottom plate at y = −H in the negative x direction with speed V, relative to the stationary top plate at y = H. Given (P1−P2)/L > 0, where P1 and P2 are the pressures at two x locations separated by distance L. Which one of the following represents the x-component of the fluid velocity vector?

The correct answer is A, [(P1−P2)H²/(2μL)]·(1−(y/H)²) + (V/2)·((y/H)−1).

GATE 2024 official key: (A). Solving μ·d²u/dy² = −(P1−P2)/L with u(H)=0 and u(−H)=−V gives u(y) = [(P1−P2)H²/(2μL)]·(1−(y/H)²) + (V/2)·((y/H)−1).

GATE 2024, Q59

Water of density 1000 kg/m³ is pumped at a volumetric flow rate of 3.14×10⁻² m³/s, through a pipe of inner diameter 10 cm and length 100 m, from a large Reservoir 1 to another large Reservoir 2 at a height 50 m above Reservoir 1, as shown in the figure. The flow in the pipe is in the turbulent regime with a Darcy friction factor f = 0.06, and a kinetic energy correction factor α = 1. Take g = 9.8 m/s². If all minor losses are negligible, and the pump efficiency is 100%, the pump power, in kW, rounded off to 2 decimal places, is ______

The correct answer is 30.4 to 30.5.

GATE 2024 official key: 30.40 to 30.50. v=Q/A=0.0314/(π×0.05²)=4.0 m/s. h_f=f(L/D)(v²/2g)=0.06×1000×(16/19.6)≈48.98 m. Total head=50+48.98≈98.98 m. Power=ρgQH=1000×9.8×0.0314×98.98≈30,460 W ≈ 30.46 kW.

GATE 2024, Q60

A Venturi meter with a throat diameter d = 2 cm measures the flow rate in a pipe of diameter D = 6 cm, as shown in the figure. A U-tube manometer is connected to measure the pressure drop. Assume the discharge coefficient is independent of the Reynolds number and geometric ratios. If the volumetric flow rate through the pipe is doubled, Q2 = 2Q1, the corresponding ratio of the manometer readings Δh2/Δh1, rounded off to the nearest integer, is _______

The correct answer is 4.

GATE 2024 official key: 4. For a Venturi meter, Q ∝ √Δh, so Δh ∝ Q². Doubling Q gives Δh2/Δh1 = 2² = 4.

GATE 2026, Q13

A body is placed inside a perfectly black enclosure and is allowed to reach thermal equilibrium. According to the Kirchhoff's identity, which one of the following is equal to the emissivity of the body at a given wavelength?

The correct answer is A, absorptivity of the body at the same wavelength.

GATE 2026 official key: (A). Kirchhoff's law: at thermal equilibrium, a body's emissivity equals its absorptivity at the same wavelength.

GATE 2026, Q14

Which one of the following ratios does Grashof number represent?

The correct answer is B, buoyancy force to viscous force.

GATE 2026 official key: (B). Gr = gβΔTL³/ν² compares the buoyancy force driving natural convection to the viscous force resisting it.

GATE 2026, Q52

In a double pipe cocurrent heat exchanger, operating at steady state, oil (specific heat capacity = 2100 J kg⁻¹ °C⁻¹) entering at 7 kg s⁻¹ at 100°C is used to heat water (specific heat capacity = 4200 J kg⁻¹ °C⁻¹) flowing at 3.5 kg s⁻¹ from 20°C to 50°C. If the overall heat transfer coefficient is 291 W m⁻² °C⁻¹, the required heat transfer area (in m²) is _____ (rounded off to one decimal place).

The correct answer is 34.5 to 35.5.

GATE 2026 official key: 34.5 to 35.5. Q = 3.5×4200×30 = 441 kW; oil exits at 70°C. Cocurrent LMTD = (80−20)/ln(80/20) ≈ 43.3°C. A = Q/(U×LMTD) = 441000/(291×43.3) ≈ 35.0 m².

GATE 2026, Q53

A pipe with outer diameter of 0.02 m carries hot water at a surface temperature of 70°C. It is covered with two 0.01 m-thick layers of insulation: felt (k = 0.12 W m⁻¹ °C⁻¹, inner layer) and asbestos (k = 0.15 W m⁻¹ °C⁻¹, outer layer), exposed to ambient air at 20°C with a convection coefficient of 3 W m⁻² °C⁻¹ at the outer surface. At steady state, neglecting radiation, the heat loss (in W m⁻¹) is _____ (rounded off to two decimal places).

The correct answer is 15.5 to 16.5.

GATE 2026 official key: 15.5 to 16.5. Per-length resistances: felt ln(2)/(2π·0.12)≈0.92, asbestos ln(1.5)/(2π·0.15)≈0.43, convection 1/(2π·0.03·3)≈1.77; total ≈3.12 m·K/W. q' = 50/3.12 ≈ 16.0 W/m.

GATE 2025, Q17

In industrial heat exchanger design, the overall heat transfer coefficient U is estimated from the equation 1/U = 1/hᵢ + 1/hₒ, where hᵢ and hₒ are the convective heat transfer coefficients on the inner and outer side of the tube, respectively. This is valid for (i) ___ tube of (ii) ___ thermal conductivity. Which one of the following is the CORRECT option to fill in the gaps (i) and (ii)?

The correct answer is B, (i) thin-walled, (ii) high.

GATE 2025 official key: (B). Neglecting wall conduction resistance (as this simplified equation does) is only valid for a thin-walled tube made of a high thermal conductivity material, where the wall resistance is negligible.

GATE 2025, Q30

Which of the following statements regarding multiple effect evaporators is/are TRUE?

The correct answers are B. Backward feed is preferred over forward feed for cold feed.; C. Backward feed is preferred over forward feed for highly viscous concentrated product..

GATE 2025 official key: (B, C). The fresh-steam effect operates at the highest pressure/temperature (not lowest), ruling out (A) and (D). Backward feed is preferred for cold, viscous feeds since the feed first meets the hottest, least viscous conditions at the last effect it enters.

GATE 2025, Q38

A hot plate is placed in contact with a cold plate of a different thermal conductivity, as shown in the figure. The initial temperature (at time t=0) of the hot plate and cold plate are T_h and T_c, respectively. Assume perfect contact between the plates. Which one of the following is an appropriate boundary condition at the surface S for solving the unsteady state, one-dimensional heat conduction equations for the hot plate and cold plate for t > 0?

The correct answer is A, Temperature at S is same for both the plates.

GATE 2025 official key: (A). Perfect thermal contact requires temperature continuity at the interface (equal temperature on both sides); the temperature gradients differ because the two plates have different thermal conductivities, so (B) is false.

GATE 2025, Q51

Water flowing at 70 kg/min is heated from 25°C to 65°C in a counter-flow double pipe heat exchanger using hot oil. The oil enters at 110°C and exits at 65°C. If the overall heat transfer coefficient is 300 W/(m²K), the heat exchanger area is ____ m² (rounded off to 1 decimal place). Given: specific heat of water and oil are 4.2 kJ/(kg·°C) and 2 kJ/(kg·°C), respectively.

The correct answer is 15.2 to 15.6.

GATE 2025 official key: 15.2 to 15.6 m². Q = (70/60)×4200×40 ≈ 196,000 W. Counter-flow LMTD = (45−40)/ln(45/40) ≈ 42.45°C. Area = Q/(U·LMTD) = 196000/(300×42.45) ≈ 15.4 m².

GATE 2025, Q52

Consider laminar flow of water over a wide flat plate maintained at a uniform temperature of 50°C, as shown in the figure. The freestream velocity and temperature of water are 1.0 m/s (parallel to the plate) and 20°C, respectively. The distance x from the leading edge, at which the thermal boundary layer thickness δ_T = 0.01 m, is ____ m (rounded off to 1 decimal place). Given: kinematic viscosity ν = 1.0 × 10⁻⁶ m²/s; Prandtl number Pr = 7.01; velocity boundary layer thickness δ_H = 4.91x/√(V_x/ν).

The correct answer is 14.8 to 15.6.

GATE 2025 official key: 14.8 to 15.6 m. Using δ_H ≈ δ_T·Pr^(1/3) = 0.01×7.01^(1/3) ≈ 0.0191 m, and δ_H = 4.91√x/1000, solving gives x ≈ 15.2 m.

GATE 2025, Q53

An electrical wire of 2 mm diameter and 5 m length is insulated with a plastic layer of thickness 2 mm and thermal conductivity k = 0.1 W/(m·K). It is exposed to ambient air at 30°C. For a current of 5 A, the potential drop across the wire is 2 V. The air-side heat transfer coefficient is 20 W/(m²K). Neglecting the thermal resistance of the wire, the steady state temperature at the wire-insulation interface is ____ °C (rounded off to 1 decimal place).

The correct answer is 38.5 to 39.1.

GATE 2025 official key: 38.5 to 39.1°C. Heat generated q' = IV/L = 10/5 = 2 W/m. R'_cond = ln(r₂/r₁)/(2πk) ≈ 1.75, R'_conv = 1/(h·2πr₂) ≈ 2.65 (m·K/W). ΔT = q'(R'_cond+R'_conv) ≈ 8.8°C, so T_interface ≈ 30+8.8 ≈ 38.8°C.

GATE 2024, Q27

If the Prandtl number Pr = 0.01, which of the following statements is/are correct?

The correct answers are B. The thickness of the momentum boundary layer is much smaller than that of the thermal boundary layer.; D. The momentum diffusivity is much smaller than the thermal diffusivity..

GATE 2024 official key: (B, D). Pr = ν/α = 0.01 ≪ 1 means momentum diffusivity ν is much smaller than thermal diffusivity α (D true, A false), and correspondingly the momentum boundary layer is much thinner than the thermal boundary layer (B true, C false).

GATE 2024, Q34

The opposite faces of a metal slab of thickness 5 cm and thermal conductivity 400 W/(m·K) are maintained at 500°C and 200°C. The area of each face is 0.02 m². Assume that the heat transfer is steady and occurs only in the direction perpendicular to the faces. The magnitude of the heat transfer rate, in kW, rounded off to the nearest integer, is _______

The correct answer is 48.

GATE 2024 official key: 48. Steady, 1-D conduction perpendicular to the faces → Fourier's law Q = kAΔT/L applies directly: Q = 400×0.02×(500−200)/0.05 = 48,000 W = 48 kW.

GATE 2024, Q37

The temperatures of two large parallel plates of equal emissivity are 900 K and 300 K. A reflective radiation shield of low emissivity and negligible conductive resistance is placed parallel between them. The steady-state temperature of the shield, in K, is

The correct answer is A, 759.

GATE 2024 official key: (A). For a shield with the same emissivity on both faces, symmetry of the radiative network gives T_shield⁴ = (T1⁴+T2⁴)/2 = (900⁴+300⁴)/2, independent of the shield's emissivity value. This gives T_shield ≈ 759 K.

GATE 2024, Q38

Hot oil at 110°C heats water from 30°C to 70°C in a counter-current double-pipe heat exchanger. The flow rates of water and oil are 50 kg/min and 100 kg/min, respectively, and their specific heat capacities are 4.2 kJ/(kg·°C) and 2.0 kJ/(kg·°C), respectively. Assume the heat exchanger is at steady state. If the overall heat transfer coefficient is 200 W/(m²·°C), the heat transfer area in m² is

The correct answer is A, 17.9.

GATE 2024 official key: (A). Q = (50/60)×4200×40 ≈ 140,000 W. Oil outlet: 140000 = (100/60)×2000×(110−T_out) ⇒ T_out = 68°C. LMTD (counter-current) = (40−38)/ln(40/38) ≈ 39.0°C. Area = 140000/(200×39.0) ≈ 17.9 m².

GATE 2024, Q39

A solid slab of thickness H₁ is initially at a uniform temperature T₀. At time t=0, the temperature of the top surface at y=H₁ is increased to T₁, while the bottom surface at y=0 is maintained at T₀ for t≥0. Assume heat transfer occurs only in the y-direction, and all thermal properties of the slab are constant. The time required for the temperature at y=H₁/2 to reach 99% of its final steady value is t₁. If the thickness of the slab is doubled to H₂=2H₁, and the time required for the temperature at y=H₂/2 to reach 99% of its final steady value is t₂, then t₂/t₁ is

The correct answer is C, 4.

GATE 2024 official key: (C). Transient conduction time scales with the square of the characteristic length (t ~ L²/α). Since the dimensionless position (y/H) is the same in both cases, t₂/t₁ = (H₂/H₁)² = 2² = 4.

GATE 2026, Q25

A process exhibits an inverse response to a step input. Which of the following statements is/are necessarily TRUE about the process?

The correct answers are A. Its transfer function has a positive zero.; C. The initial direction of the step response is opposite to the final steady state value..

GATE 2026 official key: (A, C). Inverse response arises from a positive (right-half-plane) zero, which makes the step response initially move opposite to its eventual steady-state direction. A RHP zero alone doesn't make the system unstable (that requires a RHP pole), so (D) is false.

GATE 2026, Q44

A control valve with hyperbolic characteristics has a turndown ratio (ratio of maximum flow to minimum controllable flow) of 50. The flow rate through the valve at 70% open is 5 m³ s⁻¹. Assuming constant fluid density and pressure drop across the valve, which one of the following is the flow rate (in m³ s⁻¹) through the valve at 30% open?

The correct answer is B, 2.2.

GATE 2026 official key: (B). For an equal-percentage (hyperbolic) valve, f(x) = R^(x−1); solving with turndown ratio 50 and the 70%-open flow of 5 m³/s gives ≈2.2 m³/s at 30% open.

GATE 2026, Q50

Consider three identical non-interacting first order processes in series, each having unit gain and a time constant of 2 min. Tuning of a proportional controller using closed loop Ziegler-Nichols technique is considered. Which one of the following is the ultimate period of sustained cycling (in min per cycle)?

The correct answer is C, 4π / √3.

GATE 2026 official key: (C). For 3 identical first-order lags in series, 3·arctan(ωτ) = 180° gives ωτ = √3, ω = √3/τ. With τ = 2 min, the ultimate period Pu = 2π/ω = 4π/√3 min/cycle.

GATE 2026, Q51

A thermometer initially at a steady temperature of 30°C is inserted in a water bath maintained at 90°C. The initial rate of temperature rise of the thermometer is 2°C/s. Assuming first order behavior, the thermometer reading (in °C) after one minute is ______ (rounded off to one decimal place).

The correct answer is 81 to 83.

GATE 2026 official key: 81.0 to 83.0. dT/dt|0 = (90−30)/τ = 2 gives τ = 30 s. T(t) = 90 − 60e^(−t/30). At t = 60 s: T = 90 − 60e⁻² ≈ 81.9°C.

GATE 2025, Q25

Choose the transfer function that best fits the output response to a unit step input change shown in the figure, where the output response shows an initial delay, then rises and overshoots before settling to the new steady state.

The correct answer is A, (αs + 1)e^(−θs) / [(τ₁s + 1)(τ₂s + 1)²].

GATE 2025 official key: (A). The S-shaped step response with an inflection point and no initial overshoot matches a lead/lag numerator combined with dead time over a second-order-plus-repeated-pole denominator.

GATE 2025, Q39

The first-order irreversible liquid phase reaction A → B occurs inside a constant volume (V) isothermal CSTR with the initial steady state conditions shown in the figure: C_A0 = 2.5 kmol/m³, F = 1 m³/h, V = 10 m³, C_A = 1.0 kmol/m³. The gain, in (kmol/m³)/(m³/h), of the transfer function relating the reactor effluent A concentration, C_A, to the inlet flow rate, F, is

The correct answer is C, 0.6.

GATE 2025 official key: (C). Steady state: F·C_A0 = F·C_A + kVC_A ⇒ k = F(C_A0−C_A)/(VC_A) = 1×1.5/10 = 0.15/h. C_A(F) = FC_A0/(F+kV); gain = dC_A/dF = C_A0·kV/(F+kV)² = 2.5×1.5/2.5² = 3.75/6.25 = 0.6.

GATE 2025, Q60

Consider a process with transfer function G_p = 2e^(−s) / (5s+1)². A first-order plus dead time (FOPDT) model is to be fitted to the unit step process reaction curve (PRC) by applying the maximum slope method. Let τ_m and θ_m denote the time constant and dead time, respectively, of the fitted FOPDT model. The value of τ_m/θ_m is ____ (rounded off to 2 decimal places). Given (as shown in the figure): for G = 1/(τs+1)², the unit step output response y(t) = 1−(1+t/τ)e^(−t/τ), dy(t)/dt = (t/τ²)e^(−t/τ), and d²y(t)/dt² = (1/τ²)(1−t/τ)e^(−t/τ).

The correct answer is 5.6 to 5.7.

GATE 2025 official key: 5.60 to 5.70. The inflection point occurs at t = θ₀+τ = 6, with maximum slope K·e⁻¹/τ. Constructing the tangent line there gives θ_p ≈ 2.41 and τ_p ≈ 13.59, so τ_p/θ_p ≈ 5.64.

GATE 2025, Q62

The block diagram of a series cascade control system (with time in minutes) is shown in the figure: a primary PI controller (K_c)^m·(τ_Is+1)/(τ_Is) sets the setpoint for a secondary proportional controller (K_c)^s, whose output drives the inner process 1/(2s+1), followed by the outer process 2/[(8s+1)(4s+1)]. For τ_I = 8 min and (K_c)^s = 1, the maximum value of (K_c)^m, below which the cascade control system is stable, is ____ (rounded off to the nearest integer).

The correct answer is 10.

GATE 2025 official key: 10. Applying the Routh-Hurwitz stability criterion to the characteristic equation of the cascade loop shown in the official figure gives a maximum stable gain of (K_c)^m = 10.

GATE 2024, Q22

Consider the block diagram in the figure with control input u, disturbance d and output y. The disturbance path is Gd = 1/(s+1)², the manipulated-variable path (process) is Gp = 2/(0.5s+1)², and the feedforward controller is Gf = K[(αs+1)/(βs+1)]². For perfect disturbance rejection (feedforward controller cancels the effect of d on y), the ordered pair (K, α/β) is

The correct answer is B, (−0.5, 0.5).

GATE 2024 official key: (B). Perfect feedforward cancellation requires Gf·Gp + Gd = 0 ⇒ Gf = −Gd/Gp = −[1/(s+1)²]/[2/(0.5s+1)²] = −(0.5s+1)²/[2(s+1)²]. Matching forms gives K = −0.5, α = 0.5, β = 1, so α/β = 0.5.

GATE 2024, Q23

Consider the control structure for the overhead section of a distillation column shown in the figure. The composition controller (CC) controls the heavy key impurity in the distillate by adjusting the setpoint of the reflux flow controller in a cascade arrangement, while the pressure controller (PC) manipulates a valve on the overhead vapor/condenser duty. The sign of the controller gain for the pressure controller (PC) and that for the composition controller (CC) are, respectively,

The correct answer is D, positive, negative.

GATE 2024 official key: (D). Tracing the air-to-open/air-to-close valve actions and the direction of each measured variable's response to its manipulated variable in the figure gives a positive gain for PC and a negative gain for CC.

GATE 2024, Q48

For the block diagram shown in the figure, the correct expression for the transfer function Gd = y1(s)/d(s) is

The correct answer is C, −Gc2Gp1 / [1+Gc2Gp2+Gc1Gc2Gp1].

GATE 2024 official key: (C). With y1sp=0, tracing the secondary loop error e2=−Gc1y1−y2, u=Gc2e2, y2=Gp2u+d, y1=Gp1u, and eliminating u and y2 gives y1/d = −Gc2Gp1/(1+Gc2Gp2+Gc1Gc2Gp1).

GATE 2024, Q63

Consider the surge drum in the figure. Initially the system is at steady-state with a hold-up V̄ = 5 m³, which is 50% of full tank capacity, V_full, and volumetric flow rates F̄_in = F̄_out = 1 m³/h. The high hold-up alarm limit V_high = 0.8×V_full while the low hold-up alarm limit V_low = 0.2×V_full. A proportional (P-only) controller manipulates the outflow to regulate the hold-up V as F_out = K_c(V−V̄) + F̄_out. At t=0, F_in increases as a step from 1 m³/h to 2 m³/h. Assume linear control valves and instantaneous valve dynamics. Let K_c,min be the minimum controller gain that ensures V never exceeds V_high. The value of K_c,min, in h⁻¹, rounded off to 2 decimal places, is _________

The correct answer is 0.32 to 0.34.

GATE 2024 official key: 0.32 to 0.34. V_full=10 m³, so V_high=8, giving allowable rise V_high−V̄=3 m³. The step response V(t)−V̄ = (ΔF_in/K_c)(1−e^(−K_c t)) approaches a maximum offset of ΔF_in/K_c = 1/K_c as t→∞. Requiring 1/K_c ≤ 3 gives K_c,min = 1/3 ≈ 0.33 h⁻¹.

GATE 2024, Q64

A PD controller with transfer function G_c = K_c(τ_Ds+1)/[(τ_D/20)s+1] is used to stabilize an open-loop unstable process with transfer function G_p = 1/[(s−1)(10s+1)], shown in the figure, and time is in minutes. From the necessary conditions for closed-loop stability, the maximum feasible value of τ_D, in minutes, rounded off to 1 decimal place, is ____________

The correct answer is 22.1 to 22.3.

GATE 2024 official key: 22.1 to 22.3. The closed-loop characteristic equation 1+G_cG_p=0 expands to (τ_D/2)s³ + [10−9τ_D/20]s² + [−9−τ_D/20+K_cτ_D]s + (K_c−1) = 0. A necessary Routh-Hurwitz condition (independent of K_c) requires all same-sign coefficients, so the s² coefficient must stay positive: 10−9τ_D/20 > 0 ⇒ τ_D < 200/9 ≈ 22.2 min.

GATE 2026, Q11

Which one of the following is NOT a type of chain conveyor?

The correct answer is D, screw conveyor.

GATE 2026 official key: (D). Apron, bucket, and scraper conveyors are chain-driven; a screw conveyor instead moves material via a rotating helical screw.

GATE 2026, Q30

Consider two successive screen sizes in the Tyler standard screen scale, viz. 150 meshes per inch and 200 meshes per inch. Their linear sizes of the openings are L150 and L200, respectively. If the value of L200 is 2.9 × 10⁻³ inch, then the value of L150 (in inch) is _____ × 10⁻³ (rounded off to one decimal place).

The correct answer is 4 to 4.2.

GATE 2026 official key: 4.0 to 4.2. Successive Tyler screens have a fixed size ratio of √2, so L150 = L200 × √2 ≈ 2.9 × 1.414 ≈ 4.1 × 10⁻³ inch.

GATE 2026, Q45

The gross energy requirement, to reduce a very large feed of coal to such a size that 80% of the product passes through a 100 µm screen, is 13 kWh per ton of feed. In a process, 250 tons h⁻¹ of coal is crushed. 80% of the feed passes through an opening of 100 mm, and 80% of the product is to pass through an opening of 25 mm. According to Bond's law, which one of the following is the power consumption (in kW)?

The correct answer is D, 102.7.

GATE 2026 official key: (D). Bond's work index from the given data is Wi = 13. Applying Bond's law to F80=100 mm, P80=25 mm gives E ≈ 0.411 kWh/ton; Power = 0.411 × 250 ≈ 102.7 kW.

GATE 2026, Q49

Laboratory filtration is conducted at constant pressure drop of 200 kPa on a slurry of CaCO3 in water at room temperature: 1×10⁻³ m³ filtrate collected in 40 s, 2×10⁻³ m³ in 100 s. The filter area is 0.05 m² and viscosity of filtrate is 10⁻³ Pa·s. Which one of the following is the filter medium resistance (in m⁻¹)?

The correct answer is D, 3 × 10¹¹.

GATE 2026 official key: (D). From the t/V vs V data, the intercept μR_m/(AΔP) ≈ 30000 s/m³; solving for R_m with A=0.05 m², ΔP=200 kPa, μ=10⁻³ Pa·s gives R_m ≈ 3×10¹¹ m⁻¹.

GATE 2025, Q34

Oil is extracted from mustard seeds having 20 wt% oil and 80 wt% solids, using hexane as a solvent. After extraction, the hexane-free residual cake contains 1 wt% oil. Assuming negligible dissolution of cake in hexane, the percentage oil recovery in hexane is ____% (rounded off to the nearest integer).

The correct answer is 95 to 97.

GATE 2025 official key: 95 to 97%. Basis 100 kg seed: 80 kg solids, 20 kg oil. Residual cake oil = 1 wt% of cake, so oil left = (1/99)×80 ≈ 0.808 kg. Recovery = (20−0.808)/20 ≈ 96%.

GATE 2025, Q41

A catalyst particle is modeled as a symmetrical double cone solid, as shown in the figure. For each conical sub-part, the radius of the base is r and the height is h. The sphericity of the particle is given by

The correct answer is C, 2(r²h/2)^(2/3) / [r√(r²+h²)].

GATE 2025 official key: (C). Sphericity is the ratio of the surface area of a sphere of equal volume to the actual surface area of the particle; for the double-cone geometry this reduces to 2(r²h²)^(2/3) / [r√(r²+h²)].

GATE 2025, Q49

A leaf filter is operated at 1 atm (gauge). The volume of filtrate collected (V in m³) is related with the volumetric flow rate of the filtrate (q in m³/s) as: 1/q=1/(dV/dt) = 50V + 100. The volumetric flow rate of the filtrate at 1 hour is ____ × 10⁻³ m³/s (rounded off to 2 decimal places).

The correct answer is 1.61 to 1.68.

GATE 2025 official key: 1.61 to 1.68 (×10⁻³). Integrating dt = (50V+100)dV from V=0 gives t = 25V²+100V. At t=3600 s, solving 25V²+100V−3600=0 gives V≈10.17 m³, so dV/dt = 1/(50×10.17+100) ≈ 1.64×10⁻³ m³/s.

GATE 2025, Q65

A wet solid of 100 kg containing 30 wt% moisture is to be dried to 2 wt% moisture in a tray dryer. The critical moisture content is 10 wt% and the equilibrium moisture content is 1 wt%. The drying rate during the constant rate period is 10 kg/(h·m²). The drying curve in the falling rate period is linear. If the drying area is 5 m², the time required for drying is ____ h (rounded off to 1 decimal place). Note: all the moisture values given are on dry-solid basis.

The correct answer is 0.5 to 0.9.

GATE 2025 official key: 0.5 to 0.9 h. Dry solids L_s = 100/1.30 ≈ 76.9 kg. Constant rate period: t_c = L_s(X₀−X_c)/(A·R_c) ≈ 0.31 h. Falling rate period: t_f = [L_s(X_c−X*)/(A·R_c)]·ln[(X_c−X*)/(X₂−X*)] ≈ 0.30 h. Total ≈ 0.61 h.

GATE 2024, Q43

Alumina particles with an initial moisture content of 5 kg per kg dry solid are dried in a batch dryer. For the first two hours, the measured drying rate is constant at 2 kg/(m²·h). Thereafter, in the falling-rate period, the rate decreases linearly with the moisture content. The equilibrium moisture content is 0.05 kg per kg dry solid and the drying area of the particles is 0.5 m² per kg dry solid. The total drying time, in h, to reduce the moisture content to half its initial value is

The correct answer is B, 2.55.

GATE 2024 official key: (B). Critical moisture: X_c = X₀ − a·R_c·t_c = 5 − (0.5×2)(2) = 3. Target X_final=2.5 is below X_c, so it lies in the falling-rate period. t_f = [(X_c−X*)/(aR_c)]·ln[(X_c−X*)/(X_final−X*)] = 2.95×ln(2.95/2.45) ≈ 0.548 h. Total t = 2 + 0.548 ≈ 2.55 h.

GATE 2024, Q58

A metallic spherical particle of density 7001 kg/m³ and diameter 1 mm is settling steadily due to gravity in a stagnant gas of density 1 kg/m³ and viscosity 10⁻⁵ kg/(m·s). Take g = 9.8 m/s². Assume that the settling occurs in the regime where the drag coefficient C_D is independent of the Reynolds number, and equals 0.44. The terminal settling velocity of the particle, in m/s, rounded off to 2 decimal places, is ____

The correct answer is 14.3 to 14.6.

GATE 2024 official key: 14.30 to 14.60. Newton's law regime: v_t = √[4gd(ρp−ρf)/(3C_Dρf)] = √[4×9.8×0.001×7000/(3×0.44×1)] = √207.9 ≈ 14.42 m/s.

GATE 2024, Q65

Consider a tray-column of diameter 120 cm. Each downcomer (there are two per tray: one inlet and one outlet) has a cross-sectional area of 575 cm². For a tray, the percentage column cross-sectional area not available for vapour flow due to the downcomers, rounded off to 1 decimal place, is _____________

The correct answer is 10 to 10.3.

GATE 2024 official key: 10.0 to 10.3. Column area = π(60)² ≈ 11,309.7 cm². Total downcomer area (2 × 575) = 1150 cm². Percentage = 1150/11309.7×100 ≈ 10.17%.

GATE 2026, Q18

In a traditional continuous Kraft (Sulfate) pulping process, consider the following major steps: Bleaching (BL), Chipping (CH), Debarking (DE), Digestion (DI), and Pulp Washing (WA). Which one of the following is the CORRECT sequence of steps for this process?

The correct answer is B, DE → CH → DI → WA → BL.

GATE 2026 official key: (B). The correct Kraft process order is Debarking → Chipping → Digestion → Washing → Bleaching.

GATE 2026, Q24

Which one of the following is produced by catalytic reforming of straight run gasoline and naphtha?

The correct answer is C, high octane gasoline.

GATE 2026 official key: (C). Catalytic reforming converts low-octane naphtha/gasoline into high-octane aromatics-rich gasoline via dehydrogenation, isomerization, and cyclization.

GATE 2026, Q26

Urea has its major use as a solid fertilizer for nitrogen fixation. Which of the following is/are other application(s) of urea?

The correct answers are A. manufacturing of resins and plastics; B. melamine production; D. sulfamic acid production.

GATE 2026 official key: (A, B, D). Urea is used to make urea-formaldehyde resins (A), melamine via pyrolysis (B), and sulfamic acid (D). Muriatic acid (HCl) is unrelated to urea chemistry.

GATE 2025, Q11

To manufacture paper from (i) ___, the (ii) ___ must be freed from the binding matrix of (iii) ___ in the pulping step. Which one of the following is the CORRECT option to fill in the gaps (i), (ii) and (iii)?

The correct answer is A, (i) wood, (ii) cellulose fibers, (iii) lignin.

GATE 2025 official key: (A). Paper is made from wood; pulping frees the cellulose fibers from the lignin that binds them together.

GATE 2025, Q27

In the production of polyvinyl chloride (PVC) from ethylene and chlorine, the sequential order of reactions is

The correct answer is A, Chlorination followed by Dehydrochlorination.

GATE 2025 official key: (A). Ethylene is first chlorinated to 1,2-dichloroethane (EDC), which is then cracked via dehydrochlorination (pyrolysis) to yield vinyl chloride monomer.

GATE 2025, Q28

In the CONTACT PROCESS for manufacturing sulphuric acid, the reaction converting SO₂ to SO₃ is

The correct answer is A, Exothermic and reversible.

GATE 2025 official key: (A). Catalytic oxidation of SO₂ to SO₃ over V₂O₅ is exothermic and reversible, which is why the process uses staged conversion with intermediate cooling to shift equilibrium favorably.

GATE 2024, Q25

In an ammonia manufacturing facility, the necessary hydrogen is generated from methane. The facility consists of the following process units, P: Methanator, Q: CO shift converter, R: CO₂ stripper, S: Reformer, T: Ammonia converter. The correct order of these units, starting from methane feed, is

The correct answer is A, S, Q, R, P, T.

GATE 2024 official key: (A). Methane is first reformed (S) to syngas, CO is shifted to CO₂/H₂ (Q), CO₂ is stripped out (R), residual CO/CO₂ traces are methanated (P), and the purified H₂/N₂ mixture is fed to the ammonia converter (T).

GATE 2024, Q28

For the electrolytic cell in a chlor-alkali plant, which of the following statements is/are correct?

The correct answers are A. A membrane cell operates at a higher brine concentration than a diaphragm cell.; C. Hydrogen gas is produced at the cathode.; D. The caustic product stream exits the cathode compartment..

GATE 2024 official key: (A, C, D). Membrane cells use more concentrated, purer brine than diaphragm cells (A). Chlorine is evolved at the anode, not the cathode, making (B) false. Hydrogen and caustic soda are both produced/collected at the cathode compartment (C, D true).

GATE 2024, Q29

Which of the following statements with reference to the petroleum/petrochemical industry is/are correct?

The correct answers are A. Catalytic hydrocracking converts heavier hydrocarbons to lighter hydrocarbons.; B. Catalytic reforming converts straight-chain hydrocarbons to aromatics.; C. Cumene is manufactured by the catalytic alkylation of benzene with propylene..

GATE 2024 official key: (A, B, C). Hydrocracking breaks heavy hydrocarbons into lighter ones (A); reforming converts paraffins/naphthenes to aromatics (B); cumene is made via benzene + propylene alkylation (C). Vinyl acetate is actually made from ethylene (not methane) + acetic acid + O₂ over a Pd catalyst, so (D) is false.

GATE 2026, Q29

Which of the following methods for calculating profitability does/do NOT consider the time value of money?

The correct answers are A. rate of return on investment; C. payback period.

GATE 2026 official key: (A, C). Simple rate of return on investment and (simple) payback period ignore the timing of cash flows; discounted cash flow rate of return and net present worth explicitly discount cash flows.

GATE 2026, Q46

In a certain project, 15% of the total investment is the working capital. The minimum acceptable rate of return is 4.95% and the period of evaluation is 15 years. Which one of the following is the maximum acceptable project payback period (in years)?

The correct answer is B, 8.

GATE 2026 official key: (B). With 15% working capital and a 4.95% minimum rate of return over 15 years, the discounted payback criterion yields a maximum acceptable payback of about 8 years.

GATE 2025, Q26

The capital cost (CC) of an industrial equipment varies with its capacity (S) as CC ∝ S^β. The rule-of-thumb value of the exponent β is

The correct answer is B, 0.6.

GATE 2025 official key: (B). This is the well-known "six-tenths rule" used for scaling equipment capital cost with capacity.

GATE 2025, Q63

It is proposed to install thermal insulation in a residence to save on the summer-monsoon season air-conditioning costs. The estimated yearly saving is 20 thousand rupees. The cost of installation of the insulation is 150 thousand rupees. The life of the insulation is 12 years. For a compound interest rate of 9% per annum, the minimum salvage value of the insulation for which the proposal is competitive, is ____ thousand rupees (rounded off to nearest integer).

The correct answer is 18 to 20.

GATE 2025 official key: 18 to 20 thousand rupees. Setting NPV = 0: −150 + 20×PVIFA(9%,12) + S×PVIF(9%,12) = 0. PVIFA(9%,12) ≈ 7.161, so −150+143.2+0.3555S=0, giving S ≈ 19.

GATE 2024, Q35

The capital cost of a distillation column is Rs. 90 lakhs. The cost is to be fully depreciated (salvage value is zero) using the double-declining balance method over 10 years. At the end of two years of continuous operation, the book-value of the column, in lakhs of rupees, rounded off to 1 decimal place, is _______

The correct answer is 57.5 to 57.7.

GATE 2024 official key: 57.5 to 57.7. DDB rate = 2/n = 2/10 = 20%/yr. BV₁ = 90×0.8 = 72; BV₂ = 72×0.8 = 57.6 lakhs.

GATE 2024, Q49

For purchasing a batch reactor, three alternatives P, Q and R have emerged, as summarized in the table. For a compound interest rate of 10% per annum, choose the correct option that arranges the alternatives, in order, from the least expensive to the most expensive.

The correct answer is C, R, Q, P.

GATE 2024 official key: (C). Annualized cost = Installed Cost×CRF(10%,n) + Maintenance. P: 15×0.4021+4≈10.03; Q: 25×0.2638+3≈9.59; R: 35×0.2054+2≈9.19 lakh/yr. Least to most expensive: R, Q, P.

GATE 2026, Q47

A continuous distillation column separates an equimolar mixture of diethylamine (DEA) and methanol. Saturated liquid feed enters at 30 mol/s; distillate (92 mol% DEA) is withdrawn at 10 mol/s. Using the equilibrium curve shown and a reboiler latent heat of 35 kJ/mol, with constant molal overflow, which one of the following is the minimum reboiler heat duty (in kW)?

The correct answer is D, 1470.

GATE 2026 official key: (D). Reading the minimum-reflux pinch off the equilibrium curve and applying the reboiler energy balance under constant molal overflow gives a minimum reboiler duty of about 1470 kW.

GATE 2025, Q54

A binary AB liquid mixture containing 30 mol% A is subjected to differential (Rayleigh) distillation at atmospheric pressure in order to recover 60 mol% A in the distillate. Assuming a constant relative volatility α_AB = 2.2, the average composition of the collected distillate is ____ mol% A (rounded off to nearest integer).

The correct answer is 41 to 45.

GATE 2025 official key: 41 to 45 mol% A. Applying the Rayleigh equation with the given recovery target and relative volatility yields an average distillate composition of ≈43 mol% A.

GATE 2025, Q57

Components A and B form an azeotrope. The saturation vapour pressures of A and B at the boiling temperature of the azeotrope are 87 kPa and 72.7 kPa, respectively. The azeotrope composition is ____ mol% A (rounded off to the nearest integer). Given: ln(γ_A/γ_B) = 0.9((x_B)² − (x_A))²), where x_i and γ_i are the liquid phase mole fraction and activity coefficient of component i, respectively.

The correct answer is 58 to 62.

GATE 2025 official key: 58 to 62 mol% A. At the azeotrope, γ_A/γ_B = P°_B/P°_A = 72.7/87 ≈ 0.836, so ln(0.836) ≈ −0.18 = 0.9(1−2x_A), giving x_A ≈ 0.60, i.e., 60 mol% A.

GATE 2024, Q14

A homogeneous azeotropic distillation process separates an azeotropic AB binary feed using a heavy entrainer, E, as shown in the figure. The loss of E in the two product streams is negligible so that E circulates around the process in a closed circuit. For a distillation column with fully specified feed(s), given operating pressure, a single distillate stream and a single bottoms stream, the steady-state degrees of freedom equals 2. For the process in the figure with a fully specified AB feed stream and given column operating pressures, the steady-state degrees of freedom equals

The correct answer is C, 5.

GATE 2024 official key: (C). Combining the base 2 DOF per column across the two interconnected columns and accounting for the closed entrainer recycle loop (which removes one otherwise-free specification) gives a net steady-state DOF of 5.

GATE 2024, Q42

A simple distillation column separates a binary mixture of A and B. The relative volatility of A with respect to B is 2. The steady-state composition of A in the vapour leaving the 1st, 2nd and 3rd trays in the rectifying section are 94, 90 and 85 mol%, respectively. For ideal trays and constant molal overflow, the reflux-to-distillate ratio is

The correct answer is B, 2.7.

GATE 2024 official key: (B). Using equilibrium x=y/(α−(α−1)y) to get x₁=0.8868, x₂=0.8182, and the rectifying operating line y_{n+1}=(L/V)x_n+(D/V)x_D between consecutive trays (with x_D=y1=0.94) gives L/V≈0.729, so L/D=(L/V)/(1−L/V)≈2.7.

GATE 2026, Q35

Using single step trapezoidal rule, the value of ∫₀^0.5 (1 + 16x − 20x²) dx is ______ (rounded off to two decimal places).

The correct answer is 1.24 to 1.26.

GATE 2026 official key: 1.24 to 1.26. f(0)=1, f(0.5)=1+8−5=4. Single-interval trapezoidal rule: (0.5/2)(f(0)+f(0.5)) = 0.25×5 = 1.25.

GATE 2025, Q46

The Newton-Raphson method is used to find the root of f(x) ≡ x² − x − 1 = 0. Starting with an initial guess x_(0) = 1, the second iterate x_(2) is ____ (rounded off to 2 decimal places).

The correct answer is 1.65 to 1.69.

GATE 2025 official key: 1.65 to 1.69. x⁽¹⁾ = 1 − f(1)/f'(1) = 1 − (−1)/1 = 2. x⁽²⁾ = 2 − f(2)/f'(2) = 2 − 1/3 ≈ 1.667.

GATE 2024, Q50

The Newton-Raphson method is used to solve f(x) = 0, where f(x) = eˣ − 5x. If the initial guess x⁽⁰⁾ = 1.0, the value of the next iterate, x⁽¹⁾, rounded off to 2 decimal places, is ______

The correct answer is -0.01 to 0.01.

GATE 2024 official key: −0.01 to 0.01. f(1)=e−5≈−2.2817, f'(x)=eˣ−5, f'(1)≈−2.2817. x⁽¹⁾ = 1 − (−2.2817)/(−2.2817) = 1 − 1 = 0.00.

GATE 2026, Q12

In the P&ID shown below, which one of the following is the function of PAH in the process?

The correct answer is B, to alert when high pressure is detected in the tank.

GATE 2026 official key: (B). PAH = Pressure Alarm High, it triggers an alert when vessel pressure exceeds a high setpoint.

GATE 2025, Q24

The vortex shedding meter is primarily used for measuring

The correct answer is A, Fluid Flow Rate.

GATE 2025 official key: (A). A bluff body sheds vortices at a frequency proportional to flow velocity (Strouhal relation), making it a fluid flow rate meter.

GATE 2024, Q19

The ratio of the activation energy of a chemical reaction to the universal gas constant is 1000 K. The temperature-dependence of the reaction rate constant follows collision theory (k ∝ T^(1/2)·e^(−Ea/RT)). The ratio of the rate constant at 600 K to that at 400 K is

The correct answer is A, 2.818.

GATE 2024 official key: (A). k₆₀₀/k₄₀₀ = √(600/400) × exp(1000/400 − 1000/600) = √1.5 × exp(0.833) ≈ 1.225 × 2.300 ≈ 2.818.