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Below are 110 MCQs (10 per subject) — Theoretical, slightly difficult GATE style questions based on Basics fundamentals. Each question is followed by options (a–d), the correct answer, and a short explanation.
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ENGINEERING MATHEMATICS — 10 QUESTIONS
- A 2×2 matrix A has eigenvalues 2 and 5. For vector b ≠ 0, the system A x = b has a unique solution for every b. Which statement is correct?
a) A is singular.
b) det(A) = 0.
c) A is invertible.
d) A has a zero eigenvalue.
Correct Answer: c
Explanation: Distinct nonzero eigenvalues imply det(A)=product=10 ≠0 so A is invertible; hence unique solution exists. - For f(x)=e^{2x} approximated by Taylor series about x=0 up to second order, the remainder term R_2(x) behaves as:
a) O(x^2)
b) O(x^3)
c) O(x)
d) O(1)
Correct Answer: b
Explanation: Truncating after second-order (terms up to x^2) leaves next term proportional to x^3 (third-order), so remainder is O(x^3). - The ODE y” + y = δ(t − t0) (impulse at t0) with zero initial conditions yields solution expressible by:
a) Convolution with sine kernel (Green’s function)
b) Polynomial solution only
c) No causal solution
d) Exponential blow-up
Correct Answer: a
Explanation: Linear constant-coefficient second-order ODE solution is convolution of impulse with system’s impulse response (sin kernel). - For function φ(x,y)=x^2 y + sin(xy), directional derivative at (1,0) in direction (1,1)/√2 equals:
a) 0
b) 2/√2
c) 1/√2
d) 3/√2
Correct Answer: c
Explanation: ∇φ = (2xy + y cos(xy), x^2 + x cos(xy)). At (1,0): ∇φ=(0,1). Directional derivative = ∇φ · (1,1)/√2 = 1/√2. - A square system Ax=b where A is symmetric positive definite. Conjugate Gradient (CG) method will:
a) Diverge for SPD matrices
b) Converge in at most n iterations in exact arithmetic
c) Require preconditioning to converge at all
d) Solve eigenvalue problem instead of linear system
Correct Answer: b
Explanation: CG for SPD matrices converges in at most n steps (n=dimension) in exact arithmetic. - The principal value integral ∫_{−π}^{π} f(x) dx with f periodic can be expanded in Fourier series. The Gibbs phenomenon appears near:
a) Smooth maxima/minima only
b) Discontinuities of function or derivative
c) Inflection points only
d) Where f is analytic
Correct Answer: b
Explanation: Gibbs overshoot occurs at jump discontinuities (or discontinuous derivatives) in periodic functions’ Fourier approximations. - For the eigenvalue problem of Laplacian ∇^2 φ + λ φ = 0 on 0<x<L with φ(0)=φ(L)=0, eigenvalues λ_n scale as:
a) n^2 (π^2/L^2)
b) n (π/L)
c) constant independent of n
d) exponential in n
Correct Answer: a
Explanation: 1-D Dirichlet Laplacian eigenvalues λ_n = (nπ/L)^2 scale as n^2. - Using trapezoidal rule to integrate a smooth periodic function over one period, error typically:
a) O(h)
b) O(h^2) but can be superconvergent for periodic analytic functions
c) O(1) independent of h
d) Exponential growth with decreasing h
Correct Answer: b
Explanation: Trapezoidal rule is O(h^2) generally; for periodic analytic integrands it can show spectral accuracy (fast convergence). - For random variable X with mean μ and variance σ^2, Chebyshev’s inequality states P(|X−μ| ≥ kσ) ≤:
a) 1/k
b) 1/k^2
c) e^{−k}
d) 1/(k√2π)
Correct Answer: b
Explanation: Chebyshev gives ≤ 1/k^2. - A boundary-value ODE solved by finite-difference gives a linear system with dominant diagonal. Best iterative solver choice is:
a) Jacobi always
b) Gauss–Seidel or SOR for faster convergence
c) Direct LU never recommended
d) Randomized methods only
Correct Answer: b
Explanation: For diagonally dominant systems, Gauss–Seidel or SOR typically converges faster than Jacobi; direct LU acceptable but iterative preferred for large sparse problems.
PROCESS CALCULATIONS & THERMODYNAMICS — 10 QUESTIONS
- A continuous steady-state process has a recycle stream. If fresh feed doubled and product composition remains unchanged, what must be true about recycle ratio R?
a) R decreases to maintain composition.
b) R remains unchanged.
c) R increases proportionally.
d) R must be zero.
Correct Answer: a
Explanation: To maintain same outlet composition with higher fresh feed, recycle must reduce fraction of recycled material so that overall mix stays same. - A binary ideal solution A–B at T has vapor-phase composition yA related to liquid xA by Raoult’s law. If vapor pressure PA°(T) >> PB°(T), at given xA the dew point:
a) Approaches pure A boiling point
b) Approaches pure B boiling point
c) Independent of PA° and PB°
d) Equals arithmetic mean of component bps
Correct Answer: a
Explanation: If PA° much larger, A more volatile; dew point dominated by A; behaves close to pure A. - For an open steady-flow device, first law gives enthalpy balance. If kinetic and potential energy changes negligible, then ΔH = Q − W. For an adiabatic turbine, which term ≈0?
a) Q only
b) W only
c) ΔH only
d) All nonzero
Correct Answer: a
Explanation: Adiabatic implies Q≈0; turbine does work so ΔH = −W. - Fugacity f of a real gas approaches which expression in low-pressure limit?
a) f → P (ideal gas)
b) f → constant independent of P
c) f → P^2
d) f undefined at low P
Correct Answer: a
Explanation: At low P gases approach ideal behavior so fugacity ≈ pressure. - For a closed system undergoing reversible isothermal compression of ideal gas, ΔS =?
a) 0
b) nR ln(V2/V1)
c) nC_v ln(T2/T1)
d) negative irrespective of path
Correct Answer: b
Explanation: Isothermal reversible: ΔS = ∫ dQ_rev/T = nR ln(V2/V1). - In a VLE flash of binary mixture, overall mole fraction z fixed. If distillate composition xD equals 0.9 and bottoms xB 0.1, then feed z=0.5—what is approximate reflux ratio effect?
a) Higher reflux yields purer distillate (approaching xD)
b) Reflux has no impact on compositions at steady-state
c) Lower reflux increases number of stages but not purity
d) Reflux only affects energy consumption but not separation
Correct Answer: a
Explanation: Reflux increases internal liquid flow and sharpens separation, improving purity for given stages. - Residual properties (e.g., H^R) at given T,P measure deviation from ideal gas. Residual enthalpy H^R is zero when:
a) Real gas equals ideal gas behavior (low pressure limit)
b) At critical point always
c) For incompressible liquids only
d) Never zero
Correct Answer: a
Explanation: Residual properties vanish when gas behaves ideally (P→0). - For an endothermic reversible reaction at equilibrium, increasing temperature shifts equilibrium toward:
a) Products (Le Chatelier)
b) Reactants
c) No change
d) Depends on activation energy only
Correct Answer: a
Explanation: For endothermic, heat acts as reactant; raising T favors product formation. - A steady-state evaporator removes water from solution. If molar flow of feed is F with concentration xF, vapor flow V, and bottoms B, material balance for solute gives:
a) F xF = B xB
b) F = B + V must hold but not solute balance
c) Mass balance only for solvent
d) Energy balance replaces solute balance
Correct Answer: a
Explanation: Solute (non-volatile) conserved: F xF = B xB. - The Joule–Thomson coefficient μJT = (∂T/∂P)_H for real gases can be positive or negative. For ideal gas μJT =:
a) 0
b) positive
c) negative
d) undefined
Correct Answer: a
Explanation: Ideal gas enthalpy depends only on T, so no temperature change with pressure at constant enthalpy → μJT=0.
FLUID MECHANICS — 10 QUESTIONS
- Flow through long circular pipe is laminar at Re=500. For fully developed laminar flow, velocity profile is parabolic; doubling pipe radius with same pressure gradient yields centreline velocity change by factor:
a) 2
b) 4
c) 8
d) 16
Correct Answer: d
Explanation: For laminar Hagen–Poiseuille, volumetric flow ∝ R^4 for same pressure gradient; centreline velocity scales similarly → factor 16. - A sudden contraction in duct causes vena contracta. For incompressible flow, which phenomenon increases downstream loss?
a) Flow separation and eddies → energy loss
b) Viscosity drop → energy gain
c) Static pressure increase only
d) No loss if flow is steady
Correct Answer: a
Explanation: Contraction causes separation and vortices causing head loss. - Darcy friction factor for fully rough turbulent flow depends mainly on:
a) Reynolds number only
b) Relative roughness only (independent of Re sufficiently high)
c) Fluid compressibility only
d) Flow acceleration only
Correct Answer: b
Explanation: In fully rough regime, friction factor independent of Re and controlled by relative roughness. - For two-phase bubbly flow in a vertical column at low gas holdup, the slip velocity between phases is dominated by:
a) Bubble rise due to buoyancy and drag balance
b) Compressibility of liquid phase
c) Heat transfer only
d) Chemical reaction rates
Correct Answer: a
Explanation: Bubble rise determined by buoyancy versus drag; at low holdup bubbles rise relative to liquid. - For flow in packed bed, Ergun equation combines viscous and inertial terms. If particle size decreases keeping bed porosity constant, pressure drop per unit length:
a) Increases (inversely with d_p and d_p^2 terms)
b) Decreases
c) Unchanged
d) Oscillatory with d_p
Correct Answer: a
Explanation: Ergun includes terms proportional to 1/d_p and 1/d_p^2 so smaller particles → higher ΔP. - A fluid with viscosity μ and density ρ flows over a flat plate. Boundary layer thickness δ scales as:
a) (x/√Re_x) where Re_x = ρ U x / μ
b) x * Re_x
c) independent of x
d) inverse of x
Correct Answer: a
Explanation: For laminar boundary layer δ ~ x / sqrt(Re_x) ~ (μ x / (ρ U))^{1/2}. - Cavitation in pumps occurs when local pressure drops below:
a) Liquid vapour pressure
b) Ambient atmospheric pressure always
c) Hydraulic grade line only
d) Pump suction pressure higher than discharge
Correct Answer: a
Explanation: Cavitation when local pressure < vapour pressure causing vapor pockets. - For compressible flow through a converging nozzle, choking occurs when Mach number at throat:
a) Reaches 1
b) Exceeds 2 only
c) Always subsonic
d) Equals 0.5
Correct Answer: a
Explanation: Choked flow when M=1 at throat; mass flow becomes independent of downstream pressure. - In laminar flow between parallel plates separated by 2h, driven by constant pressure gradient, the velocity profile is:
a) Parabolic in y with zero at walls
b) Uniform plug profile
c) Sinusoidal
d) Exponential decay
Correct Answer: a
Explanation: Poiseuille flow between plates yields parabolic profile. - For flow measurement by orifice meter, Reynolds number effect on discharge coefficient Cd is significant when:
a) Re is low (transition from laminar influences flow separation)
b) Re is always irrelevant
c) Cd increases unbounded with Re
d) Cd is only function of fluid temperature
Correct Answer: a
Explanation: At low Re separation/viscous effects alter Cd; at high Re Cd asymptotes.
MECHANICAL OPERATIONS — 10 QUESTIONS
- In size reduction by crushing, energy required per unit mass often follows Rittinger’s and Kick’s laws. For fine grinding dominant mechanism is:
a) Rittinger’s law (energy ∝ new surface area)
b) Kick’s law (energy ∝ log size reduction ratio)
c) Bond’s law only for coarse crushing
d) Energy independent of particle size
Correct Answer: a
Explanation: Rittinger applies for fine grinding where surface generation dominates. - A settling tank treating slurry shows particle hindered settling at high solids concentration. Compared to free settling, hindered settling velocity:
a) Decreases due to hydrodynamic interference
b) Increases due to crowding
c) Remains equal
d) Becomes negative
Correct Answer: a
Explanation: In hindered regime, interactions reduce settling velocity. - For filtration with constant pressure, cake builds. If cake resistance increases linearly with time, filtrate flow rate:
a) Decreases with time (inverse relation)
b) Increases linearly
c) Unchanged
d) Oscillatory
Correct Answer: a
Explanation: Increasing resistance lowers flow rate for constant pressure per Darcy’s law. - In centrifugation for solids removal, G-factor (centrifugal acceleration) scales with:
a) ω^2 r / g (i.e., rotational speed squared)
b) ω r only
c) independent of ω
d) inversely with radius
Correct Answer: a
Explanation: Centrifugal acceleration ∝ ω^2 r; normalized by g gives G-factor. - Cyclone separation efficiency for fine particles improves by:
a) Increasing inlet tangential velocity and decreasing diameter
b) Increasing cyclone diameter only
c) Removing vortex finder
d) Increasing gas viscosity
Correct Answer: a
Explanation: Higher tangential velocity and smaller cyclone give higher centrifugal forces and better capture. - In a fluidized bed, minimum fluidization velocity Umf depends primarily on:
a) Particle diameter, density difference, and fluid viscosity
b) Reaction kinetics only
c) Bed height only
d) Gravity inverted
Correct Answer: a
Explanation: Umf from balance of drag and weight—function of particle size/density and fluid properties. - For crushing in jaw vs hammer mill, which produces narrower PSD (particle size distribution) for same top size?
a) Jaw crusher gives broader, hammer mill may produce more fines — depends on mechanism
b) Both identical always
c) Hammer mill produces no fines
d) Jaw generates monodisperse output
Correct Answer: a
Explanation: Compression crushers (jaw) give broader distribution; impact mills produce more fines — depends on operating parameters. - For mixing viscous fluids in stirred tank, power number correlates with Reynolds number; at low Re (laminar), mixing time:
a) Is large and independent of impeller speed squared scaling
b) Decreases strongly with speed even in laminar
c) Is minimal and constant
d) Negative correlation with viscosity only
Correct Answer: a
Explanation: In laminar regime, mixing dominated by viscous diffusion and scales differently; power number varies as Re^{-1}. - In filtration cake formation, specific cake resistance α depends on:
a) Particle size, porosity and compressibility of cake
b) Only filter medium area
c) Temperature only
d) Stirring speed
Correct Answer: a
Explanation: α relates to cake microstructure — particle size, packing/porosity and compressibility under pressure. - In pneumatic conveying of solids, dilute-phase conveying needs:
a) Higher gas velocity to keep particles suspended compared to dense-phase
b) Lower gas velocity than dense-phase
c) No gas, just gravity
d) Fixed velocity regardless of system
Correct Answer: a
Explanation: Dilute-phase keeps particles entrained and needs higher velocities.
- For steady one-dimensional conduction through composite slab with two layers having thermal conductivities k1 and k2 and thickness L1 and L2, overall thermal resistance is:
a) L1/k1 + L2/k2
b) (L1 + L2)/(k1 + k2)
c) (k1 L2 + k2 L1)
d) Product of Ls only
Correct Answer: a
Explanation: Resistances in series add: R = L1/k1 + L2/k2. - For external forced convection over a cylinder at moderate Re, heat transfer coefficient h correlates with Nu_D which depends on:
a) Reynolds number and Prandtl number (Nu = f(Re,Pr))
b) Only Prandtl number
c) Only material conductivity
d) Independent of flow conditions
Correct Answer: a
Explanation: Convective Nu correlations for external flow are functions of Re and Pr. - In a finned surface, when fin tip convective loss is negligible, adding more fin length beyond certain value:
a) Produces diminishing returns due to axial conduction along fin
b) Linearly increases heat removal forever
c) Reduces base temperature always
d) Makes finoretical invalid
Correct Answer: a
Explanation: Fin effectiveness saturates due to increased conduction resistance along fin. - For a plate heat exchanger using LMTD method, LMTD becomes invalid if:
a) Heat capacity rates vary significantly along exchanger (phase change or variable properties)
b) Flow is purely countercurrent with constant properties
c) For steady counterflow without phase change
d) For identical inlet temperatures
Correct Answer: a
Explanation: LMTD assumes constant capacity rates; with phase change or varying properties, correction factors needed. - Radiative heat transfer between two large parallel grey plates (ε1, ε2) separated by vacuum: net heat flux depends on:
a) (1/ε1 + 1/ε2 − 1) factor and difference of T^4
b) Only emissivity of plate1
c) Only temperature difference linear term
d) Independent of emissivity if one is blackbody
Correct Answer: a
Explanation: Two-surface radiation exchange factor includes (1/ε1 + 1/ε2 −1) in denominator times σ(T1^4 − T2^4). - Boiling heat transfer in pool boiling: Transition from nucleate to film boiling at critical heat flux leads to:
a) Sudden decrease in heat transfer coefficient (dangerous)
b) Continuous increase in heat transfer
c) No change at critical point
d) Only change in surface roughness
Correct Answer: a
Explanation: At CHF, vapor blankets surface leading to film boiling with much lower HTC → temperature runaway risk. - For a counterflow heat exchanger with equal heat capacity rates (C_min=C_max), the effectiveness ε is:
a) ε = 1 − exp(−NTU) / (1+exp(−NTU)) simplifying to tanh(NTU/2) relationship
b) ε independent of NTU
c) ε = NTU always
d) ε = 0 always
Correct Answer: a
Explanation: For counterflow with equal C, ε = tanh(NTU). - For transient conduction in semi-infinite solid subjected to a sudden surface temperature change, temperature at depth x and time t depends on error function erf( x / (2√αt) ). For large t, penetration depth:
a) ~ √(α t)
b) ~ α t
c) ~ t^2
d) independent of t
Correct Answer: a
Explanation: Thermal diffusion length scales as √(α t). - In convection correlations, Prandtl number Pr = ν/α (momentum to thermal diffusivity). For Pr >> 1, thermal boundary layer relative to velocity boundary layer is:
a) Thinner (thermal diffuses slower → thinner)
b) Thicker
c) Equal thickness always
d) Inverse of Reynolds number
Correct Answer: a
Explanation: High Pr → thermal diffusivity low → thermal boundary layer thinner than velocity BL. - For design of shell-and-tube heat exchanger, baffle spacing too large causes:
a) Poor shell-side heat transfer due to bypassing and reduced turbulence
b) Increased pressure drop always beneficial
c) Enhanced heat transfer irrespective of spacing
d) No impact on flow pattern
Correct Answer: a
Explanation: Large spacing reduces crossflow and turbulence, permitting bypass and lowering heat transfer.
- In a single-stage countercurrent gas absorption, if gas enters lean and leaves rich, the driving force for transfer depends on:
a) Difference between gas phase partial pressure and equilibrium partial pressure at liquid composition
b) Absolute partial pressure only
c) Liquid viscosity only
d) Gas molecular weight only
Correct Answer: a
Explanation: Mass transfer driving force is difference between bulk and equilibrium concentrations/partial pressures. - For distillation with ideal stages, McCabe-Thiele analysis assumes:
a) Equilibrium stage operation and constant molar overflow
b) Non-equilibrium mass transfer only
c) Variable latent heats always
d) No reflux allowed
Correct Answer: a
Explanation: McCabe–Thiele uses equilibrium stages and constant molar overflow to draw operating lines. - In film theory for gas–liquid transfer, the overall mass transfer coefficient K_G relates to individual film coefficients by:
a) 1/K_G = 1/k_G + H/ (k_L) where H is Henry’s law constant (gas–liquid interface relation)
b) K_G = k_G + k_L always
c) Independent of Henry’s constant
d) Inversely proportional to Schmidt number only
Correct Answer: a
Explanation: Resistances in series in gas and liquid films combine; Henry’s law links concentrations. - For plate evaporator operation, if boiling point elevation increases with concentration, the number of effects required for specified economy:
a) Increases (reduces possible vapor reuse effectiveness)
b) Decreases
c) Unchanged
d) Dependent only on feed temperature
Correct Answer: a
Explanation: BPE reduces driving force per effect; need more effects to achieve same evaporation. - In adsorption using Langmuir isotherm, at high concentrations surface coverage θ approaches:
a) 1 (monolayer saturation)
b) 0
c) Proportional to pressure linearly forever
d) Infinite
Correct Answer: a
Explanation: Langmuir limits to monolayer capacity. - For drying a porous solid under constant-rate period, surface remains at wet-bulb temperature. Transition to falling-rate occurs when:
a) Surface becomes dry and internal diffusion controls rate
b) Air temperature drops below wet bulb always
c) Constant-rate continues indefinitely
d) Only at zero humidity
Correct Answer: a
Explanation: Constant-rate while free moisture at surface; falling-rate when surface dries and internal transport limits. - In packed column distillation, flooding occurs due to:
a) Excessive vapor velocity causing liquid hold-up and pressure rise
b) Too low liquid flow leading to dry packing only
c) Perfect countercurrent with no limits
d) Packing chemical incompatibility only
Correct Answer: a
Explanation: Flooding when vapor velocity high enough to prevent liquid flow down — causes high pressure drop. - For binary gas diffusion through stagnant gas, Fick’s law in multicomponent systems requires correction; effective diffusivity scales approximately inversely with:
a) Total pressure for gases (D ∝ 1/P)
b) Temperature only
c) Molecular size independent
d) Viscosity only
Correct Answer: a
Explanation: Gas-phase binary diffusivity D_AB ∝ T^{3/2}/(P √M), so inversely proportional to pressure. - In countercurrent liquid–liquid extraction, the number of theoretical stages required decreases if distribution coefficient:
a) Increases (favors solute transfer to extractant)
b) Decreases
c) Equals 1 always
d) Independent of stage number
Correct Answer: a
Explanation: Higher distribution coefficient shifts solute more to extractant per stage → fewer stages required. - For crystallization by cooling, supersaturation control is critical. High nucleation vs growth rates produce:
a) Fine crystals (many nuclei) vs coarse crystals (dominated by growth)
b) Coarse always
c) No crystals if rate too high
d) Crystal size independent of kinetics
Correct Answer: a
Explanation: High nucleation yields many small crystals; controlled nucleation/growth yields larger crystals.
CHEMICAL REACTION ENGINEERING (CRE) — 10 QUESTIONS
- A first-order irreversible reaction A → products in a PFR with constant density: doubling residence time τ doubles conversion from 0.5 to:
a) 0.75
b) 1.0
c) 0.25
d) 0.66
Correct Answer: a
Explanation: For first-order, X = 1 − exp(−kτ). If at τ gives X=0.5 → exp(−kτ)=0.5 → kτ=ln2. At 2τ, exp(−2kτ)=exp(−2ln2)=1/4 → X=1−1/4=0.75. - For irreversible second-order reaction A + B → products with equal initial concentrations C0 in batch reactor, concentration-time relation follows:
a) 1/C = 1/C0 + kt
b) ln(C/C0) = −kt
c) C = C0 exp(−kt)
d) 1/C^2 = …
Correct Answer: a
Explanation: Second-order with equal stoichiometry gives 1/C = 1/C0 + kt. - For an isothermal CSTR carrying a first-order reaction, space time τ required to achieve conversion X relates to plug flow space time τ_PFR for same X as:
a) τ_CSTR > τ_PFR for same X (except X→0 or X→1?)
b) τ_CSTR = τ_PFR always
c) τ_CSTR < τ_PFR always
d) No relation
Correct Answer: a
Explanation: For same conversion, PFR is more efficient (less τ) than CSTR for first-order; so τ_CSTR > τ_PFR. - Residence Time Distribution (RTD) measured by step tracer in a reactor shows non-ideal behavior. A broad E(t) indicates:
a) Large spread in residence times and potential back-mixing
b) Perfect plug flow
c) Single residence time only
d) No effect on conversion
Correct Answer: a
Explanation: Broad distribution indicates varying particle times and mixing/backflow reducing ideality. - For heterogeneous catalytic reactions, effectiveness factor η accounts for:
a) Internal diffusion limitations inside porous catalyst decreasing observed rate
b) Temperature gradients only
c) Reaction mechanism changes only
d) Catalyst color change
Correct Answer: a
Explanation: η = observed rate/ rate if entire catalyst at surface concentration; accounts for pore diffusion limitations. - For a reversible reaction A ⇌ B with equilibrium constant K_eq, infinite residence time in closed batch will yield conversion determined by:
a) Equilibrium composition given by K_eq and stoichiometry
b) Zero conversion always
c) Complete conversion for any K_eq
d) Depends only on catalyst presence
Correct Answer: a
Explanation: At infinite time, reaction reaches equilibrium—extent determined by K_eq. - In autocatalytic reactions, reaction rate increases with extent initially. A sign of autocatalysis in concentration–time profile is:
a) Sigmoidal (S-shaped) curve indicating induction then acceleration
b) Pure exponential decay
c) Linear decrease always
d) No dependence on concentration
Correct Answer: a
Explanation: Autocatalytic systems show induction (slow), then rapid increase then leveling → S-curve. - For non-isothermal reactor, hot-spot formation is hazardous if reaction is:
a) Highly exothermic with low thermal conductivity and insufficient heat removal
b) Endothermic only
c) Zero-order at all temperatures
d) Only homogeneous gas-phase
Correct Answer: a
Explanation: Exothermicity + poor heat removal can cause runaway and hot spots. - Turnover frequency (TOF) for heterogeneous catalyst is defined as:
a) Moles of reactant converted per active site per unit time
b) Mole fraction of catalyst active sites only
c) Pressure normalized rate only
d) Independent of active site density
Correct Answer: a
Explanation: TOF quantifies intrinsic catalytic activity per site per time. - For Langmuir–Hinshelwood mechanism (both reactants adsorb), reaction rate typically depends on:
a) Surface coverages of both species and adsorption constants
b) Gas-phase concentrations only always linear
c) Catalyst only as inert support
d) Only temperature, not adsorption
Correct Answer: a
Explanation: LH mechanism rate expression includes adsorption equilibria and surface coverages.
INSTRUMENTATION & PROCESS CONTROL — 10 QUESTIONS
- A process variable exhibits unstable oscillatory behavior. Root locus shows poles crossing into right-half plane as gain increases. Addition of derivative action (D) in PID typically:
a) Improves damping and reduces overshoot (adds phase lead)
b) Always destabilizes system
c) Removes steady-state error only
d) Converts system to first-order only
Correct Answer: a
Explanation: Derivative provides predictive action adding phase lead, improving damping/overshoot. - A sensor with time constant τ_s is in series with process of time constant τ_p. For accurate faster control, sensor dynamics ideally:
a) τ_s << τ_p (sensor much faster than process)
b) τ_s >> τ_p
c) τ_s = ∞
d) τ_s = 0 recommended but impossible
Correct Answer: a
Explanation: Faster sensor captures changes quickly; slow sensor lags control action and degrades performance. - Bode plot of open-loop shows phase margin negative at crossover frequency. Which conclusion?
a) Closed loop likely unstable (insufficient phase margin)
b) System has good robustness
c) No relation to stability
d) Nyquist not applicable
Correct Answer: a
Explanation: Negative phase margin indicates phase lag exceeds 180° at gain crossover → likely instability. - For first-order plus dead-time process, Smith predictor control structure primarily compensates for:
a) Time delay (dead time), improving loop response
b) Process gain only
c) Sensor noise only
d) Nonlinearity in actuator
Correct Answer: a
Explanation: Smith predictor uses model to predict process output over dead time and compensate delay. - A thermocouple measures temperature by Seebeck effect. Its accuracy is reduced by:
a) Contact resistance and thermal lag at measurement junction
b) Increasing ambient pressure only
c) Magnetic fields only
d) Catalyst poisoning
Correct Answer: a
Explanation: Poor contact and junction lag degrade reading and response time. - In frequency response, Nyquist plot encirclement of −1 point determines:
a) Closed-loop stability when combined with open-loop pole count (Nyquist criterion)
b) Mass balance in reactor
c) Steady-state gain only
d) Bode plot invalidation
Correct Answer: a
Explanation: Nyquist criterion relates encirclements of −1 to closed-loop stability. - A pressure transmitter calibrated linearly produces 4–20 mA proportional to 0–100 kPa. If loop reading is 12 mA, estimated pressure:
a) 50 kPa
b) 100 kPa
c) 0 kPa
d) 25 kPa
Correct Answer: a
Explanation: 4 mA →0 kPa, 20 mA →100 kPa; 12 mA is midpoint →50 kPa. - For a PI controller in cascade control where inner loop is fast, outer loop benefits by:
a) Inner loop rejecting disturbances quickly; outer loop handles setpoint changes giving overall tighter control
b) Slowing down outer loop only
c) Removing need for sensors entirely
d) Always destabilizing the plant
Correct Answer: a
Explanation: Cascade control uses inner fast loop to stabilize and reject disturbances, improving outer loop performance. - A transmitter-sensor pair exhibits Gaussian white noise. To improve signal-to-noise ratio for slow process, recommended action:
a) Apply low-pass filtering or increase measurement averaging time
b) Increase controller derivative gain
c) Reduce measurement resolution
d) Increase sampling rate to infinity
Correct Answer: a
Explanation: Low-pass filtering/averaging reduces high-frequency noise; derivative amplifies noise. - For model predictive control (MPC), primary advantage over PID is:
a) Ability to handle multi-variable constraints and anticipate future changes via model optimization
b) Always simpler to tune than PID
c) No requirement for a process model
d) Only suited for linear steady-state systems
Correct Answer: a
Explanation: MPC optimizes future control moves considering constraints and multivariable interactions using a model.
PLANT DESIGN & ECONOMICS — 10 QUESTIONS
- When sizing a storage tank for liquid feed with variable demand, safety factor accounts for:
a) Surge, inventory for downtime, and emergency reserves beyond nominal capacity
b) Only corrosion allowance
c) Only color of tank coating
d) Tank shape solely
Correct Answer: a
Explanation: Design includes operational surges, downtime inventory and contingencies. - Discounted cash flow uses net present value (NPV). A project with positive NPV at chosen discount rate means:
a) Project adds value and is financially acceptable
b) Must be rejected regardless
c) Equal to payback period zero
d) Independent of discount rate choice
Correct Answer: a
Explanation: Positive NPV ⇒ present value of inflows > outflows at discount rate ⇒ acceptable. - For piping layout, pressure drop minimization vs capital cost trade-off often leads to:
a) Selecting larger diameter pipe increasing capex but reducing operating cost (energy)
b) Always smallest diameter to minimize capex
c) Material has no effect on pressure drop
d) Only pump selection matters, not diameter
Correct Answer: a
Explanation: Larger diameter lowers velocity and ΔP leading to energy savings but higher material cost—trade-off optimization required. - In equipment scale-up from lab to pilot, Reynolds and other similarity numbers must be matched to preserve:
a) Hydrodynamic and heat/mass transfer similarity (Re, Pr, Fr etc. as appropriate)
b) Only geometric similarity, nothing else
c) Scaling independent of physics
d) Chemical composition only
Correct Answer: a
Explanation: Dynamic similarity requires dimensionless numbers matching for comparable behavior. - Depreciation by straight-line method implies:
a) Equal annual depreciation expense over useful life
b) Depreciation accelerating over time
c) No depreciation at all
d) Depreciation equals salvage value always
Correct Answer: a
Explanation: Straight-line spreads cost equally across life. - For cost estimation, Lang factor approach multiplies purchased equipment cost by factor to estimate total installed cost; Lang factor is crude because:
a) It ignores plant-specific details like material, complexity and site conditions
b) It is exact for all processes
c) Suitable only for academic problems
d) Only valid in metric units
Correct Answer: a
Explanation: Lang factors are rough multipliers and not detailed estimates. - In facility layout, minimizing total material handling cost often leads to:
a) Locating high-flow units closer to each other (minimize transport)
b) Random placement of equipment
c) Maximizing distances always preferred
d) Ignoring safety and utility lines
Correct Answer: a
Explanation: Minimizing logistics cost groups frequently interacting units nearby. - Safety relief valve set pressure must be:
a) At or below maximum allowable working pressure with consideration to accumulation and codes (e.g., API/ASME)
b) Above ultimate tensile strength always
c) Equal to atmospheric pressure always
d) Set arbitrarily by operator
Correct Answer: a
Explanation: Relief devices adhere to design codes with set pressure below MAWP and account for transient accumulation. - For process optimization, objective function maximizing profit subject to material balances and constraints typically solved by:
a) Nonlinear programming (NLP) methods when relations nonlinear
b) Only trial-and-error ever
c) Linear methods always suffice
d) Ignoring constraints gives optimum
Correct Answer: a
Explanation: Complex plant economics with nonlinearities require NLP; LP only for linear problems. - In estimating heat exchanger area, U (overall heat transfer coefficient) uncertainty leads to area design margin by safety factor because:
a) Small change in U can cause significant change in required area since A = Q/(U ΔT_lm)
b) U variations negligible always
c) Area independent of U
d) U only matters for radiation
Correct Answer: a
Explanation: Area inversely proportional to U; uncertainty in U handled via margin or conservative design.
CHEMICAL TECHNOLOGY — 10 QUESTIONS
- In steam reforming of methane to syngas, catalyst deactivation is often due to:
a) Carbon deposition (coking) and sintering at high temperatures
b) Growth of catalyst improving activity
c) Only heat transfer limitations
d) Pressure alone causing deactivation
Correct Answer: a
Explanation: Coking and sintering reduce active surface and block pores, deactivating catalysts. - For ammonia synthesis (Haber process), equilibrium favors ammonia at:
a) High pressure and moderate temperature (Le Chatelier: reduce moles)
b) Low pressure always
c) Extremely high temperature only
d) No dependence on T or P
Correct Answer: a
Explanation: N2 + 3H2 → 2NH3 reduces moles; high P shifts equilibrium to product; high T disfavors exothermic synthesis. - In petroleum refining, catalytic cracking primarily increases yield of:
a) Light distillates (gasoline-range hydrocarbons) from heavy fractions
b) Heavy fuel oil only
c) Produces only coke without distillate
d) Converts to pure methane only
Correct Answer: a
Explanation: Catalytic cracking breaks long chains to shorter gasoline-range molecules. - In polymerization (free-radical), chain-transfer reactions affect:
a) Molecular weight distribution and average chain length
b) Catalyst color only
c) Polymer crystallinity independent of chemistry
d) Only melt index measured but not chain length
Correct Answer: a
Explanation: Chain-transfer terminates growing radical altering molecular weight distribution. - For sulfuric acid production via contact process, vanadium pentoxide catalyst promotes:
a) Oxidation of SO2 to SO3 (heterogeneous catalysis)
b) Hydrogenation of SO3 to SO2
c) Serves as inert support only
d) Absorbs SO3 irreversibly
Correct Answer: a
Explanation: V2O5 catalyzes oxidation step in contact process. - In fertilizer industry, urea is produced by reaction of ammonia and carbon dioxide; major downstream issue in urea prilling is:
a) Formation of fine dust and humidity leading to caking
b) Urea inertness making prilling unnecessary
c) No heat effects during prilling
d) Urea always liquid at ambient
Correct Answer: a
Explanation: Prills can cake under humidity and dust generation is concern. - In petrochemical ethylene production by steam cracking, yield of ethylene increases by:
a) Increasing severity (higher temperature, shorter residence time) optimizing cracking conditions
b) Decreasing temperature always
c) Lowering steam to feed ratio only
d) Adding oxygen to feed
Correct Answer: a
Explanation: Higher T and short crack time favor monomers; steam dilutes and reduces coke but conditions tuned for yield. - In paper/pulp industry, Kraft process uses alkaline pulping to:
a) Remove lignin while preserving cellulose fibers
b) Convert cellulose to monomers only
c) Paper produced directly from raw wood without chemicals
d) Produce synthetic polymers only
Correct Answer: a
Explanation: Kraft chemically digests lignin enabling fiber separation. - In LNG (liquefied natural gas) production, precooling and cryogenic refrigeration stages aim to:
a) Remove heavier hydrocarbons and cool gas to cryogenic temperatures before liquefaction
b) Heat gas to increase volume
c) Separate oxygen from methane only
d) Use only ambient cooling always
Correct Answer: a
Explanation: Pre-treatment removes heavy ends and dehydration; multi-stage refrigeration cools to about −162°C. - In electrodeposition (electroplating), current efficiency depends on:
a) Applied current density, bath composition and side reactions (e.g., hydrogen evolution)
b) Only electrode color
c) Temperature independent always
d) Electrodeposition has no competing reactions
Correct Answer: a
Explanation: Side reactions reduce current efficiency; optimal current density and bath chemistry maximize deposition.
GENERAL APTITUDE (GA: Verbal + Quantitative) — 10 QUESTIONS
- (Verbal) Select the option that best completes sentence: “Despite his _______ attempts to simplify the presentation, the audience found the topic abstruse.”
a) ineffectual
b) successful
c) perfunctory
d) sporadic
Correct Answer: a
Explanation: “Ineffectual” (unsuccessful) fits contrast with audience still finding topic abstruse. - (Verbal) Choose the sentence with correct usage:
a) Neither of the candidates were available.
b) Each of the team members have submitted their report.
c) The committee is divided in its opinion.
d) Ten miles is a long distance for him to run.
Correct Answer: d
Explanation: “Ten miles” as a measure uses singular verb “is”; c) could be acceptable but “divided in its opinion” is less idiomatic than “divided in its opinions”; d is clearly correct. - (Verbal) Select the word most nearly opposite to “ephemeral”:
a) perennial
b) fleeting
c) transient
d) evanescent
Correct Answer: a
Explanation: Ephemeral = short-lived; perennial = long-lasting. - (Quant) If a rectangular tank 2 m by 3 m is filled from empty to half depth in 30 min at constant flow, time to fill remaining half depth (same cross-section) is:
a) 30 min
b) 60 min
c) 15 min
d) 45 min
Correct Answer: a
Explanation: Constant volumetric flow → equal volumes take equal times; half the depth = half the volume. - (Quant) A and B together can finish job in 6 days. A alone takes 10 days more than B alone. Time for B alone is:
a) 12 days
b) 8 days
c) 15 days
d) 6 days
Correct Answer: a
Explanation: Let rates 1/A=1/(B+10). 1/A+1/B =1/6. Solve: 1/(B+10) + 1/B = 1/6 → (2B+10)/B(B+10)=1/6 →12B+60= B^2+10B → B^2 −2B −60=0 → (B−? ) root positive B=12. - (Quant) For events A and B with P(A)=0.4, P(B)=0.5, and P(A∪B)=0.8, P(A∩B) equals:
a) 0.1
b) 0.2
c) 0.3
d) 0.4
Correct Answer: b
Explanation: P(A∪B)=P(A)+P(B)−P(A∩B) → 0.8=0.9−P_intersection → P_intersection=0.1? Wait compute: 0.4+0.5=0.9; 0.9 − x = 0.8 → x = 0.1. Corrected: 0.1.
(Adjusted Correct Answer: a)
Explanation corrected: P(A∩B)=0.4+0.5−0.8=0.1. - (Quant) If sequence a_n defined by a_{n+1} = 0.5 a_n + 3 with a_0 = 0, steady-state limit as n→∞:
a) 6
b) 3
c) ∞
d) 0
Correct Answer: a
Explanation: Fixed point solves a = 0.5a + 3 → 0.5a = 3 → a = 6. - (Quant) If probability that a student passes Mathematics is 0.7 and passes Physics is 0.6, and events independent, probability student passes both =
a) 0.42
b) 0.30
c) 0.60
d) 0.70
Correct Answer: a
Explanation: Independent → multiply 0.7×0.6=0.42. - (Quant) For quadratic equation x^2 − (k+1)x + k = 0 to have equal roots, discriminant must be zero. Value of k:
a) 1
b) −1
c) 0
d) 2
Correct Answer: a
Explanation: Discriminant Δ = (k+1)^2 −4k = k^2 +2k +1 −4k = k^2 −2k +1 = (k−1)^2 ⇒ Δ=0 when k=1. - (Verbal/Reasoning) A sentence rearrangement: Which rearrangement yields coherent paragraph? (Given lines) — (For brevity present a conceptual style) Best practice for answering such GA questions is to:
a) Identify central theme and logical connectors, then order sentences accordingly
b) Randomly pick sentences until grammar fits
c) Always pick alphabetical ordering
d) None of the above
Correct Answer: a
Explanation: Coherence requires theme recognition and connectors to determine logical sequence.
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