The GATE 2025 Chemical Engineering (CH) Question paper with Solution PDF is available to download here. GATE 2025 was conducted by IIT Roorkee. Following the latest exam pattern, it consists of 65 questions for 100 marks—10 from General Aptitude and 55 from subject-specific topics in Chemical Engineering. The overall difficulty level of the exam was moderate.
GATE 2025 Chemical Engineering Question Paper with Solutions PDF
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GATE 2025 Chemical Engineering Questions with Solutions
Question 1:
Is there any good show _____ television tonight? Select the most appropriate option to complete the above sentence.
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 sum of the following infinite series is: \[ 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \dots \]
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 to form the cube?
The figures I, II, and III are parts of a sequence. Which one of the following options comes next in the sequence at IV?
Based only on the information provided in the above passage, which one of the following statements is true?
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?
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?
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:
An object is said to have an n-fold rotational symmetry if the object, rotated by an angle of \( \frac{2\pi}{n} \), 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?
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)?
Consider a Cartesian coordinate system defined over a 3-dimensional vector space with orthogonal unit basis vectors \(\hat{i}, \hat{j}\), and \(\hat{k}\). Let vector \(\mathbf{a} = \sqrt{2}\hat{i} + \frac{1}{\sqrt{2}}\hat{k}\), and vector \(\mathbf{b} = \frac{1}{\sqrt{2}}\hat{i} + \sqrt{2}\hat{j} - \hat{k}\). The inner product of these vectors (\(\mathbf{a} \cdot \mathbf{b}\)) is:
Consider two complex numbers \( z_1 = 1 - i \) and \( z_2 = i \). The argument of \( z_1z_2 \) is:
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 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 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:
In industrial heat exchanger design, the overall heat transfer coefficient \( U \) is estimated from the equation: \[ \frac{1}{U} = \frac{1}{h_i} + \frac{1}{h_o} \]
where \( h_i \) and \( h_o \) 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 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:
Choose the CORRECT option for pathlines, streaklines and streamlines for a STEADY flow field.
Choose the CORRECT ordering of the diameter \( d \) of the different types of pores in a solid catalyst.
Schmidt number is defined as
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?
Choose the CORRECT statement that describes the dependence of the variance (\( \sigma^2_\Theta \)) 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 vortex shedding meter is primarily used for measuring
Choose the transfer function that best fits the output response to a unit step input change shown in the figure:
The capital cost (CC) of an industrial equipment varies with its capacity (S) as \( CC \propto S^\beta \). The rule-of-thumb value of the exponent \( \beta \) is
In the production of polyvinyl chloride (PVC) from ethylene and chlorine, the sequential order of reactions is
In the CONTACT PROCESS for manufacturing sulphuric acid, the reaction converting \( SO_2 \) to \( SO_3 \) is
Choose the option that correctly matches the items in Group 1 with those in Group 2.
Which of the following statements regarding multiple effect evaporators is/are TRUE?
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 following data is given for a ternary \(ABC\) gas mixture at 12 MPa and 308 K:
\(y_i\): mole fraction of component \(i\) in the gas mixture
\(\hat{\phi}_i\): fugacity coefficient of component \(i\) in the gas mixture at 12 MPa and 308 K
The fugacity of the gas mixture is ____ MPa (rounded off to 3 decimal places).
Ideal nonreacting gases A and B are contained inside a perfectly insulated chamber, separated by a thin partition, as shown in the figure. The partition is removed, and the two gases mix till final equilibrium is reached. The change in total entropy for the process is \( \_\_ \) J/K (rounded off to 1 decimal place).
% Given
Given: Universal gas constant \( R = 8.314 \) J/(mol K), \( T_A = T_B = 273 \) K, \( P_A = P_B = 1 \) atm, \( V_B = 22.4 \) L, \( V_A = 3V_B \).
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 residence-time distribution (RTD) function of a reactor (in min\(^{-1}\)) is
\(E(t) = \begin{cases} 1 - 2t, & if t \leq 0.5 min
0, & if t > 0.5 min \end{cases}\)
The mean residence time of the reactor is ____ min (rounded off to 2 decimal places).
Consider a Cartesian coordinate system with orthogonal unit basis vectors \( \hat{i}, \hat{j} \) defined over a domain: \( x, y \in [0,1] \). Choose the condition for which the divergence of the vector field \( \mathbf{v} = ax\hat{i} - by\hat{j} \) is zero.
A probability distribution function is given as: \[ p(x) = \begin{cases} \frac{1}{a}, & x \in (0, a)
0, & otherwise \end{cases} \]
where \( a \) is a positive constant. For a function \( f(x) = x^2 \), the expectation of \( f(x) \) is
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 first-order irreversible liquid phase reaction \(A \to B\) occurs inside a constant volume \(V\) isothermal CSTR with the initial steady-state conditions shown in the figure. The gain, in kmol/m³·h, of the transfer function relating the reactor effluent \(A\) concentration \(c_A\) to the inlet flow rate \(F\) is:
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:
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:
A zero-order gas phase reaction \(A \to B\) 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 \(A\), \(-\frac{dC_A}{dt}\), in mol/(L min), at \(t = 1\) min is:
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 (\(\Delta P\)) is/are TRUE?
Consider the differential equation \(\frac{dy}{dx} + \frac{y}{x} = 0\). Choose the CORRECT option(s) for the solution \(y\).
Consider the matrix: \[ A = \begin{bmatrix} 2 & 3
1 & 2 \end{bmatrix} \]
The eigenvalues of the matrix are 0.27 and ____ (rounded off to 2 decimal places).
The Newton-Raphson method is used to find the root of \[ f(x) \equiv x^2 - x - 1 = 0 \]
Starting with an initial guess \( x_0 = 1 \), the second iterate \( x_2 \) is ___ (rounded off to 2 decimal places).
Consider moist air with absolute humidity of 0.02 (kg moisture)/(kg dry air) at 1 bar pressure. The vapor pressure of water is given by the equation: \[ \ln P_{sat} = 12 - \frac{4000}{T - 40} \]
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 _____ ℃ (rounded off to the nearest integer).
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. The spring constant is 10 kN/m. At the initial equilibrium state (shown in the figure), the spring is unstretched. The gas is expanded reversibly by adding 362.5 J of heat. At the final equilibrium state, the piston presses against the stoppers. Neglecting the heat loss to the surroundings, the final equilibrium temperature of the gas is ____ K (rounded off to the nearest integer).
A leaf filter is operated at 1 atm (gauge). The volume of filtrate collected \(V\) (in \(m^3\)) is related with the volumetric flow rate of the filtrate \(q\) (in \(m^3/s\)) as: \[ \frac{1}{q} = \frac{1}{\frac{dV}{dt}} = 50V + 100 \]
The volumetric flow rate of the filtrate at 1 hour is ____ \( \times 10^{-3} \, m^3/s\) (rounded off to 2 decimal places).
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/m\(^3\), the maximum temperature rise of water across the pump is ____°C (rounded off to 3 decimal places).
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/(m²·K), the heat exchanger area is ____ m² (rounded off to 1 decimal place).
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/(m²·K). Neglecting the thermal resistance of the wire, the steady-state temperature at the wire-insulation interface is ____°C (rounded off to 1 decimal place).
GIVEN:
Kinematic viscosity: \( \nu = 1.0 \times 10^{-6} \, m^2/s \)
Prandtl number: \( Pr = 7.01 \)
Velocity boundary layer thickness: \[ \delta_H = \frac{4.91 x}{\sqrt{x \nu}} \]
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).
A binary \(A\)-\(B\) 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 \(\alpha_{AB} = 2.2\), the average composition of the collected distillate is ____ mol% \(A\) (rounded off to the nearest integer).
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).
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, \(y_i = 1.5 x_i\),
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 (\(k_x\)), \(\frac{k_y}{k_x} = 2\), then \(y_i\) equals ____ (rounded off to 3 decimal places).
Components \( A \) and \( B \) form an azeotrope. The saturation vapor 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
GIVEN: \[ \ln \left( \frac{\gamma_A}{\gamma_B} \right) = 0.9 \left( x_B^2 - x_A^2 \right) \]
where \( x_i \) and \( \gamma_i \) are the liquid phase mole fraction and activity coefficient of component \( i \), respectively.
The reaction \( A \rightarrow products \) with reaction rate, \( (-r_A) = k C_A^3 \), occurs in an isothermal PFR operating at steady state. The conversion (X) at two axial locations (1 and 2) of the PFR is shown in the figure.
The value of \( l_1/l_2 \) is ____ (rounded off to 2 decimal places).
The catalytic gas-phase reaction \( A \rightarrow products \) 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:
- \( k' = \frac{1}{kg catalyst \cdot h} \)
- \( C_A \) 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).
Consider a process with transfer function: \[ G_p = \frac{2e^{-s}}{(5s + 1)^2} \]
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 \( \tau_m \) and \( \theta_m \) denote the time constant and dead time, respectively, of the fitted FOPDT model. The value of \( \frac{\tau_m}{\theta_m} \) is ___\ (rounded off to 2 decimal places).
% Given Data
Given:
For \( G = \frac{1}{(\tau s + 1)^2} \), the unit step output response is: \[ y(t) = 1 - \left(1 + \frac{t}{\tau}\right)e^{-t/\tau} \]
The first and second derivatives of \( y(t) \) are: \[ \frac{dy(t)}{dt} = \frac{t}{\tau^2} e^{-t/\tau} \] \[ \frac{d^2y(t)}{dt^2} = \frac{1}{\tau^2} \left(1 - \frac{t}{\tau}\right) e^{-t/\tau} \]
Methanol is produced by the reversible, gas-phase hydrogenation of carbon monoxide: \[ CO + 2H_2 \rightleftharpoons CH_3OH \]
CO and H\(_2\) 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 H\(_2\) in the product is 0.4. Assuming ideal gas behavior, the mole fraction of methanol in the product is ____ (rounded off to 2 decimal places).
The block diagram of a series cascade control system (with time in minutes) is shown in the figure. For \( \tau_1 = 8 \) min and \( K_s^c = 1 \), the maximum value of \( K_m^c \), below which the cascade control system is stable, is ____ (rounded off to the nearest integer).
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).
Consider the flowsheet in the figure for manufacturing C via the reaction \( A + B \rightarrow C \) in an isothermal CSTR. The split in the separator is perfect so that the recycle stream is free of C and the product stream is pure C. Let \( x_i \) denote the mole fraction of species \( i \) (where \( i = A, B, C \)) 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 \( (-r_A) = k x_A \), where \( k_x = 5.0 \, kmol/(m^3 \cdot h) \).
The reactor volume \( V \) in \( m^3 \) is to be optimized to minimize the cost objective \( J = V + 0.25 R \), where \( R \) is the recycle rate in \( kmol/h \). For a product rate \( P = 100 \, kmol/h \), the optimum value of \( V \) is ____ \( m^3 \) (rounded off to the nearest integer).
Given: \[ \frac{d}{dz} \left( \frac{z}{(1-z)^2} \right) = \frac{1}{(1 - 2z)^2} \]
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).
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