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QUESTION: 1

**Q. 1 – Q. 5 carry one mark each.**

**Q. **Which one of the following options is the closest in meaning to the word given below?

Mitigate

Solution:

QUESTION: 2

C hoose the most appropriate alternative from the options given below to complete the following

sentence:

Despite several ––––––––– the mission succeeded in its attempt to resolve the conflict.

Solution:

QUESTION: 3

The cost function for a product in a firm is given by 5q^{2}, where q is the amount of production. The firm can sell the product at a market price of 50 per unit. The number of units to be produced by the firm such that the profit is maximized is

Solution:

QUESTION: 4

C hoose the most appropriate alternative from the options given below to complete the following

sentence:

Suresh’s dog is the one ––––––––– was hurt in the stampede

Solution:

QUESTION: 5

C hoose the grammatically INCORRECT sentence:

Solution:

QUESTION: 6

**Q. 6 - Q. 10 carry two marks each.**

**Q.**

A n automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies

60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.

The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable.

Of Y’s shock absorbers, 72% are reliable.

The probability that a randomly chosen shock absorber, which is found to be reliable, is made by

Y is

Solution:

QUESTION: 7

A political party orders an arch for the entrance to the ground in which the annual convention is

being held. The profile of the arch follows the equation y = 2x – 0.1x^{2} where y is the height of the

arch in meters. The maximum possible height of the arch is

Solution:

QUESTION: 8

W anted Temporary, Part-time persons for the post of Field Interviewer to conduct personal

interviews to collect and collate economic data. Requirements: High School-pass, must be

available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed.

Which one of the following is the best inference from the above advertisement?

Solution:

Gender is not mentioned in the advertisement and B clearly eliminated

QUESTION: 9

G iven the sequence of terms, AD CG FK JP, the next term is

Solution:

QUESTION: 10

W hich of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list

Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list

R: Doubling each entry in a list doubles the mean of the list

S: Doubling each entry in a list leaves the standard deviation of the list unchanged

Solution:

P and R a;ways hold true

Else consider a sample ser {1,2,3,4} and check accordingly

QUESTION: 11

**Q. 11 – Q. 35 carry one mark each.**

**Q.**

Consider the following set of linear algebraic equations

The system has

Solution:

QUESTION: 12

If a and b are arbitrary constants, then the solution to the ordinary differential equation

is

Solution:

Consider Option (D), y= a cosh 2x+b sinh 2x;

dy/dx= 2sinh 2x + 2b cosh 2x;

QUESTION: 13

F or the function the Taylor series approximation for is.

Solution:

QUESTION: 14

A box containing 10 identical compartments has 6 red balls and 2 blue balls. If each compartment

can hold only one ball, then the number of different possible arrangements are

Solution:

QUESTION: 15

C onsider the following (2 x 2) matrix

Which one of the following vectors is NOT a valid eigenvector of the above matrix ?

Solution:

QUESTION: 16

In a throttling process, the pressure of an ideal gas reduces by 50 %. If C_{P} and C_{V} are the heat

capacities at constant pressure and constant volume, respectively the specific

volume will change by a factor of

Solution:

QUESTION: 17

I f the temperature of saturated water is increased infinitesimally at constant entropy, the resulting

state of water will be

Solution:

QUESTION: 18

In a parallel flow heat exchanger operating under steady state, hot liquid enters at a temperature

T_{h,in} and leaves at a temperature T_{h,out} . Cold liquid enters at a temperature T_{c,in} and leaves at a

temperature T_{c,out} . Neglect any heat loss from the heat exchanger to the surrounding. If

T_{h,in} >> T_{c,in} , then for a given time interval, which ONE of the following statements is true?

Solution:

QUESTION: 19

F or an exothermic reversible reaction, which one of the following correctly describes the

dependence of the equilibrium constant ( K ) with temperature (T ) and pressure ( P ) ?

Solution:

QUESTION: 20

W ater is flowing under laminar conditions in a pipe of length L . If the diameter of the pipe is

doubled, for a constant volumetric flow rate, the pressure drop across the pipe

Solution:

QUESTION: 21

The local velocity of a fluid along a streamline can be measured by

Solution:

QUESTION: 22

F or uniform laminar flow (in the x -direction) past a flat plate at high Reynolds number, the local

boundary layer thickness (δ ) varies with the distance along the plate ( x ) as

Solution:

For a flow over a flat plate, the local boundary thichness (δ) varies with x^{0.5 } for laminar flow.

x^{0.8} for fully developed turbulent flow

QUESTION: 23

I n a mixing tank operating at very high Reynolds number (> 10^{4} ), if the diameter of the impeller is

doubled (other conditions remaining constant), the power required increases by a factor of

Solution:

For mixing tank

power required

QUESTION: 24

F or heat transfer across a solid-fluid interface, which one of the following statements is NOT true

when the Biot number is very small compared to 1?

Solution:

QUESTION: 25

A solid sphere with an initial temperature T_{i} is immersed in a large thermal reservoir of

temperature T_{o} . The sphere reaches a steady temperature after a certain time t_{1} . If the radius of the

sphere is doubled, the time required to reach steady-state will be

Solution:

QUESTION: 26

I f the Nusselt number ( Nu ) for heat transfer in a pipe varies with Reynolds number (Re ) as

then for constant average velocity in the pipe, the heat transfer coefficient varies with

the pipe diameter D as

Solution:

QUESTION: 27

I n the McCabe-Thiele diagram, if the x -coordinate of the point of intersection of the q -line and

the vapor-liquid equilibrium curve is greater than the x -coordinate of the feed point, then the

quality of the feed is

Solution:

The present case falls under the case of (1)

QUESTION: 28

F or which of the following combinations, does the absorption operation become gas-film

controlled?

P. The solubility of gas in the liquid is very high

Q. The solubility of gas in the liquid is very low

R. The liquid-side mass transfer coefficient is much higher than the gas-side mass transfer

coefficient

S. The liquid-side mass transfer coefficient is much lower than the gas-side mass transfer

coefficient

Solution:

QUESTION: 29

The half-life of an nth order reaction in a batch reactor depends on

Solution:

QUESTION: 30

C onsider the reaction scheme shown below

Both the reactions are first-order. The activation energies for k_{1} and k_{2 } are 80 and 20 kJ/mol,

respectively. To maximize the yield of B, it is preferable to use

Solution:

High Temprature and high concentration of C_{A }is needed for maximum yield of B

QUESTION: 31

I n petroleum refining, catalytic reforming is used to convert

Solution:

QUESTION: 32

T he final boiling points of gasoline, diesel, atmospheric gas oil (AGO) and lubricating oils vary as

Solution:

QUESTION: 33

T he main unit processes used for the production of hydrogen from natural gas are steam reforming

(SR), pressure swing adsorption (PSA), low temperature water gas shift reaction (LT WGS) and

high temperature water gas shift reaction (HT WGS). The correct sequence of these in the plant is

Solution:

QUESTION: 34

A thermometer initially at 100°C is dipped at t = 0 into an oil bath, maintained at 150°C. If the

recorded temperature is 130°C after 1 minute, then the time constant of thermometer (in min) is

Solution:

QUESTION: 35

T he Bode stability criterion is applicable when

Solution:

QUESTION: 36

**Q. 36 to Q. 65 carry two marks each.**

^{Q.}

**The one - dimensional unsteady state heat conduction equation in a hollow cylinder with a constant
heat source q is**

If A and B are arbitrary constants, then the steady state solution to the above equation is

Solution:

QUESTION: 37

If a is a constant, then the value of the integral is

Solution:

QUESTION: 38

The Newton – Raphson method is used to find the roots of the equation

f(x)= x- cosπx 0x1

If the initial guess for the root is 0.5, then the value of x after the first iteration is

Solution:

QUESTION: 39

If i = , the value of the integral

using the Cauchy residue theorem is

Solution:

QUESTION: 40

A n insulated, evacuated container is connected to a supply line of an ideal gas at pressure P_{s} , temperature T_{s} and specific volume v_{s} . The container is filled with the gas until the pressure in the container reaches P_{s} . There is no heat transfer between the supply line to the container, and kinetic and potential energies are negligible. If C_{P} and C_{V} are the heat capacities at constant pressure and constant volume, respectively then the final temperature of the gas in the container is

Solution:

QUESTION: 41

Consider a binary liquid mixture at constant temperature T and pressure P . If the enthalpy change

of mixing, ΔH = 5x_{1}x_{2} , where x_{1} and x_{2} are the mole fraction of species 1 and 2 respectively, and

the entropy change of mixing ΔS =-R[x_{1} in x_{1}+x_{2} in x_{2}](with R = 8.314 J/mol.K), then the minimum value of the Gibbs free energy change of mixing at 300 K occurs when

Solution:

QUESTION: 42

A bed of spherical glass beads (density 3000 kg/m^{3}, diameter 1 mm, bed porosity 0.5) is to be

fluidized by a liquid of density 1000 kg/m^{3} and viscosity 0.1 Pa.s. Assume that the Reynolds

number based on particle diameter is very small compared to one. If g = 10 m/s^{2}, then the

minimum velocity (in m/s) required to fluidize the bed is

Solution:

QUESTION: 43

F or the enclosure formed between two concentric spheres as shown below ( R_{2} = 2R_{1} ), the fraction

of radiation leaving the surface area A_{2} that strikes itself is

Solution:

QUESTION: 44

H eat is generated at a steady rate of 100 W due to resistance heating in a long wire (length = 5 m, diameter = 2 mm). This wire is wrapped with an insulation of thickness 1 mm that has a thermal conductivity of 0.1 W/m.K. The insulated wire is exposed to air at 30°C. The convective heat transfer between the wire and surrounding air is characterized by a heat transfer coefficient of 10 W/m^{2}.K. The temperature (in °C) at the interface between the wire and the insulation is

Solution:

QUESTION: 45

I n a counter-flow double pipe heat exchanger, oil (m = 2 kg/s, P C = 2.1 kJ/kg.°C) is cooled from

90 °C to 40 °C by water ( m = 1 kg/s, P C = 4.2 kJ/kg.°C) which enters the inner tube at 10 °C. The

radius of the inner tube is 3 cm and its length is 5 m. Neglecting the wall resistance, the overall heat

transfer coefficient based on the inner radius, in kW/ m^{2}.K, is

Solution:

QUESTION: 46

T he rate-controlling step for the solid-catalyzed irreversible reaction

A+B → C

is known to be the reaction of adsorbed A with adsorbed B to give adsorbed C . If i P is the partial

pressure of component i and K_{i} is the adsorption equilibrium constant of component i , then the

form of the Langmuir-Hinshelwood rate expression will be

Solution:

QUESTION: 47

C onsider the drying operation shown in the figure below for a solid loading (dry basis) of 50 kg/m^{2}

with a constant drying rate of 5 kg/m^{2}.h. The falling rate of drying is linear with moisture content.

The drying time (in hrs) required to reduce an initial moisture content of 25% to a final moisture

content of 2% is

Solution:

QUESTION: 48

A n equimolar mixture of A and B (A being more volatile) is flash distilled continuously at a feed

rate of 100 kmol/h, such that the liquid product contains 40 mol % of A. If the relative volatility

is 6, then the vapor product, in kmol/h, is

Solution:

QUESTION: 49

A thermocouple having a linear relationship between 0^{o}C and 350 ^{o}C shows an emf of zero and

30.5 mV, respectively at these two temperatures. If the cold junction temperature is shifted from

0 ^{o}C to 30 ^{o}C, then the emf correction (in mV) is

Solution:

since, the releationship is linear

QUESTION: 50

The characteristic equation for a system is

s^{3}+9s^{2} +26s +12(2+k_{c}) =0

Using the Routh test, the value of K_{c} that will keep the system on the verge of instability is

Solution:

QUESTION: 51

The elementary reversible exothermic gas-phase reaction

a+3B ⇔ 2C

is to be conducted in a non-isothermal, non-adiabatic plug flow reactor. The maximum allowable

reactor temperature is T_{max} . To minimize the total reactor volume, the variation of reactor

temperature (T ) with axial distance from the inlet ( z ) should be

Solution:

QUESTION: 52

The block diagram of a system with a proportional controller is shown below

A unit step input is introduced in the set point. The value of K_{c} to provide a critically damped

response for

Solution:

QUESTION: 53

A batch reactor produces 1x10^{5} kg of a product per year. The total batch time (in hours) of the reactor is , where P_{B} is the product per batch in kg and . The operating cost

of the reactor is Rs. 200/h. The total annual fixed charges are Rs. 340 × P_{B} and the annual raw

material cost is Rs. 2 x10^{6} . The optimum size (in kg) of each batch (adjusted to the nearest

integer) is

Solution:

QUESTION: 54

Heat integration is planned in a process plant at an investment Rs. 2x10^{6} . This would result in a

net energy savings of 20 GJ per year. If the nominal rate of interest is 15% and the plant life is

3 years, then the breakeven cost of energy, in Rs. per GJ (adjusted to the nearest hundred), is

Solution:

QUESTION: 55

In a 1-1 pass floating head type shell and tube heat exchanger, the tubes (od = 25 mm; id = 21 mm)

are arranged in a square pitch. The tube pitch is 32 mm. The thermal conductivity of the shell side

fluid is 0.19 W/m.K, and the Nusselt number is 200. The shell-side heat transfer coefficient

(in W/m^{2}.K), rounded off to the nearest integer, is

Solution:

QUESTION: 56

Match the process in Group I with the catalyst in Group II

Solution:

QUESTION: 57

M atch the polymer in Group I to the polymer characteristic in Group II

Solution:

QUESTION: 58

**Common Data for Questions 58 and 59:**

**A counter-current extraction column is designed to remove 99% of solute C from a solution of solvent A and solute C using pure solvent B. The initial concentration of solute in the solution of A + C is 20 wt % and the total flow of solution is 1000 kg/h. If the equilibrium relationship is Y = 2X , where
Y = mass of C/mass of A and X = mass of C/mass of B.**

**Q.**

The minimum flow rate of solvent B required (in kg/h) is

Solution:

QUESTION: 59

**A counter-current extraction column is designed to remove 99% of solute C from a solution of solvent A and solute C using pure solvent B. The initial concentration of solute in the solution of A + C is 20 wt % and the total flow of solution is 1000 kg/h. If the equilibrium relationship is Y = 2X , where
Y = mass of C/mass of A and X = mass of C/mass of B.**

**Q.**

**If the flow rate of B is 2400 kg/h, then the theoretical number of stages in the column, using
Kremser’s equation (adjusted to the next integer) is**

**Correct answer will be updated soon**

Solution:

QUESTION: 60

**Common Data for Questions**

The reaction is carried out in a reactor followed by a separator as shown

below

Notation:

Molar flow rate of fresh B is FB F

Molar flow rate of A is A F

Molar flow rate of recycle gas is RG F

Mole fraction of B in recycle gas is RB Y

Molar flow rate of purge gas is PG F

Molar flow rate of C is C F

Here, F_{FB} = 2 mol/s; F_{A} = 1 mol/s, F_{B }/ F_{A} = 5 and A is completely converted.

Q.If Y_{RB} = 0.3, the ratio of recycle gas to purge gas ( F_{RG} /F_{PG}) is

Solution:

QUESTION: 61

The reaction is carried out in a reactor followed by a separator as shown

below

Notation:

Molar flow rate of fresh B is FB F

Molar flow rate of A is A F

Molar flow rate of recycle gas is RG F

Mole fraction of B in recycle gas is RB Y

Molar flow rate of purge gas is PG F

Molar flow rate of C is C F

Here, F_{FB} = 2 mol/s; F_{A} = 1 mol/s, F_{B }/ F_{A} = 5 and A is completely converted.

Q.

I f the ratio of recycle gas to purge gas ( F_{RG/} F_{PG} ) is 4 then Y_{RB} is

Solution:

QUESTION: 62

A Newtonian fluid of viscosity μ flows between two parallel plates due to the motion of the bottom plate

(as shown below), which is moved with a velocity V . The top plate is stationary.

**Q.**

**The steady, laminar velocity profile in the x -direction is**

Solution:

QUESTION: 63

A Newtonian fluid of viscosity μ flows between two parallel plates due to the motion of the bottom plate

(as shown below), which is moved with a velocity V . The top plate is stationary.

**Q.**

**T he force per unit area (in the x -direction) that must be exerted on the bottom plate to maintain the
flow is**

Solution:

QUESTION: 64

**The first order liquid phase reaction A→P is conducted isothermally in a plug flow reactor of 5 liter
volume. The inlet volumetric flow rate is 1 liter/min and the inlet concentration of A is 2 mole/liter.**

**Q.**

**If the exit concentration of A is 0.5 mole /liter, then the rate constant, in min ^{−1}, is**

Solution:

QUESTION: 65

**The first order liquid phase reaction A→P is conducted isothermally in a plug flow reactor of 5 liter
volume. The inlet volumetric flow rate is 1 liter/min and the inlet concentration of A is 2 mole/liter.**

**Q.**

T he plug flow reactor is replaced by 3 mixed flow reactors in series, each of 2.0 liters volume. The

exact conversion of A (in %) is

Solution:

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