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QUESTION: 1

**Q.No-1-5 Carry One Mark Each**

**Q.**

A student is required to demonstrate a high level of comprehension of the subject, especially

in the social sciences.

The word closest in meaning to comprehension is

Solution:

QUESTION: 2

Choose the most appropriate word from the options given below to complete the following

sentence.

One of his biggest ______ was his ability to forgive.

Solution:

QUESTION: 3

Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently. Which one of the statements below is logically valid and can be inferred from the above sentences?

Solution:

QUESTION: 4

If y = 5x^{2} + 3, then the tangent at x = 0, y = 3

Solution:

*Answer can only contain numeric values

QUESTION: 5

A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs

800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per

tonne for a daily production of 100 tonnes?

Solution:

Fixed cost = Rs. 50,000

Variable cost = Rs. 800Q

Q = daily production in tones

For 100 tonnes of production daily, total cost of production

= 50,000+800×100 = 130,000

So, cost of production per tonne of daily production = 130000/100 = Rs. 1300

QUESTION: 6

Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK

Solution:

ALRVX→only one vowel

EPVZB→only one vowel

ITZDF→only one vowel

OYEIK→three vowels

QUESTION: 7

Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed

building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an

even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live

on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does

not live on a floor immediately above or immediately below Bhola. Faisal lives three floors

above Dilip. Which of the following floor-person combinations is correct?

Solution:

(a) Anuj: Even numbered floor (2,4,6)

(b) Bhola: Even numbered floor (2,4,6)

(c) Chandan lives on the floor above that of Faisal.

(d) Dilip: not on 2nd floor.

(e) Eswar: does not live immediately above or immediately below Bhola

From the options its clear, that only option (B) satisfies condition (e).

So, correct Ans is (B).

*Answer can only contain numeric values

QUESTION: 8

The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.

The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is

twice its smallest angle. What is the sum, in degrees, of the second largest angle of the

triangle and the largest angle of the quadrilateral?

Solution:

Let the angles of quadrilateral are 3x, 4x, 5x, 6x

So, 3x+4x+5x+6x = 360

x = 20

Smallest angle of quadrilateral = 3×20 = 60°

Smallest angle of triangle = 2/3 x 60^{o} = 40^{o}

Largest angle of triangle = 2×40° = 60°

Three angles of triangle are 40°, 60°, 80°

Largest angle of quadrilateral is 120°

Sum (2nd largest angle of triangle + largest angle of quadrilateral)

= 60°+120°=180°.

QUESTION: 9

One percent of the people of country X are taller than 6 ft. Two percent of the people of

country Y are taller than 6 ft. There are thrice as many people in country X as in country Y.

Taking both countries together, what is the percentage of people taller than 6 ft?

Solution:

Let number of people in country y = 100

So, number of people in country x = 300

Total number of people taller than 6ft in both the countries

QUESTION: 10

The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following

figure. Which of the following are true? (k percentile is the value such that k percent of the

data fall below that value)

(i) On average, it rains more in July than in December

(ii) Every year, the amount of rainfall in August is more than that in January

(iii) July rainfall can be estimated with better confidence than February rainfall

(iv) In August, there is at least 500 mm of rainfall

Solution:

In the question the monthly average rainfall chart for 50 years has been given.

Let us check the options.

(i) On average, it rains more in July than in December correct.

(ii) Every year, the amount of rainfall in August is more than that in January.

⇒ may not be correct because average rainfall is given in the question.

(iii) July rainfall can be estimated with better confidence than February rainfall.

⇒ From chart it is clear the gap between 5 percentile and 95 percentile from average is higher in February than that in July ⇒ correct.

(iv) In August at least 500 mm rainfall

⇒May not be correct, because its 50 year average.

So correct option (B) (i) and (iii).

QUESTION: 11

**Q.No-11-35 Carry One Mark Each**

**Q.**

**Gradient of a scalar variable is always**

Solution:

QUESTION: 12

For the time domain function, f(t) = t^{2} ,which ONE of the following is the Laplace transform

of

Solution:

QUESTION: 13

If f*(x) is the complex conjugate of f(x) = cos(x) + i sin(x), then for real a and b,

Solution:

QUESTION: 14

If f(x) is a real and continuous function of x, the Taylor series expansion of f(x) about

its minima will NEVER have a term containing

Solution:

So, Taylor series expansion of f(x) about ‘a’ will never contain first derivative term.

QUESTION: 15

From the following list, identify the properties which are equal in both vapour and

liquid phases at equilibrium

P. Density Temperature

R. Chemical potential S. Enthalpy

Solution:

QUESTION: 16

In a closed system, the isentropic expansion of an ideal gas with constant specific heats is

represented by

Solution:

QUESTION: 17

Match the following :

Solution:

QUESTION: 18

In order to achieve the same conversion under identical reaction conditions and feed flow rate

for a non-autocatalytic reaction of positive order, the volume of an ideal CSTR is

Solution:

QUESTION: 19

Integral of the time-weighted absolute error (ITAE) is expressed as

Solution:

Let number of people in country y = 100

So, number of people in country x = 300

Total number of people taller than 6ft in both the countries

% of people taller than 6ft in both the countries =

QUESTION: 20

A unit IMPULSE response of a first order system with time constant and steady

state gain K_{p} is given by

Solution:

QUESTION: 21

In a completely opaque medium, if 50% of the incident monochromatic radiation is absorbed,

then which of the following statements are CORRECT?

(P) 50% of the incident radiation is reflected

(Q) 25% of the incident radiation is reflected

(R) 25% of the incident radiation is transmitted

(S) No incident radiation is transmitted

Solution:

QUESTION: 22

In case of a pressure driven laminar flow of a Newtonian fluid of viscosity (μ) through a

horizontal circular pipe, the velocity of the fluid is proportional to

Solution:

QUESTION: 23

Which of the following statements are CORRECT?

(P) For a rheopectic fluid, the apparent viscosity increases with time under a constant applied

shear stress

(Q) For a pseudoplastic fluid, the apparent viscosity decreases with time under a constant

applied shear stress

(R) For a Bingham plastic, the apparent viscosity increases exponentially with the

deformation rate

(S) For a dilatant fluid, the apparent viscosity increases with increasing deformation rate

Solution:

QUESTION: 24

Assume that an ordinary mercury-in-glass thermometer follows first order dynamics with a

time constant of 10s. It is at a steady state temperature of 0°C. At time t = 0, the thermometer

is suddenly immersed in a constant temperature bath at 100°C. The time required (in s) for

the thermometer to read 95°C, approximately is

Solution:

QUESTION: 25

Packed towers are preferred for gas-liquid mass transfer operations with foaming liquids

because

Solution:

QUESTION: 26

A spherical storage vessel is quarter–filled with toluene. The diameter of the vent at the top of

the vessel is 1/20th of the diameter of the vessel. Under the steady state condition, the

diffusive flux of toluene is maximum at

Solution:

Diffusive flux is maximum at the vent and remains same throughout the vent line at steady state.

QUESTION: 27

In order to produce fine solid particles between 5 and 10 μm, the appropriate size reducing

equipment is

Solution:

QUESTION: 28

Slurries are most conveniently pumped by a

Solution:

QUESTION: 29

Assuming the mass transfer coefficients in the gas and the liquid phases are comparable, the

absorption of CO_{2} from reformer gas (CO_{2}+H_{2}) into an aqueous solution of diethanolamine is

controlled by

Solution:

QUESTION: 30

Which ONE of the following statements is CORRECT for the surface renewal theory?

Solution:

QUESTION: 31

Steam economy of a multiple effect evaporator system is defined as

Solution:

QUESTION: 32

Decomposition efficiency (D) of an electrolytic cell used for producing NaOH is defined as

Solution:

QUESTION: 33

The vessel dispersion number for an ideal CSTR is

Solution:

QUESTION: 34

Catalytic cracking is

Solution:

QUESTION: 35

Which ONE of the following statements is CORRECT?

Solution:

*Answer can only contain numeric values

QUESTION: 36

**Q.No-36-65 Carry Two Marks Each**

**Q.**

Consider the following differential equation

The solution of this equation at x = 0.4 using Euler method with a step size of h= 0.2 is

Solution:

QUESTION: 37

The integrating factor for the differential equation

Solution:

Given differential equation

QUESTION: 38

The differential equation

Solution:

This is clearly a linear differential equation

Order = 2

Degree = 1.

QUESTION: 39

Consider the following two normal distributions

If μ and σ denote the mean and standard deviation, respectively, then

Solution:

*Answer can only contain numeric values

QUESTION: 40

In rolling of two fair dice, the outcome of an experiment is considered to be the sum of the

numbers appearing on the dice. The probability is highest for the outcome of ___________

Solution:

Where X is a random variable denotes the sum of the numbers appearing on the dice.

P(x) = corresponding probabilities

The probability is highest for the outcome “7” i.e., 6/36

QUESTION: 41

A spherical ball of benzoic acid (diameter = 1.5 cm) is submerged in a pool of still water. The solubility and diffusivity of benzoic acid in water are 0.03 kmol/m^{3} and 1.25 x 10^{-9} m^{2}/s respectively. Sherwood number is given as Sh = 2.0 + 0.6 0.33 Re^{0.5} Sc^{0.33} . The initial rate of dissolution (in kmol/s) of benzoic acid approximately is

Solution:

*Answer can only contain numeric values

QUESTION: 42

A wet solid of 100 kg is dried from a moisture content of 40wt% to 10wt%. The critical moisture content is 15wt% and the equilibrium moisture content is negligible. All moisture contents are on dry basis. The falling rate is considered to be linear. It takes 5 hours to dry the material in the constant rate period. The duration (in hours) of the falling rate period is

Solution:

Given X_{1} = 0.4

X_{2} = 0.10

X_{C} = 0.15

X* = 0

Constant rate period

*Answer can only contain numeric values

QUESTION: 43

A brick wall of 20 cm thickness has thermal conductivity of 0.7 W m^{-1} K^{-1}. An insulation of thermal conductivity 0.2 W m^{-1} K^{-1} is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. The required thickness (in cm) of the insulation is ____________

Solution:

*Answer can only contain numeric values

QUESTION: 44

An oil with a flow rate of 1000 kg/h is to be cooled using water in a double-pipe counter-flow heat exchanger from a temperature of 70°C to 40°C. Water enters the exchanger at 25°C and leaves at 40°C. The specific heats of oil and water are 2 kJ kg^{-1} K^{-1} and 4.2 kJ kg^{-1} K^{-1}, respectively. The overall heat transfer coefficient is 0.2 kW m^{-2} K^{-1}. The minimum heat exchanger area (in m^{2}) required for this operation is ______________

Solution:

Given Cpo =2 kJkg^{-1 }K^{-1}

^{ }C_{po} =4.2 kJkg^{-1 }K^{-1}

U= 0.2kW m^{-2}K^{-1}

QUESTION: 45

Which ONE of the following is CORRECT for an ideal gas in a closed system?

Solution:

*Answer can only contain numeric values

QUESTION: 46

A binary distillation column is operating with a mixed feed containing 20 mol% vapour. If

the feed quality is changed to 80 mol% vapour, the change in the slope of the q-line is

Solution:

QUESTION: 47

A homogeneous reaction (R → P) occurs in a batch reactor. The conversion of the reactant R is 67% after 10 minutes and 80% after 20 minutes. The rate equation for this reaction is

Solution:

QUESTION: 48

A vapour phase catalytic reaction (Q + R →S) follows Rideal mechanism (R and S are not adsorbed). Initially, the mixture contains only the reactants in equimolar ratio. The surface reaction step is rate controlling. With constants a and b, the initial rate of reaction ( −r_{0} ) in terms of total pressure (P_{T}) is given by

Solution:

*Answer can only contain numeric values

QUESTION: 49

A incompressible fluid is flowing through a contraction section of length L and has a 1-D (x

direction) steady state velocity distribution, If u_{0} = 2m/ s and L = 3m, the

convective acceleration (in m/s^{2}) of the fluid at L is _______

Solution:

QUESTION: 50

Match the following:

Solution:

Tank in series model → PFR with axial mixing

Liquid-liquid extraction → Mixer settler

Optimum temperature progression → Non-isothermal reaction

Thiele modulus → Solid catalyst reaction.

*Answer can only contain numeric values

QUESTION: 51

Two elemental gases (A and B) are reacting to form a liquid (C) in a steady state process as per the reaction. A + B→C. The single-pass conversion of the reaction is only 20% and hence recycle is used. The product is separated completely in pure form. The fresh feed has 49 mol% of A and B each along with 2 mol% impurities. The maximum allowable impurities in the recycle stream is 20 mol%. The amount of purge stream (in moles) per 100 moles of the fresh feed is ___________

Solution:

Basis = 100 moles of fresh feed

A = 49 moles; B = 49 moles;

Inert, z = 2 moles

Overall balance on inert

2 = P×0.2 ⇒ P = 10

*Answer can only contain numeric values

QUESTION: 52

Carbon monoxide (CO) is burnt in presence of 200% excess pure oxygen and the flame

temperature achieved is 2298 K. The inlet streams are at 25 °C. The standard heat of

formation (at 25 °C) of CO and CO_{2} are -110kJ mol^{-1} and -390kJ mol^{-1}, respectively. The

heat capacities (in J mol^{-1} K^{-1}) of the components are

where, T is the temperature in K. The heat loss (in kJ) per mole of CO burnt

is_____________

Solution:

Basis: 1 mole of CO burnt

O_{2} supplied = 0.5×3 = 1.5 mole

Unreacted O_{2} in product = 1 mole

Standard heat of reaction = - 390 – (-110) = - 280 kJ/mol.

Heat of reactants = 0 (at 298k)

*Answer can only contain numeric values

QUESTION: 53

A cash flow of Rs. 12,000 per year is received at the end of each year (uniform periodic

payment) for 7 consecutive years. The rate of interest is 9% per year compounded annually.

The present worth (in Rs.) of such cash flow at time zero is __________

Solution:

*Answer can only contain numeric values

QUESTION: 54

A polymer plant with a production capacity of 10,000 tons per year has an overall yield of 70%, on mass basis (kg of product per kg of raw material). The raw material costs Rs. 50,000 per ton. A process modification is proposed to increase the overall yield to 75% with an investment of Rs. 12.5 crore. In how many years can the invested amount be recovered with the additional profit? ___________

Solution:

*Answer can only contain numeric values

QUESTION: 55

A step change of magnitude 2 is introduced into a system having the following transfer

function :

The percent overshoot is ___________________.

Solution:

QUESTION: 56

Given below is a simplified block diagram of a feedforward control system

The transfer function of the process is and the disturbance transfer function is

The transfer function of the PERFECT feed forward controller, Gf(s) is

Solution:

*Answer can only contain numeric values

QUESTION: 57

The bottom face of a horizontal slab of thickness 6 mm is maintained at 300^{o}C. The top face is exposed to a flowing gas at 30^{o}C. The thermal conductivity of the slab is 1.5 W m^{-1} K^{-1} and the convective heat transfer coefficient is 30 W m^{-2} K^{-1}. At steady state, the temperature (in ^{o}C) of the top face is __________ .

Solution:

At steady state

heat flux due to conduction = heat flux due to convection

*Answer can only contain numeric values

QUESTION: 58

In a steady incompressible flow, the velocity distribution is given by where, V is in m/s and x, y, and z are in m. In order to satisfy the mass conservation, the value

of the constant P (in s^{-1}) is ____________.

Solution:

QUESTION: 59

Match the following

Solution:

Turbulence: Characterized by fluctuating velocity.

Ergun equation: for calculating pressure drop in packed bed.

Power number: For calculating power consumption in mixing tank.

*Answer can only contain numeric values

QUESTION: 60

In a steady and incompressible flow of a fluid (density = 1.25 kg m^{-3}), the difference between stagnation and static pressures at the same location in the flow is 30 mm of mercury (density = 13600 kg m^{-3}). Considering gravitational acceleration as 10 m s^{-2}, the fluid speed (in m s^{-1}) is ______________

Solution:

*Answer can only contain numeric values

QUESTION: 61

Consider a binary liquid mixture at equilibrium with its vapour at 25OC. Antoine equation for this system is given as where t is in OC and p in Torr.

The Antoine constants (A, B, and C) for the system are given in the following table.

The vapour phase is assumed to be ideal and the activity coefficients ( γ_{i}) for the non-ideal

liquid phase are given by

If the mole fraction of component 1 in liquid phase (x1) is 0.11, then the mole fraction of

component 1 in vapour phase (y1) is ___________

Solution:

QUESTION: 62

A process with transfer function is to be controlled by a feedback proportional controller with a gain K_{c}. If the transfer functions of all other elements in the control loop are unity, then which ONE of the following conditions produces a stable closed loop response?

Solution:

*Answer can only contain numeric values

QUESTION: 63

Consider the following block diagram for a closed-loop feedback control system

A proportional controller is being used with K_{C} = −4 . If a step change in disturbance of magnitude 2 affects the system, then the value of the offset is ____________

Solution:

QUESTION: 64

Determine the correctness or otherwise of the following Assertion [a] and Reason [r].

Assertion: Significant combustion of coke takes place only if it is heated at higher

temperature in presence of air.

Reason: C + O_{2} →CO_{2} is an exothermic reaction

Solution:

Both [a] and [r] are true but [r] is not the correct reason for [a].

QUESTION: 65

Match the raw materials of Groups 1 and 2 with the final products of Group 3

Solution:

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