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QUESTION: 1

**Q. No. 1 – 5 Carry One Mark Each**

**Q.**

If 3 X 5 and 8 Y 11 then which of the following options is TRUE?

Solution:

QUESTION: 2

The Headmaster to speak to you.

Which of the following options is incorrect to complete the above sentence?

Solution:

QUESTION: 3

Mahatama Gandhi was known for his humility as

Solution:

P and R are true

QUESTION: 4

__"All engineering students"__ "__should learn mechanics"__, "__mathematics and"__ "__how to do computation."__

I II III IV

Which of the above underlined parts of the sentence is not appropriate?

Solution:

QUESTION: 5

Select the pair that best expresses a relationship similar to that expressed in the

pair:

water: pipe::

Solution:

QUESTION: 6

**Q. No. 6 – 10 Carry Two Marks Each**

**Q.**

**Velocity of an object fired directly in upward direction is given by V = 80 − 32 t,
where t (time) is in seconds. When will the velocity be between 32 m/sec and 64
m/sec?**

Solution:

QUESTION: 7

In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured

by M2?

Solution:

Let E_{1} be the machine M1 manufacture auto companies

Let E_{2} be the event of machine M2 manufacture auto companies

Given P(E_{1} )= 60% = 60/100

A randomly draw on auto component from the lot is sound defective the

probability it was manufactured by M_{2} is P(E_{2} / A) we have

QUESTION: 8

Following table gives data on tourists from different countries visiting India in the

year 2011.

Which two countries contributed to the one third of the total number of tourists

who visited India in 2011?

Solution:

QUESTION: 9

If |−2X + 9| = 3 then the possible value of |−X| − X^{2} would be:

Solution:

QUESTION: 10

All professors are researchers

Some scientists are professors

Which of the given conclusions is logically valid and is inferred from the above

arguments:

Solution:

QUESTION: 11

**Q. No. 11 – 25 Carry One Mark Each**

**Q.**

The number of emails received on six consecutive days is 11, 9, 18, 18, 4 and 15,

respectively.

What are the median and the mode for these data?

Solution:

By arranging the data in ascending order, the data is 4, 9, 11, 15, 18, 18

Median =(15+11)/2=13

Mode=Maximum number of times occurred value =18

*Answer can only contain numeric values

QUESTION: 12

For two rolls of a fair die, the probability of getting a 4 in the first roll and a

number less than 4 in the second roll, up to 3 digits after the decimal point, is _______

**Imp : you should answer only the numeric value**

Solution:

We known that, if two dice are thrown then total number of out comes

=6^{2}=39

Let E be the event of getting 4 in the first roll and a number less than 4 is the

second.

Then favorable cases to occur E are

(4,1) (4,2), (4,3)

Re quired probability =3/36=1/12 =0.0833

QUESTION: 13

Which of the following statements are TRUE?

P. The eigen values of a symmetric matrix are real

Q. The value of the determinant of an orthogonal matrix can only be +1

R. The transpose of a square matrix A has the same eigen values as those of A

S. The inverse of an ‘n × n’ matrix exists if and only if the rank is less than ‘n’

Solution:

P and R are true

QUESTION: 14

Evaluate

(Note: C is a constant of integration)

Solution:

*Answer can only contain numeric values

QUESTION: 15

A gaseous system contains H2, I2, and HI, which participate in the gas-phase

reaction

At a state of reaction equilibrium, the number of thermodynamic degrees of

freedom is

**Imp : you should answer only the numeric value**

Solution:

As we know F = C - P+ 2

Here C = 2, P = 1 so F= 2- 1+ 2

F = 3

QUESTION: 16

The thermodynamic state of a closed system containing a pure fluid changes from

(T1, p1) to (T2, p2), where T and p denote the temperature and pressure,

respectively. Let Q denote the heat absorbed (> 0 if absorbed by the system) and

W the work done (> 0 if done by the system). Neglect changes in kinetic and

potential energies. Which one of the following is CORRECT?

Solution:

C

Q −W = ΔU

ΔU which solely depends only on initial and final temperature. It is independent

of path.

QUESTION: 17

An equation of state is explicit in pressure p and cubic in the specific volume v. At

the critical point ‘c’, the isotherm passing through ‘c’ satisfies

Solution:

QUESTION: 18

The units of the isothermal compressibility are

Solution:

*Answer can only contain numeric values

QUESTION: 19

An open tank contains two immiscible liquids of densities (800 kg/m^{3} and 1000 kg/m^{3}) as shown in the figure. If g = 10 m/s^{2}, under static conditions, the gauge pressure at the bottom of the tank in Pa is _____________

**Important : you should answer only the numeric value**

Solution:

QUESTION: 20

The apparent viscosity of a fluid is given by is the velocity gradient. The fluid is

Solution:

QUESTION: 21

The mass balance for a fluid with density (ρ) and velocity vector is

Solution:

QUESTION: 22

An incompressible Newtonian fluid, filled in an annular gap between two concentric cylinders of radii R_{1} and R_{2} as shown in the figure, is flowing under steady state conditions. The outer cylinder is rotating with an angular velocity of ? while the inner cylinder is stationary. Given that ( R_{1}-R_{2}) ? R_{1} the profile of the θ -component of the velocity V_{θ} can be approximated by,

Solution:

QUESTION: 23

For a Newtonian fluid flowing in a circular pipe under steady state conditions in

fully developed laminar flow, the Fanning friction factor is

Solution:

QUESTION: 24

In the Tyler standard screen scale series, when the mesh number increases from

3 mesh to 10 mesh, then

Solution:

*Answer can only contain numeric values

QUESTION: 25

Taking the acceleration due to gravity to be 10 m/s^{2}, the separation factor of a cyclone 0.5 m in diameter and having a tangential velocity of 20 m/s near the wall is_____

**Important : you should answer only the numeric value**

Solution:

QUESTION: 26

The effectiveness of a heat exchanger in the ε − NTU method is defined as

Solution:

QUESTION: 27

In a pool boiling experiment, the following phenomena were observed.

P. Natural convection

Q. Film boiling

R. Transition boiling

S. Nucleate boiling

What was the CORRECT sequence of their occurrence?

Solution:

Sequence is

(P) Natural convection (S) Nucleate convection

(R) Transition boiling (Q) Film boiling

*Answer can only contain numeric values

QUESTION: 28

A hole of area 1 cm^{2} is opened on the surface of a large spherical cavity whose inside temperature is maintained at 727 °C. The value of Stefan-Boltzmann constant is 5.67×10^{-8} W/m2-K^{4}. Assuming black body radiation, the rate at which the energy is emitted (in W) by the cavity through the hole, up to 3 digits after the decimal point, is __________

**Important : you should answer only the numeric value**

Solution:

QUESTION: 29

The packing of an existing absorption tower is replaced with a new type of packing. The height of the packing and the inlet conditions are maintained the same as before. Tests reveal that the number of transfer units is lower than before. This indicates that the tower with the new packing, when compared to

that with the old packing, will

Solution:

Here NTU is lowered which suggests that new packing have a lower rate of

absorption of solute from the gas stream in comparison to old packing.

QUESTION: 30

A wet solid is dried over a long period of time by unsaturated air of nonzero constant relative humidity. The moisture content eventually attained by the solid is termed as the

Solution:

Equilibrium moisture is attained by the solid after drying over a long period of

time.

*Answer can only contain numeric values

QUESTION: 31

The exit age distribution for a reactor is given by E(t) = δ(t − 4), where t is in seconds. A first order liquid phase reaction (k = 0.25 s^{-1}) is carried out in this reactor under steady state and isothermal conditions. The mean conversion of the reactant at the exit of the reactor, up to 2 digits after the decimal point, is

**Important : you should answer only the numeric value**

Solution:

General equation for first order

*Answer can only contain numeric values

QUESTION: 32

An isothermal liquid phase zero order reaction A→B (k = 0.5 mol/m^{3}-s) is carried out in a batch reactor. The initial concentration of A is 2 mol/m3. At 3 seconds from the start of the reaction, the concentration of A in mol/m^{3} is

**Important : you should answer only the numeric value**

Solution:

*Answer can only contain numeric values

QUESTION: 33

The overall rates of an isothermal catalytic reaction using spherical catalyst particles of diameters 1 mm and 2 mm are r_{A1} and r_{A2} (in mol (kg-catalyst)^{-1} h^{-1}), respectively. The other physical properties of the catalyst particles are identical. If pore diffusion resistance is very high, the ratio r_{A2}/r_{A1} is

**Important : you should answer only the numeric value**

Solution:

QUESTION: 34

In the manufacture of sulphuric acid by the contact process, the catalytic

oxidation of SO_{2} is carried out in multiple stages mainly to

Solution:

C

To increase the overall conversion interstage cooling is provided.

QUESTION: 35

Match the following

Solution:

(P)-3, (Q)-4, (R)-2, (S)-1

*Answer can only contain numeric values

QUESTION: 36

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

For the function

The residue at z=2 is___________

Solution:

Required answer is residue at z=2

Z=2 is a simple pole, therefore

QUESTION: 37

The solution of the differential equation

given y = 1 at x= 0 is

Solution:

QUESTION: 38

The solution of the differential equation

Solution:

*Answer can only contain numeric values

QUESTION: 39

The value of the integral

evaluated by Simpson’s rule using 4 subintervals (up to 3 digits after the decimal

point) is______

**Important : you should answer only the numeric value**

Solution:

QUESTION: 40

In a process occurring in a closed system F, the heat transferred from F to the surroundings E is 600 J. If the temperature of E is 300 K and that of F is in the range 380 - 400 K, the entropy changes of the surroundings (SSE) and system (ΔSF), in J/K, are given by

Solution:

*Answer can only contain numeric values

QUESTION: 41

A binary liquid mixture is in equilibrium with its vapor at a temperature T = 300 K. The liquid mole fraction x_{1} of species 1 is 0.4 and the molar excess Gibbs free energy is 200 J/mol. The value of the universal gas constant is 8.314 J/mol-K, and γ_{i} denotes the liquid-phase activity coefficient of species i. If ln ( γ_{i} ) = 0.09,

then the value of ln( γ_{2} ), up to 2 digits after the decimal point, is

**Important : you should answer only the numeric value**

Solution:

*Answer can only contain numeric values

QUESTION: 42

Water (density 1000 kg/m^{3}) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship between the diameters of the nozzle at locations 1 and 2 is D_{1} = 4 D_{2}. The average velocity of the stream at location 2 is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa.

Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1

is _________

**Important : you should answer only the numeric value**

Solution:

QUESTION: 43

In the elutriation leg of a commercial crystallizer containing a mixture of coarse and very fine crystals of the same material, a liquid is pumped vertically upward. The liquid velocity is adjusted such that it is slightly lower than the terminal velocity of the coarse crystals only. Hence

Solution:

If velocity Terminal velocity then the very fine crystals will be carried upward

and the coarse particle will settle.

*Answer can only contain numeric values

QUESTION: 44

100 ton/h of a rock feed, of which 80% passed through a mesh size of 2.54 mm, were reduced in size such that 80% of the crushed product passed through a mesh size of 1.27 mm. The power consumption was 100 kW. If 100 ton/h of the same material is similarly crushed from a mesh size of 5.08 mm to a mesh size of 2.54 mm, the power consumption (in kW, to the nearest integer) using Bond’s law, is

Solution:

D_{p2 =} 2.54mm, D_{f2}= 5.08, D_{f1} =1.27mm, D 2.54mm

Bond' s law statement

P_{2}/100 = 0.707, P_{2}= 70.7kW

*Answer can only contain numeric values

QUESTION: 45

Calculate the heat required (in kJ, up to 1 digit after the decimal point) to raise the temperature of 1 mole of a solid material from 100°C to 1000°C. The specific heat ( C_{P} ) of the material (in J/mol-K) is expressed as C_{P} = 20 + 0.005T, where T is in K. Assume no phase change.______

**Important : you should answer only the numeric value**

Solution:

QUESTION: 46

In a double pipe counter-current heat exchanger, the temperature profiles shown in the figure were observed. During operation, due to fouling inside the pipe, the heat transfer rate reduces to half of the original value. Assuming that the flow rates and the physical properties of the fluids do not change, the LMTD (in °C) in the new situation is

Solution:

*Answer can only contain numeric values

QUESTION: 47

The vapor-liquid equilibrium curve of a binary mixture A-B, may be approximated

by a linear equation over a narrow range of liquid mole fractions ( 0.2 < xA <0.3)

as follows

Here is the mole of fraction of A in the vapor. 100 moles of a feed ( x_{A,F} = 0.28) is batch distilled to a final residue ( x_{A,W} = 0.28) . Using the Rayleigh equation, the number of moles of the residue left behind in the distillation unit, up to 2 digits after the decimal point, is __________

**Important : you should answer only the numeric value**

Solution:

QUESTION: 48

A crosscurrent cascade of N ideal stages is used to treat a feed stream of molar flow rate E. The feed stream contains a solute which is to be recovered by a pure solvent having a molar flow rate S. The solvent is divided equally between these N stages. The linear equilibrium curve relating the mole fractions x and y* of the solute in the raffinate and the extract respectively, is given by y* = m x. Assume dilute conditions. The ratio of the solute mole fraction in the original feed to that in the exit raffinate stream i.e. ( x_{0} / x_{N} )is given by

Solution:

For Cross Current Cascade Equilibrium relation is

*Answer can only contain numeric values

QUESTION: 49

A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the mass transfer coefficient k_{c} has been calculated as 1 mm/s using the correlation; Sh = 0.025 Re^{0.6} Sc^{0.33 .}If the velocity of the fluid and the diameter of the pipe are both doubled, what is the new value of kc in mm/s, up to 2 digits after the decimal point? ______

**Important : you should answer only the numeric value**

Solution:

*Answer can only contain numeric values

QUESTION: 50

The gas phase decomposition of azomethane to give ethane and nitrogen takes

place according to the following sequence of elementary reactions.

Using the pseudo-steady-state-approximation for [(CH3)2N2]*, the order with

respect to azomethane in the rate expression for the formation of ethane, in the limit of high concentrations of azomethane, is ______________

**Important : you should answer only the numeric value**

Solution:

*Answer can only contain numeric values

QUESTION: 51

A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the same overall conversion, if the CSTR is replaced by two smaller and identical isothermal CSTRs in series, the % reduction in total volume, to the nearest integer, is _____________

**Important : you should answer only the numeric value**

Solution:

QUESTION: 52

Match the reactant-product combination in Group 1 with the unit process in Group

2.

Solution:

QUESTION: 53

Identify which of the following statements are FALSE.

(P) Oils with an oleic radical (1 double bond) are more suitable than oils with a

linolenic radical (3 double bonds) as film forming vehicles for paints

(Q) Production of synthesis gas from coal and steam is an endothermic process

(R) Use of chlorine for bleaching of wood pulp results in the release of dioxins

(S) In the manufacture of urea from ammonia, the main intermediate product

formed is ammonium bicarbonate

Solution:

D

Ammonium carbamate is the main intermediate product during manufacturing of urea from NH3.

QUESTION: 54

A unit gain 2nd order underdamped process has a period of oscillation 1 second

and decay ratio 0.25. The transfer function of the process is

Solution:

*Answer can only contain numeric values

QUESTION: 55

A control valve, with a turndown ratio of 50, follows equal percentage characteristics. The flow rate of a liquid through the valve at 40% stem position is 1 m^{3}/h. What will be the flow rate in m^{3}/h at 50% stem position, if the pressure drop across the valve remains unchanged? (Up to 2 digits after the decimal

point.)

**Important : you should answer only the numeric value**

Solution:

*Answer can only contain numeric values

QUESTION: 56

The purchase cost of a heat exchanger of 20 m^{2} area was Rs. 500000 in 2006. What will be the estimated cost (in Rs. to the nearest integer) of a similar heat exchanger of 50 m^{2} area in the year 2013? Assume the six-tenths factor rule for scaling and the cost index for 2006 as 430.2. The projected cost index for the

year 2013 is 512.6.

**Important : you should answer only the numeric value**

Solution:

*Answer can only contain numeric values

QUESTION: 57

A plant manufactures compressors at the rate of N units/day. The daily fixed charges are Rs. 20000 and the variable cost per compressor is Rs. 500 + 0.2 N^{1.3.} The selling price per compressor is Rs. 1000. The number of compressors to be manufactured, to the nearest integer, in order to maximize the daily profit is

**Important : you should answer only the numeric value**

Solution:

Daily profit = selling price – cost price

*Answer can only contain numeric values

QUESTION: 58

**Common Data Questions: 58 and 59**

**A reverse osmosis unit treats feed water (F) containing fluoride and its output consists of a permeate stream (P) and a reject stream (R). Let C _{F}, C_{P}, and C_{R} denote the fluoride concentrations in the feed, permeate, and reject streams, respectively. Under steady state conditions, the volumetric flow rate of the reject is 60 % of the volumetric flow rate of the inlet stream, and C_{F} = 2 mg/L and C_{P} =0.1 mg/L**.

**Q.**

The value of CR in mg/L, up to one digit after the decimal point, is

**Important : you should answer only the numeric value**

Solution:

*Answer can only contain numeric values

QUESTION: 59

**A reverse osmosis unit treats feed water (F) containing fluoride and its output consists of a permeate stream (P) and a reject stream (R). Let CF, CP, and CR denote the fluoride concentrations in the feed, permeate, and reject streams, respectively. Under steady state conditions, the volumetric flow rate of the reject is 60 % of the volumetric flow rate of the inlet stream, and CF = 2 mg/L and CP =0.1 mg/L**

**Q.**

**A fraction f of the feed is bypassed and mixed with the permeate to obtain treated water having a fluoride concentration of 1 mg/L. Here also the flow rate of the reject stream is 60% of the flow rate entering the reverse osmosis unit (after the bypass). The value of f, up to 2 digits after the decimal point, is**

**Important : you should answer only the numeric value**

Solution:

Mass balance at Reverse osmosis in and out

P=0.4(1-f)F

Mass balance of fluoride on bypass stream

F x f x 2 = [ (F x f)+ P]

F x f x 2 = [ (F x f) + 0.4 (1- f) F]

on solving, we get

2 x f =0.4(1-f) +f

F=0.4/1.4 =0.286

*Answer can only contain numeric values

QUESTION: 60

**Common Data Questions: 60 and 61**

Liquid reactant A decomposes as follows

An aqueous feed of composition C_{A0} = 30 mol/m3, C_{R0} = 2 mol/m^{3}, and C_{S0}= 1 mol/m^{3} enters a CSTR in which the above reactions occur. Assume isothermal and steady state conditions.

**Q.**

If the conversion of A is 80 %, the concentration of R in the exit stream in

mol/m3, to the nearest integer, is______

**Important : you should answer only the numeric value**

Solution:

*Answer can only contain numeric values

QUESTION: 61

**Liquid reactant A decomposes as follows**

**An aqueous feed of composition C _{A0} = 30 mol/m3, C_{R0} = 2 mol/m^{3}, and C_{S0}= 1 mol/m^{3} enters a CSTR in which the above reactions occur. Assume isothermal and steady state conditions.**

**Q.**

**What is the % conversion of A, to the nearest integer, so that the concentration of S in the exit stream is 11.8 mol/m ^{3}?**

**Important : you should answer only the numeric value**

Solution:

QUESTION: 62

**Linked Answer Questions: Q.62 to Q.65**

**Statement for Linked Answer Questions: 62 & 63**

**The vapor liquid equilibrium relation for an ideal binary system is given by**

**Here x _{A} and are the mole fractions of species A in the liquid and vapor, respectively. The relative volatility ( α_{AB}) is greater than unity.**

**Q.**

**The liquid mole fraction at which the maximum difference between the equilibrium vapor mole fraction and liquid mole fraction occurs is**

Solution:

QUESTION: 63

**The vapor liquid equilibrium relation for an ideal binary system is given by**

**Here x _{A} and are the mole fractions of species A in the liquid and vapor, respectively. The relative volatility ( α_{AB}) is greater than unity.**

**Q.**

**A liquid having the composition found in the first part of the linked answer question, is flash distilled at a steady state to a final liquid mole fraction of 0.25. If **** is 2.5, the fraction of the feed vaporized is**

Solution:

QUESTION: 64

**Statement for Linked Answer Questions: 64 and 65**

**Consider the following transfer function**

(Note: The unit of the process time constant is in seconds.)

**Q.**

The crossover frequency (in rad/s) of the process is

Solution:

QUESTION: 65

**Consider the following transfer function**

(Note: The unit of the process time constant is in seconds.)

**Q.**

For the computation of Ziegler-Nichols settings, the ultimate period (in s/cycle)

and the ultimate gain are

Solution:

### Gate-Paper-Chemical-Engineering

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