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GATE 2021 Computer Science and Information Technology Engineering Section-I Previous Year Paper

General Aptitude (GA)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.1	The ratio of boys to girls in a class is 7 to 3. Among the options below, an acceptable value for the total number of students in the class is:
(A)	21
(B)	37
(C)	50
(D)	73

Q.3	Consider the following sentences:Everybody in the class is prepared for the exam.Babu invited Danish to his home because he enjoys playing chess. Which of the following is the CORRECT observation about the above two sentences?
(A)	(i) is grammatically correct and (ii) is unambiguous
(B)	(i) is grammatically incorrect and (ii) is unambiguous
(C)	(i) is grammatically correct and (ii) is ambiguous
(D)	(i) is grammatically incorrect and (ii) is ambiguous

Q.5	_______is to surgery as writer is to__________ Which one of the following options maintains a similar logical relation in the above sentence?
(A)	Plan, outline
(B)	Hospital, library
(C)	Doctor, book
(D)	Medicine, grammar

Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Q.6	We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm x 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is________
(A)	𝜋2
(B)	3𝜋
(C)	9𝜋
(D)	3𝜋

Q.7	temsCost (₹) P5,400—5, Profit%Marked Price (₹) 860Q—2510,000 Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost The discount on item Q as a percentage of its marked price, is _________
(A)	25
(B)	12.5
(C)	10
(D)	5

Q.8	There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is____
(A)	0.3024
(B)	0.4235
(C)	0.6976
(D)	0.8125

Q.9	Given below are two statements 1 and 2, and two conclusions I and II. Statement 1: All bacteria are microorganisms. Statement 2: All pathogens are microorganisms. Conclusion I: Some pathogens are bacteria. Conclusion II: All pathogens are not bacteria. Based on the above statements and conclusions, which one of the following options is logically CORRECT?
(A)	Only conclusion I is correct
(B)	Only conclusion II is correct
(C)	Either conclusion I or II is correct.
(D)	Neither conclusion I nor II is correct.

Q.10	Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality. Which one of the following statements summarizes the passage?
(A)	The proposed AOM addresses the core problems that cause obesity.
(B)	If obesity reduces, poverty will naturally reduce, since obesity causes poverty.
(C)	AOM are addressing the core problems and are likely to succeed.
(D)	AOM are addressing the problem superficially.

Computer Science and Information Technology

Q.1 – Q.10 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.11 – Q.15 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

Q.16 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

Q.26 – Q.39 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Q.40 – Q.47 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

Q.48 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

Answer Key

Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans
1	C	1	C	11	A; C	21	86 to 86	31	A	41	B	51	50 to 50
2	A	2	C	12	D	22	17 to 17	32	B	42	B; C; D	52	3 to 3
3	C	3	D	13	A	23	819 to 820 OR 205 to 205	33	A	43	C	53	17160 to 17160
4	A	4	C	14	A; C	24	-7.75 to -7.75	34	B	44	A; B; C	54	0.04 to 0.04
5	C	5	C	15	A; C	25	12 to 12	35	D	45	A; C	55	50 to 50
6	C	6	A	16	11 to 11	26	B	36	A	46	A; B; D
7	C	7	B	17	3 to 3	27	C	37	B	47	C
8	C	8	C	18	0.35 to 0.39	28	A	38	D	48	1023 to 1023
9	C OR D	9	C	19	65 to 65	29	A	39	A	49	50 to 52
10	D	10	D	20	0.25 to 0.25	30	C	40	A; C	50	6 to 6

GATE 2021 Chemical Engineering Previous Year Paper

General Aptitude (GA)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.1	The ratio of boys to girls in a class is 7 to 3.Among the options below, an acceptable value for the total number of students in the class is:
(A)	21
(B)	37
(C)	50
(D)	73

Q.3	Consider the following sentences:Everybody in the class is prepared for the exam.Babu invited Danish to his home because he enjoys playing chess.Which of the following is the CORRECT observation about the above two sentences?
(A)	(i) is grammatically correct and (ii) is unambiguous
(B)	(i) is grammatically incorrect and (ii) is unambiguous
(C)	(i) is grammatically correct and (ii) is ambiguous
(D)	(i) is grammatically incorrect and (ii) is ambiguous

Q.5	_______________ is to surgery as writer is to _________________.Which one of the following options maintains a similar logical relation in the above sentence?
(A)	Plan, outline
(B)	Hospital, library
(C)	Doctor, book
(D)	Medicine, grammar

Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Q.6	We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm x 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is _____________.
(A)	𝜋/2
(B)	3/𝜋
(C)	9/𝜋
(D)	3𝜋

Q.7	Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost The discount on item Q, as a percentage of its marked price, is __________.
(A)	25
(B)	12.5
(C)	10
(D)	5

Q.8	There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.The probability that at least two chocolates are identical is ________________.
(A)	0.3024
(B)	0.4235
(C)	0.6976
(D)	0.8125

Q.9	Given below are two statements 1 and 2, and two conclusions I and II. Statement 1: All bacteria are microorganisms. Statement 2: All pathogens are microorganisms. Conclusion I: Some pathogens are bacteria. Conclusion II: All pathogens are not bacteria. Based on the above statements and conclusions, which one of the following options is logically CORRECT?
(A)	Only conclusion I is correct
(B)	Only conclusion II is correct
(C)	Either conclusion I or II is correct.
(D)	Neither conclusion I nor II is correct.

Q.10	Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality.Which one of the following statements summarizes the passage?
(A)	The proposed AOM addresses the core problems that cause obesity.
(B)	If obesity reduces, poverty will naturally reduce, since obesity causes poverty.
(C)	AOM are addressing the core problems and are likely to succeed.
(D)	AOM are addressing the problem superficially.

Chemical Engineering (CH)

Q. 1– Q.15 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.1	An ordinary differential equation (ODE), dydx=2y , with an initial condition y(0) = 1, has the analytical solution y = e^2x.Using Runge-Kutta second order method, numerically integrate the ODE to calculate 𝒚 at 𝒙 = 𝟎. 𝟓 using a step size of 𝒉 = 𝟎. 𝟓.If the relative percentage error is defined as, s=[(y analytical-y numerical) / y analytical)] 100 then the value of 𝗌 at 𝒙 = 𝟎. 𝟓 is_________________.
(A)	0.06
(B)	0.8
(C)	4.0
(D)	8.0

Q.2	The function 𝐜𝐨𝐬(𝒙) is approximated using Taylor series around 𝒙 = 𝟎 as 𝐜𝐨𝐬(𝒙) ≈ 𝟏 + 𝒂𝒙 + 𝒃𝒙^𝟐 + 𝒄𝒙^𝟑 + 𝒅𝒙^𝟒. The values of a, b, c and d are
(A)	𝑎 = 1, 𝑏 = −0.5, 𝑐 = −1, 𝑑 = −0.25
(B)	𝑎 = 0, 𝑏 = −0.5, 𝑐 = 0, 𝑑 = 0.042
(C)	𝑎 = 0, 𝑏 = 0.5, 𝑐 = 0, 𝑑 = 0.042
(D)	𝑎 = −0.5, 𝑏 = 0, 𝑐 = 0.042, 𝑑 = 0

Q.3	The heat of combustion of methane, carbon monoxide and hydrogen are 𝑷, 𝑸 and 𝑹 respectively. For the reaction below,CH₄ + H₂O ⎯⎯→ CO + 3H₂the heat of reaction is given by
(A)	𝑃 − 𝑄 − 3𝑅
(B)	𝑄 + 3𝑅 − 𝑃
(C)	𝑃 − 𝑄 − 𝑅
(D)	𝑄 + 𝑅 − 𝑃

Q.4	A batch settling experiment is performed in a long column using a dilute dispersion containing an equal number of particles of type A and type B in water (density 1000 kg m^–3) at room temperature.Type A are spherical particles of diameter 30 μm and density 1100 kg m^–3. Type B are spherical particles of diameter 10 μm and density 1900 kg m^–3.Assuming that Stokes’ law is valid throughout the duration of the experiment, the settled bed would
(A)	consist of a homogeneous mixture of type A and type B particles
(B)	consist of type B particles only
(C)	be completely segregated with type B particles on top of type A particles
(D)	be completely segregated with type A particles on top of type B particles

Q.5	A three-dimensional velocity field is given by 𝑽 = 𝟓𝒙^𝟐𝒚 𝒊 + 𝑪𝒚 𝒋 − 𝟏𝟎𝒙𝒚𝒛 𝒌, where 𝒊, 𝒋, 𝒌 are the unit vectors in 𝒙, 𝒚, 𝒛 directions, respectively, describing a cartesian coordinate system. The coefficient 𝑪 is a constant. If 𝑽 describes an incompressible fluid flow, the value of 𝑪 is
(A)	–1
(B)	0
(C)	1
(D)	5

Q.6	Heat transfer coefficient for a vapor condensing as a film on a vertical surface is given by
(A)	Dittus-Boelter equation
(B)	Nusselt theory
(C)	Chilton-Colburn analogy
(D)	Sieder-Tate equation

Q.7	In a double-pipe heat exchanger of 10 m length, a hot fluid flows in the annulus and a cold fluid flows in the inner pipe. The temperature profiles of the hot (𝑻_𝒉) and cold (𝑻_𝒄) fluids along the length of the heat exchanger (x, such that x ≥ 0), are given by𝑻_𝒉(𝒙) = 𝟖𝟎 − 𝟑𝒙𝑻_𝒄(𝒙) = 𝟐𝟎 + 𝟐𝒙where 𝑻_𝒉 and 𝑻_𝒄 are in ^oC, and x is in meter.The logarithmic mean temperature difference (in ^oC) is
(A)	24.6
(B)	27.9
(C)	30.0
(D)	50.0

Q.8	For a shell-and-tube heat exchanger, the clean overall heat transfer coefficient is calculated as 250 W m^–2K^–1for a specific process condition. It is expected that the heat exchanger may be fouled during the operation, and a fouling resistance of 0.001 m²K W^–1is prescribed. The dirt overall heat transfer coefficient is _________________W m^–2K^–1.
(A)	100
(B)	150
(C)	200
(D)	250

Q.9	In reverse osmosis, the hydraulic pressure and osmotic pressure at the feed side of the membrane are P1 and π1, respectively. The corresponding values are P2 and π2 at the permeate side. The membrane, feed, and permeate are at the same temperature. For equilibrium to prevail, the general criterion that should be satisfied is
(A)	π₁ = π₂
(B)	P₁ = P₂
(C)	P₁ + π₁ = P₂ + π₂
(D)	P₁ – π₁ = P₂ – π₂

Q.11	Which of the following is NOT a standard to transmit measurement and control signals?
(A)	4 – 20 mA
(B)	3 – 15 psig
(C)	0 – 100 %
(D)	1 – 5 VDC

Q.12	A feedforward controller can be used only if
(A)	the disturbance variable can be measured
(B)	the disturbance variable can be manipulated
(C)	the disturbance variable can be ignored
(D)	regulatory control is not required

Q.13	Turnover ratio is defined as (A)fixed capital investment / Gross annual sales (B) Gross annual sales / fixed capital investment (C) fixed capital investment / Average selling price of the product (D) Average selling price of the product / Gross annual sales

Q.14	A principal amount is charged a nominal annual interest rate of 10%. If the interest rate is compounded continuously, the final amount at the end of one year would be
(A)	higher than the amount obtained when the interest rate is compounded monthly
(B)	lower than the amount obtained when the interest rate is compounded annually
(C)	equal to 1.365 times the principal amount
(D)	equal to the amount obtained when using an effective interest rate of 27.18%

Q.16 – Q.18 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

Q.19 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

Q.19

A source placed at the origin of a circular sample holder (radius 𝒓 = 𝟏 𝒎) emits particles uniformly in all directions. A detector of length 𝒍 = 𝟏 𝒄𝒎 has been placed along the perimeter of the sample holder. During an experiment, the detector registers 14 particles.The total number of particles emitted during the experiment is .

Q.21

The van der Waals equation of state is given byPr=8Tr3vr-1-3vr2where 𝑷_𝒓, 𝑻_𝒓 𝐚𝐧𝐝 𝒗_𝒓 represent reduced pressure, reduced temperature and reduced molar volume, respectively. The compressibility factor at critical point (𝒛_𝒄) is 𝟑/𝟖.If 𝒗_𝒓 = 𝟑 𝐚𝐧𝐝 𝑻_𝒓 = 𝟒/ , then the compressibility factor based on the van der Waals equation of state is________.(round off to 2 decimal places).

Q.22

Consider a steady flow of an incompressible, Newtonian fluid through a smooth circular pipe. Let 𝑎_{𝒍𝒂𝒎𝒊𝒏𝒂𝒓} and 𝑎_{𝒕𝒖𝒓𝒃𝒖𝒍𝒆𝒏𝒕} denote the kinetic energy correction factors for laminar and turbulent flow through the pipe, respectively. For turbulent flow through the pipeαturbulent=V0V32n2(3 + n) (3 + 2n)Here, 𝑽̅ is the average velocity, 𝑽𝟎 is the centerline velocity, and n is a parameter. The ratio of average velocity to the centerline velocity for turbulent flow through the pipe is given byVV0=2n2(n + 1) (2n + 1)For 𝒏 = 𝟕, 𝒕he value of αturbulentαlaminaris________. (round off to 2 decimal places).

Q.23

The molar heat capacity at constant pressure Cp (in J mol^–1 K^–1) for n- pentane as a function of temperature (T in K) is given byCpR= 2.46 + 45.4 ×10⁻³T − 14.1×10⁻⁶T ² . Take R = 8.314 J mol^–1K^–1.At 1000 K, the rate of change of molar entropy of n-pentane with respect to temperature at constant pressure is______J mol^–1K^–2(round off to 2 decimal places).

Q.25

A company invests in a recovery unit to separate valuable metals from effluent streams. The total initial capital investment of this unit is Rs. 10 lakhs. The recovered metals are worth Rs. 4 lakhs per year.If the annual return on this investment is 15%, the annual operating costs should be_______lakhs of rupees (correct to 1 decimal place).

Q.26 – Q.33 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

Q.26	Let 𝑨 be a square matrix of size 𝒏 × 𝒏 (𝒏 > 1). The elements of 𝑨 = {𝒂_𝒊𝒋} are given byThe determinant of 𝑨 is
(A)	0
(B)	1
(C)	𝑛!
(D)	(𝑛!)²

Q.27	Consider a fluid confined between two horizontal parallel plates and subjected to shear flow.In the first experiment, the plates are separated by a distance of 1 mm. It is found that a shear stress of 2 N m^–2has to be applied to keep the top plate moving with a velocity of 2 m s^–1, while the other plate is fixed.In the second experiment, the plates are separated by a distance of 0.25 mm. It is found that a shear stress of 3 N m^–2has to be applied to keep the top plate moving with a velocity of 1 m s^–1, while the other plate is fixed.In the range of shear rates studied, the rheological character of the fluid is
(A)	Newtonian
(B)	Pseudoplastic
(C)	Dilatant
(D)	Ideal and inviscid

Q.29 In a solvent regeneration process, a gas is used to strip a solute from a liquid in a countercurrent packed tower operating under isothermal condition. Pure gas is used in this stripping operation. All solutions are dilute and Henry’s law, y* = mx , is applicable. Here, y* is the mole fraction of the solute in the gas phase in equilibrium with the liquid phase of solute mole fraction x, and m is the Henry’s law constant.

Let x1 be the mole fraction of the solute in the leaving liquid, and x2 be the mole fraction of solute in the entering liquid.

When the value of the ratio of the liquid-to-gas molar flow rates is equal to m, the overall liquid phase Number of Transfer Units, NTUOL, is given by

(A) X₂-X₁ / X₁(B) X₂+X₁/ X₂-X₁(C) ln (X₂ / X₁)
(D) ln (X₂+X₁/ X₂-X₁)

Q.32	Which of the following is NOT a necessary condition for a process under closed-loop control to be stable?
(A)	Dead-time term(s) must be absent in the open-loop transfer function
(B)	Roots of the characteristic equation must have negative real part
(C)	All the elements in the left (first) column of the Routh array must have the same sign
(D)	Open-loop transfer function must have an amplitude ratio less than 1 at the critical frequency

Q.34 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).


Q.34	To solve an algebraic equation f (x) = 0, an iterative scheme of the type x_n+1= g(x_n) is proposed, where g( x) = x − f(x)/f’(x). At the solution x = s , g′(s) = 0 and g′′(s) ≠ 0 .The order of convergence for this iterative scheme near the solution is__________.

Q.38	The combustion of carbon monoxide is carried out in a closed, rigid and insulated vessel. 1 mol of CO, 0.5 mol of O2 and 2 mol of N2 are taken initially at 1 bar and 298 K, and the combustion is carried out to completion.The standard molar internal energy change of reaction ( Δu^o_R) for the combustion of carbon monoxide at 298 K = –282 kJ mol^–1. At constant pressure, the molar heat capacities of N2 and CO2 are 33.314 J mol^–1 K^– ¹and 58.314 J mol^–1K^–1, respectively. Assume the heat capacities to beindependent of temperature, and the gases are ideal. Take R = 8.314 J mol^–1 _K–1_.The final pressure in the vessel at the completion of the reaction is ___________ bar (round off to 1 decimal place).

Q.39	A gaseous mixture at 1 bar and 300 K consists of 20 mol % CO2 and 80 mol% inert gas.Assume the gases to be ideal. Take R = 8.314 J mol^–1K^–1.The magnitude of minimum work required to separate 100 mol of this mixture at 1 bar and 300 K into pure CO2 and inert gas at the same temperature and pressure is_________kJ (round off to nearest integer).

Q.40

A binary liquid mixture consists of two species 1 and 2. Let 𝜸 and 𝒙 represent the activity coefficient and the mole fraction of the species, respectively. Using a molar excess Gibbs free energy model, 𝐥𝐧 𝜸_𝟏 𝒗𝒔. 𝒙_𝟏 and 𝐥𝐧 𝜸_𝟐 𝒗𝒔. 𝒙_𝟏 are plotted. A tangent drawn to the 𝐥𝐧 𝜸_𝟏 𝒗𝒔. 𝒙_𝟏 curve at a mole fraction of 𝒙_𝟏 = 𝟎. 𝟐 has a slope = −1.728.The slope of the tangent drawn to the 𝐥𝐧 𝜸_𝟐 𝒗𝒔. 𝒙_𝟏 curve at the same mole fraction is (correct to 3 decimal places).

Q.43	A straight fin of uniform circular cross section and adiabatic tip has an aspect ratio (length/diameter) of 4. If the Biot number (based on radius of the fin as the characteristic length) is 0.04, the fin efficiency is_________% (round off to nearest integer).

Q.44

A double-effect evaporator is used to concentrate a solution. Steam is sent to the first effect at 110 ^oC and the boiling point of the solution in the second effect is 63.3 ^oC. The overall heat transfer coefficient in the first effect and second effect are 2000 W m^–2K^–1and 1500 W m^–2K^–1, respectively. The heat required to raise the temperature of the feed to the boiling point can be neglected. The heat flux in the two evaporators can be assumed to be equal.The temperature at which the solution boils in the first effect is__________^oC (round off to nearest integer).

Q.45

Consider a solid slab of thickness 2L and uniform cross section A. The volumetric rate of heat generation within the slab is 𝒈̇ (W m^–3). The slab loses heat by convection at both the ends to air with heat transfer coefficient h. Assuming steady state, one-dimensional heat transfer, the temperature profile within the slab along the thickness is given by:

where k is the thermal conductivity of the slab and 𝑻_𝒔 is the surface temperature. If 𝑻_𝒔 = 𝟑𝟓𝟎 K, ambient air temperature 𝑻_∞ = 𝟑𝟎𝟎 𝐊, and Biot number (based on L as the characteristic length) is 0.5, the maximum temperature in the slab is___________K (round off to nearest integer).

Q.46

A distillation column handling a binary mixture of A and B is operating at total reflux. It has two ideal stages including the reboiler. The mole fraction of the more volatile component in the residue ( x_W) is 0.1. The average relative volatility αAB is 4. The mole fraction of A in the distillate ( x_D) is____________(round off to 2 decimal places).

Q.47

In a batch drying experiment, a solid with a critical moisture content of 0.2 kg H2O/kg dry solid is dried from an initial moisture content of 0.35 kg H2O/kg dry solid to a final moisture content of 0.1 kg H2O/kg dry solid in 5 h. In the constant rate regime, the rate of drying is 2 kg H2O/(m².h).The entire falling rate regime is assumed to be uniformly linear. The equilibrium moisture content is assumed to be zero.The mass of the dry solid per unit area is_______kg/m²(round off to nearest integer).

Q.49

The following isothermal autocatalytic reaction,A + B ⎯⎯→ 2B ( − r ) = 0.1C_A C_B (mol L^-1 s^-1)is carried out in an ideal continuous stirred tank reactor (CSTR) operating at steady state. Pure A at 1 mol L^–1is fed, and 90% of A is converted in the CSTR. The space time of the CSTR is_________seconds.

Q.50

Reactant A decomposes to products B and C in the presence of an enzyme in a well-stirred batch reactor. The kinetic rate expression is given by-rA=0.01C0.05 + CA(mol L-1 min-1)If the initial concentration of A is 0.02 mol L^–1, the time taken to achieve 50% conversion of A is min (round off to 2 decimal places).

Q.51

The following homogeneous, irreversible reaction involving ideal gases,A → B + C ( − r_A) = 0.5C _A C_B(mol L^-1 s¹)is carried out in a steady state ideal plug flow reactor (PFR) operating at isothermal and isobaric conditions. The feed stream consists of pure A, entering at 2 m s^–1.In order to achieve 50% conversion of A, the required length of the PFR is_______meter (round off to 2 decimal places).

Q.52	A system has a transfer function G(s)=3e-4x12s + 1. When a step change of magnitude M is given to the system input, the final value of the system output is measured to be 120. The value of M is__________.

Q.53

A process has a transfer function G(s) = Y(s)X(s)=2090000s2+240s+1.Initially the process is at steady state with (𝒕 = 𝟎) = 𝟎. 𝟒 and 𝒚(𝒕 = 𝟎) = 𝟏𝟎𝟎. If a step change in 𝒙 is given from 𝟎. 𝟒 to 𝟎. 𝟓, the maximum value of 𝒚 that will be observed before it reaches the new steady state is______(round off to 1 decimal place).

Q.54

Operating labor requirements L in the chemical process industry is described in terms of the plant capacity C (kg day^–1) over a wide range (10³– 10⁶) by a power law relationshipL = αC^βwhere α and β are constants. It is known thatL is 60 when C is 2 × 10⁴L is 70 when C is 6 × 10⁴The value of L when C is 10⁵kg day^–1is_______(round off to nearest integer).

Q.55

A viscous liquid is pumped through a pipe network in a chemical plant. The annual pumping cost per unit length of pipe is given byCpump=48.13 q2D4The annual cost of the installed piping system per unit length of pipe is given by𝐂_{𝐩𝐢𝐩𝐢𝐧𝐠} = 𝟒𝟓. 𝟗𝟐𝐃Here, D is the inner diameter of the pipe in meter, q is the volumetric flowrate of the liquid in m³s^–1and μ is the viscosity of the liquid in Pa.s.If the viscosity of the liquid is 20 × 10^–3Pa.s and the volumetric flow rate of the liquid is 10^–4m³s^–1, the economic inner diameter of the pipe is _______ meter (round off to 3 decimal places).

Answer Key

Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans
1	C	1	D	11	C	21	0.83 to 0.85	31	C	41	8 to 8	51	3.49 to 3.61
2	A	2	B	12	A	22	0.52 to 0.54	32	A	42	1790 to 1800	52	40 to 40
3	C	3	A	13	B	23	0.27 to 0.29	33	B	43	42 to 44	53	102.4 to 102.6
4	A	4	A	14	A	24	0.5 to 0.5	34	2 to 2	44	89 to 91	54	73 to 77
5	C	5	B	15	C	25	2.5 to 2.5	35	0.069 to 0.071	45	362 to 363	55	0.014 to 0.016
6	C	6	B	16	A; B; C	26	D	36	0.161 to 0.169	46	0.63 to 0.65
7	C	7	B	17	A; C; D	27	B	37	40 to 40	47	34 to 35
8	C	8	C	18	A; D	28	B	38	8.9 to 9.1	48	0.24 to 0.26
9	C OR D	9	D	19	8790 to 8800	29	A	39	124 to 126	49	100 to 100
10	D	10	B	20	3 to 3	30	C	40	0.432 to 0.432	50	4.44 to 4.51

GATE 2021 Civil Engineering Section-II Previous Year Paper

GATE 2021 Civil Engineering Section-II Previous Year Paper

General Aptitude (GA)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.1	(i) Arun and Aparna are here. (ii) Arun and Aparna is here. (iii) Arun’s families is here. (iv) Arun’s family is here. Which of the above sentences are grammatically CORRECT?
(A)	(i) and (ii)
(B)	(i) and (iv)
(C)	(ii) and (iv)
(D)	(iii) and (iv)

Q.3	Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:
(A)	1/36
(B)	1/12
(C)	⅛
(D)	¼

Q.4	⊕ and ⊙ are two operators on numbers p and q such that𝑝 ⊙ 𝑞 = 𝑝 − 𝑞, and p ⊕ q = p✗ q Then, (9 ⊙ (6 ⊕ 7)) ⊙ (7 ⊕ (6 ⊙ 5))=
(A)	40
(B)	-26
(C)	-33
(D)	-40

Q.5	Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:
(A)	6
(B)	9
(C)	18
(D)	24

Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Q.6	On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P.The distance of point Q to point O, in the same units, should be_________
(A)	3
(B)	4
(C)	5
(D)	6

Q.7	The author said, “Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public speakers think they can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks.”Based on the above passage, which one of the following is TRUE?
(A)	The author is of the opinion that rehearsing is important for musicians, actors and public speakers.
(B)	The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.
(C)	The author is of the opinion that rehearsing is more important only for musicians than public speakers.
(D)	The author is of the opinion that rehearsal is more important for actors than musicians.

Q.8	1.Some football players play cricket.2.All cricket players play hockey.Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:
(A)	No football player plays hockey.
(B)	Some football players play hockey.
(C)	All football players play hockey.
(D)	All hockey players play football.

Q.10	In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer.The minimum area of the triangle PQR possible, in cm2, is
(A)	18
(B)	24
(C)	48√3
(D)	144√3

Civil Engineering

Q.1– Q.16 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.1	The value of 𝒙→∞lim 𝒙 𝐥𝐧(𝒙)𝟏+𝒙2 𝐥𝐢𝐦 is
(A)	0
(B)	1.0
(C)	0.5
(D)	∞

Q.2	The rank of the matrix is
(A)	1
(B)	2
(C)	3
(D)	4

Q.4	If A is a square matrix then orthogonality property mandates
(A)	AA^T = I
(B)	AA^T = 0
(C)	AA^T = A^-1
(D)	AA^T = A²

Q.5	In general, the CORRECT sequence of surveying operations is
(A)	Field observations → Reconnaissance → Data analysis → Map making
(B)	Data analysis → Reconnaissance → Field observations → Map making
(C)	Reconnaissance → Field observations → Data analysis → Map making
(D)	Reconnaissance → Data analysis → Field observations → Map making

Q.6	Strain hardening of structural steel means
(A)	experiencing higher stress than yield stress with increased deformation
(B)	strengthening steel member externally for reducing strain experienced
(C)	strain occurring before plastic flow of steel material
(D)	decrease in the stress experienced with increasing strain

Q.8	Seasoning of timber for use in construction is done essentially to
(A)	increase strength and durability
(B)	smoothen timber surfaces
(C)	remove knots from timber logs
(D)	cut timber in right season and geometry

Q.9	In case of bids in Two-Envelop System, the correct option is
(A)	Technical bid is opened first
(B)	Financial bid is opened first
(C)	Both (Technical and Financial) bids are opened simultaneously
(D)	Either of the two (Technical and Financial) bids can be opened first

Q.10	The most appropriate triaxial test to assess the long-term stability of an excavated clay slope is
(A)	consolidated drained test
(B)	unconsolidated undrained test
(C)	consolidated undrained test
(D)	unconfined compression test

Q.11	As per the Unified Soil Classification System (USCS), the type of soil represented by ‘MH’ is
(A)	Inorganic silts of high plasticity with liquid limit more than 50%
(B)	Inorganic silts of low plasticity with liquid limit less than 50%
(C)	Inorganic clays of high plasticity with liquid limit less than 50%
(D)	Inorganic clays of low plasticity with liquid limit more than 50%

Q.12	The ratio of the momentum correction factor to the energy correction factor for a laminar flow in a pipe is
(A)	1/2
(B)	2/3
(C)	1
(D)	3/2

Q.13	Relationship between traffic speed and density is described using a negatively sloped straight line. If 𝒗_𝒇 is the free-flow speed then the speed at which the maximum flow occurs is
(A)	0
(B)	vf4
(C)	vf2
(D)	vf

Q.14	Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].Assertion [a]: One of the best ways to reduce the amount of solid wastes is to reduce the consumption of raw materials.Reason [r]: Solid wastes are seldom generated when raw materials are converted to goods for consumption.
(A)	Both [a] and [r] are true and [r] is the correct reason for [a]
(B)	Both [a] and [r] are true but [r] is not the correct reason for [a]
(C)	Both [a] and [r] are false
(D)	[a] is true but [r] is false

Q.15	The hardness of a water sample is measured directly by titration with0.01 M solution of ethylenediamine tetraacetic acid (EDTA) using eriochrome black T (EBT) as an indicator. The EBT reacts and forms complexes with divalent metallic cations present in the water. During titration, the EDTA replaces the EBT in the complex. When the replacement of EBT is complete at the end point of the titration, the colour of the solution changes from
(A)	blue-green to reddish brown
(B)	blue to colourless
(C)	reddish brown to pinkish yellow
(D)	wine red to blue

Q.16	The softening point of bitumen has the same unit as that of
(A)	distance
(B)	temperature
(C)	time
(D)	viscosity

Q.17 Multiple Select Question (MSQ), carry ONE mark (no negative marks)

Q.17	Which of the following statement(s) is/are correct?
(A)	Increased levels of carbon monoxide in the indoor environment result in the formation of carboxyhemoglobin and the long term exposure becomes a cause of cardiovascular diseases.
(B)	Volatile organic compounds act as one of the precursors to the formation of photochemical smog in the presence of sunlight.
(C)	Long term exposure to the increased level of photochemical smog becomes a cause of chest constriction and irritation of the mucous membrane.
(D)	Increased levels of volatile organic compounds in the indoor environment will result in the formation of photochemical smog which is a cause of cardiovascular diseases.

Q.18 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

Q.18 The value (round off to one decimal place) of -11xexdx is____________.




Q.19	A solid circular torsional member OPQ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent material is 160 MPa. The absolute maximum shear stress in the member (in MPa, round off to one decimal place) is ___________________________

Q.20	A propped cantilever beam XY, with an internal hinge at the middle, is carrying a uniformly distributed load of 10 kN/m, as shown in the figure. The vertical reaction at support X (in kN, in integer) is____________

Q.21	The internal (di) and external (do) diameters of a Shelby sampler are 48 mm and 52 mm, respectively. The area ratio (Ar) of the sampler (in %, round off to two decimal places) is______________

Q.22	A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m3/s. The area of the catchment (in km2, round off to the nearest integer)is___________

Q.23	A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and the unit weight of the lake water is 9790 N/m3, the absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is________________

Q.24	In a three-phase signal system design for a four-leg intersection, the critical flow ratios for each phase are 0.18, 0.32, and 0.22. The total loss time in each of the phases is 2 s. As per Webster’s formula, the optimal cycle length (in s, round off to the nearest integer) is_____________

Q.26 – Q.35 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

Q.26	If k is a constant, the general solution of dydx-yx=1 will be in the form of
(A)	y = x ln( kx)
(B)	y = k ln( kx)
(C)	y = x ln( x)
(D)	y = xkln( k)

Q.31	A rectangular open channel of 6 m width is carrying a discharge of 20 m3/s. Consider the acceleration due to gravity as 9.81 m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for the given discharge will then be
(A)	0.82 m
(B)	1.04 m
(C)	2.56 m
(D)	3.18 m

Q.32	Read the statements given below. (i) Value of the wind profile exponent for the ‘very unstable’ atmosphere is smaller than the wind profile exponent for the ‘neutral’ atmosphere. (ii) Downwind concentration of air pollutants due to an elevated point source will be inversely proportional to the wind speed. (iii) Value of the wind profile exponent for the ‘neutral’ atmosphere is smaller than the wind profile exponent for the ‘very unstable’ atmosphere. (iv) Downwind concentration of air pollutants due to an elevated point source will be directly proportional to the wind speed.Select the correct option.
(A)	(i) is False and (iii) is True
(B)	(i) is True and (iv) is True
(C)	(ii) is False and (iii) is False
(D)	(iii) is False and (iv) is False

Q.33	A water filtration unit is made of uniform-size sand particles of 0.4 mm diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity is
(A)	5.79×10-3 m/s
(B)	6.35×10-3 m/s
(C)	0.69 cm/s
(D)	0.75 cm/s

Q.34	For a given traverse, latitudes and departures are calculated and it is found that sum of latitudes is equal to +2.1 m and the sum of departures is equal to–2.8 m. The length and bearing of the closing error, respectively, are
(A)	3.50 m and 53°7’48” NW
(B)	2.45 m and 53°7’48” NW
(C)	0.35 m and 53.13^o SE
(D)	3.50 m and 53.13^o SE

Q.35	From laboratory investigations, the liquid limit, plastic limit, natural moisture content and flow index of a soil specimen are obtained as 60%, 27%, 32% and 27, respectively. The corresponding toughness index and liquidity index of the soil specimen, respectively, are
(A)	0.15 and 1.22
(B)	0.19 and 6.60
(C)	1.22 and 0.15
(D)	6.60 and 0.19

Q.36 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

Q.36 A function is defined in Cartesian coordinate system as f (x, y) = xe^y . The value of the directional derivative of the function (in integer) at the point (2, 0) along the direction of the straight line segment from point (2, 0) to point12,2is_______________

Q.40

A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s² . The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be

Q.43

An equipment has been purchased at an initial cost of ₹160000 and has an estimated salvage value of ₹10000. The equipment has an estimated life of 5 years. The difference between the book values (in ₹, in integer) obtained at the end of 4th year using straight line method and sum of years digit method of depreciation is .

Q.46	Numerically integrate, f (x) = 10 x – 20 x² from lower limit a = 0 to upper limit b = 0.5 . Use Trapezoidal rule with five equal subdivisions. The value (in units, round off to two decimal places) obtained is _________.

Q.47	The void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of coefficient of consolidation of sample M to sample N (round off to three decimal places) is__________.

Q.52	A grit chamber of rectangular cross-section is to be designed to remove particles with diameter of 0.25 mm and specific gravity of 2.70. The terminal settling velocity of the particles is estimated as 2.5 cm/s. The chamber is having a width of 0.50 m and has to carry a peak wastewater flow of 9720 m3/d giving the depth of flow as 0.75 m. If a flow-through velocity of 0.3 m/s has to be maintained using a proportional weir at the outlet end of the chamber, the minimum length of the chamber (in m, in integer) to remove0.25 mm particles completely is ___________ .

Q.53	In an aggregate mix, the proportions of coarse aggregate, fine aggregate and mineral filler are 55%, 40% and 5%, respectively. The values of bulk specific gravity of the coarse aggregate, fine aggregate and mineral filler are 2.55, 2.65 and 2.70, respectively. The bulk specific gravity of the aggregate mix (round off to two decimal places) is ______.

Q.54	The stopping sight distance (SSD) for a level highway is 140 m for the design speed of 90 km/h. The acceleration due to gravity and deceleration rate are9.81 m/s2 and 3.5 m/s2, respectively. The perception/reaction time (in s, round off to two decimal places) used in the SSD calculation is________.

Q.55	For a 2° curve on a high speed Broad Gauge (BG) rail section, the maximum sanctioned speed is 100 km/h and the equilibrium speed is 80 km/h. Consider dynamic gauge of BG rail as 1750 mm. The degree of curve is defined as the angle subtended at its center by a 30.5 m arc. The cant deficiency for the curve (in mm, round off to integer) is _________.

Answer Key

Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans
1	B	1	A	11	A	21	17.25 to 17.45	31	B	41	129.0 to 130.0	51	37.0 to 38.0
2	B	2	C	12	B	22	595 to 598	32	D	42	56 to 56	52	9 to 9
3	D	3	B	13	C	23	677.50 to 679.50	33	B	43	20000 to 20000	53	2.58 to 2.61
4	D	4	A	14	D	24	48 to 52	34	A	44	439.00 to 442.00	54	1.90 to 2.10
5	C	5	C	15	D	25	36 to 36	35	C	45	0.32 to 0.34	55	55 to 59
6	C	6	A	16	B	26	A	36	1 to 1	46	0.38 to 0.42
7	A	7	A	17	A; B; C	27	A	37	2.5 to 2.9	47	0.090 to 0.105
8	B	8	A	18	0.0 to 0.0	28	C	38	10 to 10	48	4.2 to 4.2
9	C	9	A	19	14 to 16	29	C	39	8.10 to 8.40	49	49.0 to 50.0
10	D	10	A	20	30 to 30	30	B	40	63.50 to 63.90	50	689 to 693

GATE 2021 Civil Engineering Section-I Previous Year Paper

GATE 2021 Civil Engineering Section-I Previous Year Paper

General Aptitude (GA)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.1	Getting to the top is______________than staying on top.
(A)	more easy
(B)	much easy
(C)	easiest
(D)	easier

Q.3	In a company, 35% of the employees drink coffee, 40% of the employees drink tea and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee?
(A)	15
(B)	25
(C)	35
(D)	40

Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Q.6	Statement: Either P marries Q or X marries YAmong the options below, the logical NEGATION of the above statement is:
(A)	P does not marry Q and X marries Y.
(B)	Neither P marries Q nor X marries Y.
(C)	X does not marry Y and P marries Q.
(D)	P marries Q and X marries Y.

Q.7	Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm x 4 cm each.Folding operation 1: The sheet is folded into half by joining the short edges of the current shape.Folding operation 2: The sheet is folded into half by joining the long edges of the current shape.Folding operation 1 is carried out on Sheet M three times. Folding operation 2 is carried out on Sheet N three times.The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is___________.
(A)	13 : 7
(B)	3 : 2
(C)	7 : 5
(D)	5 : 13

Q.9	A function, l, is defined byl ( ) ìï( p – q)2 ^, if p ³ qp,q = íïî p + q, if p < q The value of the expression l (-(-3 + 2) ,(-2 + 3))(-(-2 +1))is:
(A)	−1
(B)	0
(C)	16/3
(D)	16

Q.10	Humans have the ability to construct worlds entirely in their minds, which don’t exist in the physical world. So far as we know, no other species possesses this ability. This skill is so important that we have different words to refer to its different flavors, such as imagination, invention and innovation.Based on the above passage, which one of the following is TRUE?
(A)	No species possess the ability to construct worlds in their minds.
(B)	The terms imagination, invention and innovation refer to unrelated skills.
(C)	We do not know of any species other than humans who possess the ability to construct mental worlds.
(D)	Imagination, invention and innovation are unrelated to the ability to construct mental worlds.

Q.5	Gypsum is typically added in cement to
(A)	prevent quick setting
(B)	enhance hardening
(C)	increase workability
(D)	decrease heat of hydration

Q.6	The direct and indirect costs estimated by a contractor for bidding a project is₹160000 and ₹20000 respectively. If the mark up applied is 10% of the bid price, the quoted price (in ₹) of the contractor is
(A)	200000
(B)	198000
(C)	196000
(D)	182000

Q.7	In an Oedometer apparatus, a specimen of fully saturated clay has been consolidated under a vertical pressure of 50 kN/m2 and is presently at equilibrium. The effective stress and pore water pressure immediately on increasing the vertical stress to 150 kN/m², respectively are
(A)	150 kN/m² and 0
(B)	100 kN/m² and 50 kN/m²
(C)	50 kN/m² and 100 kN/m²
(D)	0 and 150 kN/m²

Q.8	A partially-saturated soil sample has natural moisture content of 25% and bulk unit weight of 18.5 kN/m3. The specific gravity of soil solids is 2.65 and unit weight of water is 9.81 kN/m3. The unit weight of the soil sample on full saturation is
(A)	21.12 kN/m³
(B)	19.03 kN/m³
(C)	20.12 kN/m³
(D)	18.50 kN/m³

Q.9	If water is flowing at the same depth in most hydraulically efficient triangular and rectangular channel sections then the ratio of hydraulic radius of triangular section to that of rectangular section is
(A)	1/√2
(B)	√2
(C)	1
(D)	2

Q.10	‘Kinematic viscosity’ is dimensionally represented as
(A)	M/LT
(B)	M/L²T
(C)	T²/L
(D)	L²/T

Q.11	Which one of the following statements is correct?
(A)	Pyrolysis is an endothermic process, which takes place in the absence of oxygen.
(B)	Pyrolysis is an exothermic process, which takes place in the absence of oxygen.
(C)	Combustion is an endothermic process, which takes place in the abundance of oxygen.
(D)	Combustion is an exothermic process, which takes place in the absence of oxygen.

Q.12	Which one of the following is correct?
(A)	The partially treated effluent from a food processing industry, containing high concentration of biodegradable organics, is being discharged into a flowing river at a point P. If the rate of degradation of the organics is higher than the rate of aeration, then dissolved oxygen of the river water will be lowest at point P.
(B)	The most important type of species involved in the degradation of organic matter in the case of activated sludge process based wastewater treatment is chemoheterotrophs.
(C)	For an effluent sample of a sewage treatment plant, the ratio BOD5-day,20^oC upon ultimate BOD5-day,20^oC is more than 1.
(D)	A young lake characterized by low nutrient content and low plant productivity is called eutrophic lake.

Q.13	The liquid forms of particulate air pollutants are
(A)	dust and mist
(B)	mist and spray
(C)	smoke and spray
(D)	fly ash and fumes

Q.14	The shape of the most commonly designed highway vertical curve is
(A)	circular (single radius)
(B)	circular (multiple radii)
(C)	parabolic
(D)	spiral

Q.15	A highway designed for 80 km/h speed has a horizontal curve section with radius 250 m. If the design lateral friction is assumed to develop fully, the required super elevation is
(A)	0.02
(B)	0.05
(C)	0.07
(D)	0.09

Q.16	Which of the following is NOT a correct statement?
(A)	The first reading from a level station is a ‘Fore Sight’.
(B)	Basic principle of surveying is to work from whole to parts.
(C)	Contours of different elevations may intersect each other in case of an overhanging cliff.
(D)	Planimeter is used for measuring ‘area’.

Q.17 Multiple Select Question (MSQ), carry ONE mark (no negative marks).

Q.17	Which of the following is/are correct statement(s)?
(A)	Back Bearing of a line is equal to Fore Bearing ± 180^o.
(B)	If the whole circle bearing of a line is 270^o, its reduced bearing is 90^o NW.
(C)	The boundary of water of a calm water pond will represent a contour line.
(D)	In the case of fixed hair stadia tacheometry, the staff intercept will be larger, when the staff is held nearer to the observation point.

Q.26 – Q.35 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

Q.26 The solution of the second-order differential equation d2ydx2+2dydx+v=0 with boundary conditions y (0) = 1 and y (1) = 3 is




Q.27	The value of 𝟏∫ 𝒆^𝒙𝒅𝒙 using the trapezoidal rule with four equal subintervals is
(A)	1.718
(B)	1.727
(C)	2.192
(D)	2.718

Q.28	A 50 mL sample of industrial wastewater is taken into a silica crucible. The empty weight of the crucible is 54.352 g. The crucible with the sample is dried in a hot air oven at 104 °C till a constant weight of 55.129 g. Thereafter, the crucible with the dried sample is fired at 600 °C for 1 h in a muffle furnace, and the weight of the crucible along with residue is determined as 54.783 g. The concentration of total volatile solids is .
(A)	15540 mg/L
(B)	8620 mg/L
(C)	6920 mg/L
(D)	1700 mg/L

Q.30	Contractor X is developing his bidding strategy against Contractor Y. The ratio of Y’s bid price to X’s cost for the 30 previous bids in which Contractor X has competed against Contractor Y is given in the TableRatio of Y’ is bid price to X’s costNumber of bids1.0261.04121.0631.1061.123 Based on the bidding behaviour of the Contractor Y, the probability of winning against Contractor Y at a mark up of 8% for the next project is
(A)	0%
(B)	more than 0% but less than 50%
(C)	more than 50% but less than 100%
(D)	100%

Q.32	A fluid flowing steadily in a circular pipe of radius R has a velocity that is everywhere parallel to the axis (centerline) of the pipe. The velocity distributionæ r2 öalong the radial direction is Vr = U ç1- R2 ÷, where r is the radial distance asè ømeasured from the pipe axis and U is the maximum velocity at r = 0. The average velocity of the fluid in the pipe is
(A)	U/2
(B)	U/3
(C)	U/4
(D)	(5/6)U

Q.34	Ammonia nitrogen is present in a given wastewater sample as the ammonium ion (NH4+) and ammonia (NH3). If pH is the only deciding factor for the proportion of these two constituents, which of the following is a correct statement?
(A)	At pH above 9.25, only NH₄⁺ will be present.
(B)	At pH below 9.25, NH₃ will be predominant.
(C)	At pH 7.0, NH₄⁺ and NH₃ will be found in equal measures.
(D)	At pH 7.0, NH₄⁺ will be predominant.

Q.35	On a road, the speed – density relationship of a traffic stream is given by u = 70 – 0.7k (where speed, u, is in km/h and density, k, is in veh/km). At the capacity condition, the average time headway will be
(A)	0.5 s
(B)	1.0 s
(C)	1.6 s
(D)	2.1 s

Q.37	Vehicular arrival at an isolated intersection follows the Poisson distribution. The mean vehicular arrival rate is 2 vehicle per minute. The probability (round off to two decimal places) that at least 2 vehicles will arrive in any given 1-minute interval is__________

Q.51

A baghouse filter has to treat 12 m3/s of waste gas continuously. The baghouse is to be divided into 5 sections of equal cloth area such that one section can be shut down for cleaning and/or repairing, while the other 4 sections continue to operate. An air-to-cloth ratio of 6.0 m3/min-m2 cloth will provide sufficient treatment to the gas. The individual bags are of 32 cm in diameter and 5 m in length. The total number of bags (in integer) required in the baghouse is______________

Q.52	A secondary clarifier handles a total flow of 9600 m3/d from the aeration tank of a conventional activated-sludge treatment system. The concentration of solids in the flow from the aeration tank is 3000 mg/L. The clarifier is required to thicken the solids to 12000 mg/L, and hence it is to be designed for a solid flux of 3.2 kg/m².h. The surface area of the designed clarifier for thickening (in m2, in integer) is___________

Q.53	Spot speeds of vehicles observed at a point on a highway are 40, 55, 60, 65 and 80 km/h. The space-mean speed (in km/h, round off to two decimal places) of the observed vehicles is _______.

Q.55	Traversing is carried out for a closed traverse PQRS. The internal angles at vertices P, Q, R and S are measured as 92°, 68°, 123°, and 77°, respectively. If fore bearing of line PQ is 27°, fore bearing of line RS (in degrees, in integer) is____________

Answer Key –

Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans
1	D	1	B	11	A	21	2 to 2	31	A	41	100 to 130	51	30 to 30
2	B	2	D	12	B	22	0.9 to 0.9	32	A	42	2.4 to 2.6	52	375 to 375
3	C	3	D	13	B	23	4.80 to 5.00	33	B	43	0 to 0	53	55.50 to 58.50
4	B	4	B	14	C	24	2400 to 2400	34	D	44	1.18 to 1.26	54	0.30 to 0.34
5	C	5	A	15	B	25	60.7 to 61.1	35	D	45	4.20 to 4.35	55	196 to 196 OR 218 to 218
6	B	6	A	16	A	26	A	36	20.00 to 21.00	46	5.70 to 5.90
7	A	7	C	17	A; B; C	27	B	37	0.58 to 0.60	47	1.94 to 1.98
8	A	8	B	18	0.5 to 0.5	28	C	38	490 to 510	48	2.80 to 2.95
9	B	9	A	19	15 to 15	29	D	39	0 to 0	49	0.35 to 0.40
10	C	10	D	20	95 to 97	30	B	40	27.0 to 29.0	50	34 to 38

GATE 2021 Biotechnology Engineering Previous Year Paper

General Aptitude (GA)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.1	The ratio of boys to girls in a class is 7 to 3.Among the options below, an acceptable value for the total number of students in the class is:
(A)	21
(B)	37
(C)	50
(D)	73

Q.3	Consider the following sentences:(i) Everybody in the class is prepared for the exam.(ii) Babu invited Danish to his home because he enjoys playing chess.Which of the following is the CORRECT observation about the above two sentences?
(A)	(i) is grammatically correct and (ii) is unambiguous
(B)	(i) is grammatically incorrect and (ii) is unambiguous
(C)	(i) is grammatically correct and (ii) is ambiguous
(D)	(i) is grammatically incorrect and (ii) is ambiguous

Q.5	_________is to surgery as writer is to ___________ Which one of the following options maintains a similar logical relation in the above sentence?
(A)	Plan, outline
(B)	Hospital, library
(C)	Doctor, book
(D)	Medicine, grammar

Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Q.6	We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm x 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is
(A)	𝜋2
(B)	3𝜋
(C)	9𝜋
(D)	3𝜋

Q.8	There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.The probability that at least two chocolates are identical is__________
(A)	0.3024
(B)	0.4235
(C)	0.6976
(D)	0.8125

Q.9	Given below are two statements 1 and 2, and two conclusions I and II. Statement 1: All bacteria are microorganisms.Statement 2: All pathogens are microorganisms. Conclusion I: Some pathogens are bacteria.Conclusion II: All pathogens are not bacteria.Based on the above statements and conclusions, which one of the following options is logically CORRECT?
(A)	Only conclusion I is correct
(B)	Only conclusion II is correct
(C)	Either conclusion I or II is correct.
(D)	Neither conclusion I nor II is correct.

Q.10	Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality.Which one of the following statements summarizes the passage?
(A)	The proposed AOM addresses the core problems that cause obesity.
(B)	If obesity reduces, poverty will naturally reduce, since obesity causes poverty.
(C)	AOM are addressing the core problems and are likely to succeed.
(D)	AOM are addressing the problem superficially.

Biotechnology (BT)

Q.1 – Q.17 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.1	Coronavirus genome consists of
(A)	double-stranded DNA
(B)	double-stranded RNA
(C)	negative-sense single-stranded RNA
(D)	positive-sense single-stranded RNA

Q.2	The enzyme that transcribes the eukaryotic genes encoding precursor ribosomal RNAs (pre-rRNAs) of 28S, 18S and 5.8S rRNAs is
(A)	RNA polymerase I
(B)	RNA polymerase II
(C)	RNA polymerase III
(D)	RNA polymerase IV

Q.3	Number of unrooted trees in a phylogeny of five sequences is
(A)	3
(B)	15
(C)	105
(D)	945

Q.4	Which one of the following methods is used to test the significance of a predicted phylogeny?
(A)	Bootstrap
(B)	Maximum likelihood
(C)	Maximum parsimony
(D)	Minimum evolution

Q.5	The Cartesian coordinates (x, y) of a point A with polar coordinates (4, /4) is
(A)	(√3, 2 √2 )
(B)	(2, 2 √3)
(C)	(2 √2, √3 )
(D)	(2 √2, 2 √2 )

Q.7	Which one of the following statements is INCORRECT about hybridoma production?
(A)	Hybridoma cells can use hypoxanthine and thymidine
(B)	DNA synthesis in myeloma cells is blocked by aminopterin
(C)	Hybridoma cells are made to produce polyclonal antibodies
(D)	Polyethylene glycol is used to fuse myeloma cells to B-cells

Q.8	d [ln (2x)] is equal todx
(A)	1/2x
(B)	1/
(C)	1/2
(D)	x

Q.9	Which one of the following techniques/tools is NOT used for inserting a foreign gene into a cell?
(A)	DNA microarray
(B)	Electroporation
(C)	Gene gun
(D)	Microinjection

Q.10	Under standard temperature ( T ) and pressure ( P ) conditions, 128 g of an ideal gas molecule A occupies a volume of 1L . The gas molecule A obeys the relationship RT = 0.25PV . R and V are universal gas constant and ideal gas volume, respectively. The molecule A is
(A)	CO2
(B)	H2
(C)	N2
(D)	O2

Q.11	CRISPR-Cas system is associated with
(A)	adaptive immunity in eukaryotes
(B)	adaptive immunity in prokaryotes
(C)	innate immunity in eukaryotes
(D)	innate immunity in prokaryotes

Q.12	The process by which intracellular macromolecules are supplied for lysosomal degradation during nutrient starvation is
(A)	apoptosis
(B)	autophagy
(C)	phagocytosis
(D)	pinocytosis

Q.14	A protein without its prosthetic group is known as
(A)	apoprotein
(B)	hemoprotein
(C)	holoprotein
(D)	lipoprotein

Q.15	The enzyme which adds phosphate group to the free 5¢ terminus of a DNA sequence is
(A)	adenosine kinase
(B)	alkaline phosphatase
(C)	polynucleotide kinase
(D)	terminal deoxynucleotidyl transferase

Q.16	Which one of the following is CORRECT about microbial growth medium?
(A)	Luria-Bertani broth is a synthetic medium
(B)	Nutrient broth is a defined medium
(C)	Sabouraud dextrose agar is a differential medium
(D)	Trypticase soy agar is a complex medium

Q.17	The cellular process which utilizes RNA-induced silencing complex to block gene expression is
(A)	RNA editing
(B)	RNA interference
(C)	RNA polyadenylation
(D)	RNA splicing

Q.18 – Q.19 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

Q.18	Which of the following layer(s) is/are formed from the inner cell mass of the blastocyst?
(A)	Ectoderm
(B)	Endoderm
(C)	Mesoderm
(D)	Trophectoderm

Q.19	Which of the following cell organelle(s) is/are surrounded by a single phospholipid membrane?
(A)	Golgi apparatus
(B)	Lysosome
(C)	Mitochondria
(D)	Nucleus

Q.20 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

Q.20	The sum of the infinite geometric series 1+ ⅓ + ⅓² + ⅓ ³+ … (rounded off to one decimal place) is____________.

Q.21	Three balls, colored in blue, green and red, are successively transferred from box A to box B in the order BLUE-GREEN-RED. The probability of a reverse transfer of the balls to the box A in the same order (rounded off to two decimal places)is .

Q.22	Decimal reduction time of a bacterial strain is 20 min . Specific death rate constant in min^-1 (rounded off to two decimal places) is ___________.

Q.24

A system consists of two reactors, connected by a valve. The first reactor ( R1) contains an ideal gas A of volume 5 L and the second reactor ( R2 ) has an ideal gas B of volume 10 L . Initially, the valve is closed and pressure P in R1 and R2 are 9 and 6 atm , respectively. Later, when the valve is opened, the system reaches equilibrium. If the temperature T of both the reactors is maintained constant, the final equilibrium pressure in atm of the system is .

Q.25	The enzyme α-amylase used in starch hydrolysis has an affinity constant (K_m ) value of 0.005 M . To achieve one-fourth of the maximum rate of hydrolysis, the required starch concentration in mM (rounded off to two decimal places) is .

Q.26 – Q.34 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

Q.26 Which one of the following represents non-growth associated product formation kinetics in a bioprocess system? X and P denote viable cell and product concentrations, respectively.

Q.32	Which one of the following tools is used to compare all the possible six-open reading frames of a given nucleotide query sequence with all the available six-open reading frames of the nucleotide sequence database?
(A)	BLASTN
(B)	BLASTX
(C)	TBLASTN
(D)	TBLASTX

Q.33	In Neurospora crassa, a mutation in the poky gene results in a slow growth phenotype (poky). The results of four crosses are given below. (1) wild-type ♀ × wild-type ♂ → All progeny are wild-type (2) wild-type ♀ × poky ♂ → All progeny are wild-type (3) poky ♀ × wild-type ♂ → All progeny are poky (4) poky ♀ × poky ♂ → All progeny are poky Which one of the following explains the inheritance mode of poky?
(A)	Episomal inheritance
(B)	Mendelian inheritance
(C)	Mitochondrial inheritance
(D)	X-linked inheritance

Q.34	Tertiary structure of a protein consisting of α-helices and β-strands can be determined by
(A)	circular dichroism spectroscopy
(B)	mass spectrometry
(C)	nuclear magnetic resonance spectroscopy
(D)	UV spectroscopy

Q.35 – Q.38 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

Q.35	Which of the following statement(s) is/are CORRECT about Agrobacterium tumefaciens?
(A)	It contains tumor inducing plasmid
(B)	It causes crown gall disease in dicotyledonous plants
(C)	It is a Gram-positive soil bacterium
(D)	It is used in generating transgenic plants

Q.36	Which of the following antimicrobial agent(s) is/are growth factor analog(s)?
(A)	5-Fluorouracil
(B)	Isoniazid
(C)	Sulfanilamide
(D)	Tetracycline

Q.37	Which of the following chemical messenger(s) is/are derivative(s) of tryptophan?
(A)	γ-amino butyric acid
(B)	Indole acetic acid
(C)	Melatonin
(D)	Serotonin

Q.38	Which of the following nucleus/nuclei is/are NMR active?
(A)	¹H
(B)	¹³C
(C)	¹⁶O
(D)	³²S

Q.39 – Q.55 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).

Q.39	In a Mendel’s dihybrid experiment, a homozygous pea plant with round yellow seeds was crossed with a homozygous plant with wrinkled green seeds.F1 intercross produced 560 F2 progeny. The number of F2 progeny having both dominant traits (round and yellow) is___________.

Q.40	A 0.1 mL aliquot of a bacteriophage stock having a concentration of 4´10⁹ phages mL^-1 is added to 0.5 mL of E. coli culture having a concentration of 2´10⁸ cells mL^-1 . The multiplicity of infection is_____________.

Q.41	If the area of a triangle with the vertices (k, 0) , (2, 0) and (0, – 2) is 2 square units, the value of k is______________.

Q.42	In a chemostat with a dilution rate of 0.8 h^-1 , the steady state biomass concentration and the specific product formation rate are 8 mol m^-3 and0.2 (mol product)(mol biomass)^-1 h^-1 , respectively. The steady state product concentration in mol m^-3 is______________.

Q.43	If the values of two random variables ( X , Y ) are (121, 360) , (242, 364) and (363, 362) , the value of correlation coefficient between X and Y (rounded off to one decimal place) is_____________.

Q.45

It is desired to scale-up a fermentation from 1L to 1000 L vessel by maintaining a constant power-to-volume ratio. The small fermenter is operated at an agitator speed of 300 rotations per minute (rpm) . If the value of scale up factor is 10 , agitator speed in rpm (rounded off to the nearest integer) for the large fermenter is____________.

Q.46	The specific growth rate of a mold during exponential phase of its growth in a batch cultivation is 0.15 h^-1 . If the cell concentration at 30 h is 33 g L^-1 , the cell concentration in g L^-1 (rounded off to the nearest integer) at 24 h is_______________.

Q.47

A sedimentation tank of height 100 cm is used in a conventional activated sludge process to separate a suspension of spherical shaped granular sludge biomass of 0.5 mm diameter. The viscosity of the liquid is 1 cP . The difference in density between the suspended biomass and the liquid is 0.1g cm^-3 . If the biomass reach their terminal velocity instantaneously, the biomass settling time in min (rounded off to two decimal places) is_______________.

Q.48	In a random mating population, Y and y are dominant and recessive alleles, respectively. If the frequency of Y allele in both sperm and egg is 0.70, then the frequency of Y y heterozygotes (rounded off to two decimal places) is_________________.

Q.49	Calculate the following integral

Q.51

A batch cultivation of E. coli follows zeroth order Monod’s growth kinetics. The cell growth is terminated when the residual dissolved oxygen concentration attains 10% of its saturation value and oxygen mass transfer coefficient (k_La) reaches its maximum value (80 h^-1 ) . The saturation value of dissolved oxygen concentration is 0.007 kg m^-3 . If the maximum specific growth rate and yield coefficient Equation are 0.2 h^-1 and 1.5 (kg cells) (kgO)^-1 , respectively, then the final cell concentration in kg m^-3 (rounded off to two decimal places) at the end of the batch cultivation is__________.

Q.52

Milk flowing through a stainless steel inner tube (𝟒𝟎 𝒎𝒎 inner diameter) of double tube-type heater is to be heated from 10 oC to 85 oC by saturated steam condensing at 120 oC on the outer surface of the inner tube. Total heat transferred (Q) is 𝟏𝟒𝟔𝟐𝟎𝟎 𝒌𝒄𝒂𝒍 𝒉^−𝟏 and the overall heat transfer coefficient is 𝟕𝟓𝟎 𝒌𝒄𝒂𝒍 𝒉^−𝟏 𝒎^−𝟐 ∘𝑪^−𝟏. The total length of the heating tube in 𝒎 (rounded off to one decimal place) is __________ .

Q.53

A DNA solution of 50 mg mL^-1 concentration gives an absorbance of 1.0 at 260 nm . An aliquot of 20 mL from a 50 mL purified plasmid solution is diluted with distilled water to a total volume of 1000 mL . The diluted plasmid solution gives an absorbance of 0.550 at 260 nm . The concentration of the purified plasmid in mg mL^-1 (rounded off to two decimal places) is____________ .

Q.54	The possible number of SalI restriction sites in a 9 kb double-stranded DNA, with all four bases occurring in equal proportion (rounded off to the nearest integer)is __________.

Q.55	A bacterium produces acetic acid from ethanol as per the following reaction𝟐𝑪𝑯_𝟑𝑪𝑯_𝟐𝑶𝑯 + 𝟐𝑶_𝟐 → 𝟐𝑪𝑯_𝟑𝑪𝑶𝑶𝑯 + 𝟐𝑯_𝟐𝑶The thermodynamic maximum yield of acetic acid from ethanol in g g^-1(rounded off to two decimal places) is___________.

Answer Key

Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans
1	C	1	D	11	B	21	0.16 to 0.18	31	C	41	0 to 0 OR 4 to 4	51	3.70 to 3.80
2	A	2	A	12	B	22	0.10 to 0.13	32	D	42	2 to 2	52	23.0 to 24.0
3	C	3	B	13	A	23	0.25 to 0.25	33	C	43	0.5 to 0.5	53	1.37 to 1.38
4	A	4	A	14	A	24	7 to 7	34	C	44	8 to 8	54	2 to 2
5	C	5	D	15	C	25	1.60 to 1.80	35	A; B; D	45	64 to 65	55	1.90 to 2.00
6	C	6	B	16	D	26	C	36	A; B; C	46	13 to 14
7	C	7	C	17	B	27	B	37	B; C; D	47	1.20 to 1.30
8	C	8	B	18	A; B; C	28	D	38	A; B	48	0.41 to 0.43
9	C OR D	9	A	19	A; B	29	C	39	315 to 315	49	2 to 2
10	D	10	D	20	1.5 to 1.5	30	D	40	4 to 4	50	6 to 6

GATE 2021 Biomedical Engineering Previous Year Paper

GATE 2021 Biomedical Engineering Previous Year Paper

General Aptitude (GA)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.1	(i) Arun and Aparna are here. (ii) Arun and Aparna is here. (iii) Arun’s families is here. (iv) Arun’s family is here. Which of the above sentences are grammatically CORRECT?
(A)	(i) and (ii)
(B)	(i) and (iv)
(C)	(ii) and (iv)
(D)	(iii) and (iv)

Q.3	Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:
(A)	1/36
(B)	1/12
(C)	⅛
(D)	¼

Q.4	Å and ⊙ are two operators on numbers p and q such that𝑝 ⊙ 𝑞 = 𝑝 − 𝑞, and p Å q = p✗ q Then, (9 ⊙ (6 ⊕ 7)) ⊙ (7 ⊕ (6 ⊙ 5))=
(A)	40
(B)	-26
(C)	-33
(D)	-40

Q.5	Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:
(A)	6
(B)	9
(C)	18
(D)	24

Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Q.6	On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P.The distance of point Q to point O, in the same units, should be
(A)	3
(B)	4
(C)	5
(D)	6

Q.7	The author said, “Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public speakers think they can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks.”Based on the above passage, which one of the following is TRUE?
(A)	The author is of the opinion that rehearsing is important for musicians, actors and public speakers.
(B)	The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.
(C)	The author is of the opinion that rehearsing is more important only for musicians than public speakers.
(D)	The author is of the opinion that rehearsal is more important for actors than musicians.

Q.8	1. Some football players play cricket. 2. All cricket players play hockey. Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:
(A)	No football player plays hockey.
(B)	Some football players play hockey.
(C)	All football players play hockey.
(D)	All hockey players play football.

Q.10	In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer.The minimum area of the triangle PQR possible, in cm2, is
(A)	18
(B)	24
(C)	48√3
(D)	144√3

Biomedical Engineering (BM)

Q.1 – Q.17 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3)

Q.1	For𝟏 𝒒𝒇_𝑿(𝒙) = 𝝅 ( 𝒙 + 𝒆−𝒙 )𝒆to be a valid probability distribution function of a random variable X, the value of 𝒒 is .
(A)	2
(B)	𝜋
(C)	4
(D)	−𝜋

Q.2	Given a scalar function 𝑽(𝒙, 𝒚) = 𝟏 (𝒙^𝟐 + 𝒚^𝟐), the directional derivative of𝟐𝑽 in the direction of the vector field 𝟑𝒚𝒊 – 𝟑𝒙𝒋 at the point (𝟏, 𝟏) is .(Note: 𝒊 and 𝒋 are the unit vectors along the x and y directions, respectively.)
(A)	√18
(B)	0
(C)	1√18
(D)	3/2

Q.8	For a linear stable second order system, if the unit step response is such that the peak time is twice the rise time, then the system is .
(A)	underdamped
(B)	undamped
(C)	overdamped
(D)	critically damped

Q.9	Which of the following displacement sensors is known to have a high sensitivity and a relatively larger measurement range?
(A)	Strain gauge
(B)	Capacitive sensor
(C)	LVDT
(D)	Piezoelectric sensor

Q.10	Which of the following temperature sensors is used in contact-type digital thermometers for measuring body temperature?
(A)	Thermocouple
(B)	Thermistor
(C)	Resistance temperature detector
(D)	Infrared LED-photodetector pair

Q.11	The pH of blood in a healthy human is precisely in the range of .
(A)	7.10 – 8.10
(B)	6.95 – 7.05
(C)	7.15 – 7.20
(D)	7.35 – 7.45

Q.12	Which of the following is a cranial bone in the human body?
(A)	Occipital
(B)	Mandible
(C)	Coccyx
(D)	Sternum

Q.13	Which of the following glands produces the thyroid stimulating hormone (TSH)?
(A)	Thyroid
(B)	Parathyroid
(C)	Pituitary
(D)	Pineal

Q.14	Which of the following causes Myocardial Infarction (MI)?
(A)	Obstruction in one of the arteries supplying blood to the heart
(B)	Obstruction in one of the arteries supplying blood to the brain
(C)	Obstruction in one of the veins draining blood from the heart
(D)	Obstruction in one of the veins draining blood from the brain

Q.15	If we consider blood as a suspension of RBCs in a Newtonian fluid, the shear forces experienced by the RBCs during blood flow would _______.
(A)	Randomize the orientation of blood cells
(B)	Align RBCs along their long axes with streamlines
(C)	Align RBCs along their short axes with streamlines
(D)	Create an equal distribution of RBCs aligned in their long and short axes

Q.18 – Q.20 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

Q.18	Which of the following statements are CORRECT in the context of planar X-ray imaging?
(A)	Using fast X-ray screen improves spatial resolution
(B)	Using fast X-ray screen worsens spatial resolution
(C)	Decreasing tube current decreases signal to noise ratio
(D)	Decreasing tube current increases signal to noise ratio

Q.19	While comparing parallel fiber and pinnate muscles of a given volume, which of the following statements are TRUE?
(A)	Pinnate muscles provide more muscle force
(B)	Parallel fiber muscles provide more muscle force
(C)	Pinnate muscles facilitate better muscle shortening
(D)	Parallel fiber muscles facilitate better muscle shortening

Q.20	Which of the following may cause failure of bone implants?
(A)	Stress shielding – reduction of bone density due to removal of a typical stress from bone by an implant
(B)	Aseptic loosening – loss of bond between bone and implant in the absence of an infection
(C)	Fretting fatigue – progressive deterioration of material by small scale rubbing
(D)	Osseointegration – formation of a direct interface between an implant and a bone, without intervening soft tissues

Q.21 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).


Q.21	The minimum value, 𝒇_𝒎𝒊𝒏, of the function given below is __________ . (rounded off to the nearest integer) *Equation*

Q.22	𝟔A continuous time transfer function 𝑯(𝒔) = 𝟏+𝒔/𝟏𝟎⁶/s is converted to a discrete time transfer function 𝑯(𝒛) using a bilinear transform at 100 MHz sampling rate. The pole of 𝑯(𝒛) is located at 𝒛 = _________ .

Q.23	Consider a type 2, unity feedback system. The intersection of the initial −𝟒𝟎 𝒅𝑩/𝒅𝒆𝒄 segment, of its Bode plot, with the zero dB line occurs at a frequency of 2 rad/s. The acceleration error constant of the system 𝑲_𝒂 is______.

Q.24	The radioactivity of a radionuclide with decay constant of 𝟑. 𝟐𝟐 × 𝟏𝟎^−𝟓 𝒔^−𝟏 is 6 mCi at 10:30 AM. The radioactivity of the radionuclide at 4:30 PM on the same day will be________mCi. (rounded off to two decimal places)

Q.25	A polymeric scaffold has been developed for cartilage tissue engineering. To understand the biodegradability of the material, this polymeric scaffold with a dry weight of 20 mg is kept in a lysozyme solution for 7 days. At the end of 7 days, the scaffold is freeze-dried, and the dry weight is measured to be 18 mg. The degradation of the polymeric scaffold after 7 days is________%.

Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

Q.26	The Trace and Determinant of a 𝟐 × 𝟐 nonsingular matrix 𝑨 are 12 and 32, respectively. The eigenvalues of 𝑨^−𝟏 are________and________.
(A)	0.6, 0.8
(B)	0.25, 0.125
(C)	6, 16
(D)	1/12, 1/32

Q.27	A unit step input is applied to a system with impulse response 𝑯(𝒔) =𝟏−𝒔/𝑚𝒛 at 𝒕 = 𝟎. The output of the system 𝒚(𝒕) at 𝒕 = 𝟎⁺ is __________.𝟏+𝒔/𝑚𝒑
(A)	1
(B)	−𝜔_𝑧/𝜔_𝑝
(C)	−𝜔_𝑝/𝜔_𝑧
(D)	0

Q.28	Consider the following first order partial differential equation, also known as the transport equation with initial conditions given by 𝒚(𝒙, 𝟎) = 𝐬𝐢𝐧 𝒙, − ∞ < 𝒙 < ∞. The value of𝒚(𝒙, 𝒕) 𝐚𝐭 𝒙 = 𝝅 𝐚𝐧𝐝 𝒕 = is_______.
(A)	1
(B)	2
(C)	0
(D)	0.5

Q.36	The closed-loop characteristic equation of a system is given by𝒔^𝟒 + 𝟐𝒔^𝟑 + 𝟖𝒔^𝟐 + 𝟖𝒔 + 𝟏𝟔 = 𝟎The frequency of oscillations of this closed-loop system at steady state is_____rad/s.
(A)	1
(B)	2
(C)	4
(D)	8

Q.38	In comparison to ECG amplifiers, the surface-EMG amplifiers have
(A)	A comparable gain and smaller bandwidth
(B)	A comparable gain and larger bandwidth
(C)	At least 20 dB higher gain and a larger bandwidth
(D)	At least 20 dB lower gain and a smaller bandwidth

Q.39	Match the following organs with their functions:
(A)	P-M, Q-N, R-K, S-L
(B)	P-N, Q-M, R-K, S-L
(C)	P-N, Q-K, R-L, S-M
(D)	P-L, Q-M, R-K, S-N

Q.40	An RF pulse is applied to acquire an axial MR image at the isocenter of a 1.5T MRI scanner with slice thickness of 2.5 mm. Assuming a gradient field strength of 2 Gauss/cm is applied and Gyromagnetic ratio of protons is 42.58 MHz/T, the RF pulse bandwidth required for slice selection is_________kHz.
(A)	1.06
(B)	2.13
(C)	6.66
(D)	13.31

Q.41	A longitudinal pressure wave travelling inside a muscle tissue is incident at an angle of 60° at the interface between the muscle and kidney. Let the wave impedance be Zmuscle = 1.70× 𝟏𝟎^𝟓 𝒈 𝒄𝒎^−𝟐 𝒔^−𝟏, Zkidney = 1.62× 𝟏𝟎^𝟓𝒈 𝒄𝒎^−𝟐 𝒔^−𝟏 and wave velocities in muscle and kidney tissues be 1590 and 1560 𝒎/𝒔 respectively. The transducer centre frequency is 1.5 MHz. The pressure wave propagation angle in the kidney tissue and intensity transmission coefficient at the tissue interface are degrees (rounded off to the nearest integer) and (rounded off to two decimal places), respectively.
(A)	58, 0.24
(B)	30, 0.68
(C)	58, 0.94
(D)	30, 0.99

Q.43 – Q.45 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

Q.44	An inexperienced clinician was measuring the cardiac output of a healthy human by thermodilution technique. A 2.0 mL of cold saline solution of volume (𝑽_𝒊) at 𝟕 ℃ was injected at the entrance of the right atrium. The change in blood temperature (∫𝒕𝟏 ∆𝑻 𝒅𝒕) at the pulmonary artery was measured to be −𝟐𝟎 𝑲𝒆𝒍𝒗𝒊𝒏. 𝒔𝒆𝒄𝒐𝒏𝒅.The cardiac output 𝑭 was calculated using the following formula where 𝑸 is the heat content of injectate in Joules, given by 𝑽_𝒊∆𝑻_𝒊𝝆_𝒊𝒄_𝒊 and∆𝑻_𝒊 is the temperature difference between the injectate and blood. It was assumed that the density of blood (𝝆_𝒃 in kg/m3) and the specific heat capacity of blood (𝒄_𝒃 in J/(kg. K)) were respectively equal to that of the injectate 𝝆_𝒊 and 𝒄_𝒊.The clinician realized that there was an error in the measurement of 𝑭. Which of the following is TRUE?
(A)	Cardiac output is too low because the cold saline volume was too small
(B)	Cardiac output is too low because *Equation* 𝑑𝑡 is too large
(C)	Cardiac output is too high because the cold saline volume was too large
(D)	Cardiac output is too high because *Equation* 𝑑𝑡 is too small

Q.45	Which of the following statements about smooth muscles are TRUE?
(A)	Smooth muscles are found in the walls of hollow organs
(B)	Smooth muscles are controlled by the autonomic nervous system
(C)	Smooth muscles are made up of non-striated cells
(D)	Smooth muscles are made up of striated cells

Q.46 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).


Q.46	Consider a unity feedback system with closed loop transfer functionThe steady state error with respect to a unit ramp input is________. (rounded off to one decimal place)

Q.47	The diameter of a renal artery lumen in humans is 5 mm. If the mean velocity of the blood flowing in the renal artery is 40 cm/s, the density of blood (r) is 1060 kg/m3, and the viscosity of blood (m) is 3 cP, the Reynolds number for the blood flowing in the renal artery is___________(rounded off to the nearest integer).

Q.48	A drug manufacturer believes that there is a 95% chance that the drug controller will approve a new drug the company plans to distribute if the results of the current testing show that the drug causes no side effects. The manufacturer further believes that there is a 0.50 probability that the drug will be approved even if the test shows side effects. A physician working for the drug manufacturer believes there is a 0.20 probability that tests will show side effects. If the drug is approved by the drug controller, the probability that the drug causes side effects is__________. (rounded off to three decimal places)

Q.49	In a measurement process, groups A and B recorded 10 and 15 values, respectively. The arithmetic means and standard deviations of group A are µA = 35, σA = 0.4 and group B are µB = 38, σB = 0.6, respectively. The standard deviation for the combined set of group A and group B measurements is __________. (rounded off to two decimal places)

Q.52

A pacemaker was implanted in a cardiac patient. It has a battery of 2.4 A.h (Ampere.hour). It is designed to deliver a rectangular pulse of amplitude 1.5 V for 1 ms ON time for every one second. The electrode – heart resistance is 150 W. Assuming the current drained from the battery is negligible, the lifetime of the pacemaker is______ years. (rounded off to the nearest integer)

Q.53	A radiographic system is using X-ray tube operating at 80 kVp. In order to filter the low energy X-rays, an aluminum (Al) filter of 2.5 mm thickness is used. The Al filter is replaced with a copper (Cu) filter to have the same energy filtered. The mass attenuation coefficients of Al and Cu at 80 kVp are 0.02015 m2/kg and 0.07519 m2/kg, respectively. The densities of Al and Cu are 2699 kg/m3 and 8960 kg/m3 respectively. The thickness of the new Cu filter is___________mm. (rounded off to two decimal places)

Q.54	In a radioactive isotope, N nuclei are needed to produce radioactivity level of 2 mCi. Assuming decay constant of 𝟑. 𝟐𝟐 × 𝟏𝟎^−𝟓 𝒔^−𝟏 and atomic weight of 98 𝒈/𝒎𝒐𝒍 and Avogadro’s number = 𝟔. 𝟎𝟐 × 𝟏𝟎^𝟐𝟑 𝒎𝒐𝒍^−𝟏 , the mass of N radionuclide is_________picograms. (rounded off to the nearest integer)

Q.55	A PZT crystal of thickness 1 mm and wave velocity 4000 m/s is emitting a longitudinal pressure wave, which is incident on a blood vessel at an angle of 30°. The doppler shift in the ultrasound wave for a blood flow of 10 cm/s and wave velocity in the soft tissue of 1540 m/s is________ Hz.

Answer Key

Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans	Q.No.	Ans
1	B	1	A	11	D	21	-6 to -6	31	B	41	C	51	-10 to -10
2	B	2	B	12	A	22	1 to 1	32	B	42	A	52	27 to 28
3	D	3	B	13	C	23	4 to 4	33	C	43	B; D	53	0.15 to 0.25
4	D	4	A	14	A	24	2.96 to 3.02	34	A	44	A; B	54	372 to 376
5	C	5	C	15	B	25	10 to 10	35	B	45	A; B; C	55	222 to 228
6	C	6	A	16	A	26	B	36	B	46	0.1 to 0.1
7	A	7	D	17	B	27	C	37	B	47	700 to 710
8	B	8	B	18	B; C	28	D	38	B	48	0.111 to 0.121
9	C	9	C	19	A; D	29	B	39	B	49	1.54 to 1.58
10	D	10	B	20	A; B; C	30	D	40	B	50	0.2 to 0.2

Category: Coachings

GATE 2021 Computer Science and Information Technology Engineering Section-I Previous Year Paper

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Q.1 – Q.16 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

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Q.4	A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like____.
(A)
(B)
(C)
(D)

Q.10	Ethylene adsorbs on the vacant active sites V of a transition metal catalyst according to the following mechanism. If N_T , N_V and NC₂H₄ denote the total number of active sites, number of vacant active sites and number of adsorbed C₂H₄ molecules, respectively, the balance on the total number of active sites is given by
(A)	N_T= N_V+ N_{C2 H4}
(B)	N_T= N_V+ 2N_{C2 H4}
(C)	N_T= 2N_V+ N_{C2 H4}
(D)	N_T= N_V+ 0.5N_{C2 H4}

Q.15	Match the common name of chemicals in Group – 1 with their chemical formulae in Group – 2. The correct combination is:
(A)	P – III, Q – II, R – I
(B)	P – III, Q – I, R – II
(C)	P – II, Q – III, R – I
(D)	P – II, Q – I, R – III

Q.16	For the function the CORRECT statement(s) is/are
(A)	𝑓(𝑥) is continuous at 𝑥 = 1
(B)	𝑓(𝑥) is differentiable at 𝑥 = 1
(C)	𝑓(𝑥) is continuous at 𝑥 = 0
(D)	𝑓(𝑥) is differentiable at 𝑥 = 0

Q.17	Feed solution F is contacted with solvent B in an extraction process. Carrier liquid in the feed is A and the solute is C. The ternary diagram depicting a single ideal stage extraction is given below. The dashed lines represent the tie-lines. The CORRECT option(s) is/are
(A)	For the tie-lines shown, concentration of solute in the extract is higher than that in the raffinate
(B)	Maximum amount of solvent is required if the mixture composition is at W
(C)	Y represents the composition of extract when minimum amount of solvent is used
(D)	U represents the raffinate composition if the mixture composition is at M

Q.18	The inherent characteristics of three control valves P, Q and R are shown in the figure. The CORRECT option(s) is/are
(A)	P is a quick opening valve
(B)	Q is a quick opening valve
(C)	P is an equal percentage valve
(D)	R is an equal percentage valve

Q.28	Water of density 1000 kg m^–3flows in a horizontal pipe of 10 cm diameter at an average velocity of 0.5 m s^–1. The following plot shows the pressure measured at various distances from the pipe entrance. Using the data shown in the figure, the Fanning friction factor in the pipe when the flow is FULLY DEVELOPED is
(A)	0.0012
(B)	0.0074
(C)	0.0082
(D)	0.0106

Q.30	Which of these symbols can be found in piping and instrumentation diagrams?
(A)	(Q) and (S) only
(B)	(P), (Q) and (R) only
(C)	(P), (R) and (S) only
(D)	(P), (Q), (R) and (S)

Q.31	It is required to control the volume of the contents in the jacketed reactor shown in the figure. Which one of the following schemes can be used for feedback control?
(A)	Measure L101 and manipulate valve V-2
(B)	Measure T101 and manipulate valve V-1
(C)	Measure L101 and manipulate valve V-3
(D)	Measure F101 and manipulate valve V-1

Q.33	Match the reaction in Group – 1 with the reaction type in Group – 2. The correct combination is:
(A)	P – II, Q – III, R – I, S – IV
(B)	P – III, Q – IV, R – I, S – II
(C)	P – III, Q – IV, R – II, S – I
(D)	P – I, Q – IV, R – III, S – II

Q.9	In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.The probability that any point picked randomly within the square falls in the shaded area is
(A)	4 − 𝜋/2
(B)	1/2
(C)	𝜋/-12
(D)	𝜋/4

Q.29	A frame EFG is shown in the figure. All members are prismatic and have equal flexural rigidity. The member FG carries a uniformly distributed load w per unit length. Axial deformation of any member is neglected. Considering the joint F being rigid, the support reaction at G is
(A)	0.375 wL
(B)	0.453 wL
(C)	0.482 wL
(D)	0.500 wL

Q.2	The mirror image of the above text about the x-axis is
(A)
(B)
(C)
(D)

Q.4	⊕ and ⊙ are two operators on numbers p and q such thatIf 𝒙 ⊕ 𝒚 = 𝟐 ⊙ 𝟐, then x =
(A)	y/2
(B)	y
(C)	3y/2
(D)	2 y

Q.5	Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:
(A)	2
(B)	4
(C)	6
(D)	8

Q.8	Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above.The value of q, in degrees, is___________.
(A)	36
(B)	45
(C)	72
(D)	108

Q.1	The rank of matrix is –
(A)	1
(B)	2
(C)	3
(D)	4

Q.2
(A)	r¹ 2/4
(B)	r¹ ¾
(C)	r² ⅓
(D)	r² 4/3

Q.3	The shape of the cumulative distribution function of Gaussian distribution is
(A)	Horizontal line
(B)	Straight line at 45 degree angle
(C)	Bell-shaped
(D)	S-shaped


Q.18	Consider the limit:The limit (correct up to one decimal place) is

Q.19	The volume determined from ∭𝑽 𝟖 𝒙𝒚𝒛 𝒅𝑽 for V = [2, 3]× [1, 2] × [0,1] will be (in integer)

Q.21	The equation of deformation is derived to be y = x² – xL for a beam shown in the figure. The curvature of the beam at the mid-span (in units, in integer) will be

Q.22	A truss EFGH is shown in the figure, in which all the members have the same axial rigidity R. In the figure, P is the magnitude of external horizontal forces acting at joints F and G. If R = 500×103 kN, P = 150 kN and L = 3 m, the magnitude of the horizontal displacement of joint G (in mm, round off to one decimal place)is

Q.23	The cohesion (c), angle of internal friction (ϕ) and unit weight (γ) of a soil are 15 kPa, 20° and 17.5 kN/m3, respectively. The maximum depth of unsupported excavation in the soil (in m, round off to two decimal places) is____________________.

Q.29	A wedge M and a block N are subjected to forces P and Q as shown in the figure. If force P is sufficiently large, then the block N can be raised. The weights of the wedge and the block are negligible compared to the forces P andQ. The coefficient of friction (μ) along the inclined surface between the wedge and the block is 0.2. All other surfaces are frictionless. The wedge angle is 30°. The limiting force P, in terms of Q, required for impending motion of block N to just move it in the upward direction is given as P = ∝Q . The value of the coefficient ‘∝’ (round off to one decimal place) is
(A)	0.6
(B)	0.5
(C)	2.0
(D)	0.9

Q.31	Based on drained triaxial shear tests on sands and clays, the representative variations of volumetric strain (∆V/V) with the shear strain (γ) is shown in the figure. Choose the CORRECT option regarding the representative behaviour exhibited by Curve P and Curve Q.
(A)	Curve P represents dense sand and overconsolidated clay, while Curve Q represents loose sand and normally consolidated clay
(B)	Curve P represents dense sand and normally consolidated clay, while Curve Q represents loose sand and overconsolidated clay
(C)	Curve P represents loose sand and overconsolidated clay, while Curve Q represents dense sand and normally consolidated clay
(D)	Curve P represents loose sand and normally consolidated clay, while Curve Q represents dense sand and overconsolidated clay

Q.33	A water sample is analyzed for coliform organisms by the multiple-tube fermentation method.The results of confirmed test are as follows: The most probable number (MPN) of coliform organisms for the above results is to be obtained using the following MPN Index. The MPN of coliform organisms per 100 mL is
(A)	1100000
(B)	110000
(C)	1100
(D)	110

Q.47	An unsupported slope of height 15 m is shown in the figure (not to scale), in which the slope face makes an angle 50° with the horizontal. The slope material comprises purely cohesive soil having undrained cohesion 75 kPa. A trial slip circle KLM, with a radius 25 m, passes through the crest and toe of the slope and it subtends an angle 60° at its center O. The weight of the active soil mass (W, bounded by KLMN) is 2500 kN/m, which is acting at a horizontal distance of 10 m from the toe of the slope. Consider the water table to be present at a very large depth from the ground surface. Considering the trial slip circle KLM, the factor of safety against the failure of slope under undrained condition (round off to two decimal places) is____________.

Q.48	An unlined canal under regime conditions along with a silt factor of 1 has a width of flow 71.25 m. Assuming the unlined canal as a wide channel, the corresponding average depth of flow (in m, round off to two decimal places) in the canal will be_____________

Q.49	A cylinder (2.0 m diameter, 3.0 m long and 25 kN weight) is acted upon by water on one side and oil (specific gravity = 0.8) on other side as shown in the figure. The absolute ratio of the net magnitude of vertical forces to the net magnitude of horizontal forces (round off to two decimal places) is___________.

Q.50	A tube-well of 20 cm diameter fully penetrates a horizontal, homogeneous and isotropic confined aquifer of infinite horizontal extent. The aquifer is of 30 m uniform thickness. A steady pumping at the rate of 40 litres/s from the well for a long time results in a steady drawdown of 4 m at the well face. The subsurface flow to the well due to pumping is steady, horizontal and Darcian and the radius of influence of the well is 245 m. The hydraulic conductivity of the aquifer (in m/day, round off to integer) is__________.

Q.2	A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.Which one of the following is NOT a convex polygon?
(A)
(B)
(C)
(D)

Q.13	The process and instrumentation diagram for a feedback control strategy to maintain the level (h) of a liquid by regulating a valve (V ) in a tank is shown below. F1 is inlet liquid flow rate, F2 is outlet liquid flow rate, LT is the liquid level transmitter, LC is the liquid level controller, h_sp is the setpoint value of the liquid level, hm is the measured value of the liquid level and PV is the valve pressure. The manipulating variable(s) is/are
(A)	F1 only
(B)	F2 only
(C)	hm and PV only
(D)	hsp and PV only

Q.27	Match enzymes in Group I with their corresponding industrial application in Group II.
(A)	P-2, Q-3, R-4, S-1
(B)	P-1, Q-3, R-2, S-4
(C)	P-1, Q-2, R-3, S-4
(D)	P-1, Q-4, R-2, S-3

Q.28	Match separation methods in Group I with associated properties in Group II.
(A)	P-4, Q-2, R-1, S-3
(B)	P-3, Q-1, R-2, S-4
(C)	P-1, Q-3, R-2, S-4
(D)	P-1, Q-2, R-4, S-3

Q.29	Match the autoimmune diseases in Group I with the corresponding primarily affected organ in Group II.
(A)	P-1, Q-2, R-3, S-4
(B)	P-3, Q-1, R-2, S-4
(C)	P-4, Q-2, R-1, S-3
(D)	P-1, Q-2, R-4, S-3

Q.30	Match hypersensitivity types in Group I with their corresponding condition in Group II.
(A)	P-2, Q-3, R-1, S-4
(B)	P-3, Q-1, R-4, S-2
(C)	P-2, Q-3, R-4, S-1
(D)	P-2, Q-1, R-3, S-4

Q.31	Which of the following combinations of plant hormones and their associated function are CORRECT?
(A)	P and R only
(B)	P and S only
(C)	Q and R only
(D)	Q and S only