Vidhyarthi Darpan %

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

Latest Current Affairs 27 January 2022

NATIONAL NEWS

PM Modi to host first-ever India-Central Asia Summit

Prime Minister Narendra Modi will host the first-ever India-Central Asia Summit virtually on January 27, 2022. The virtual event will see participation from Presidents of five central Asian nations- Tajikistan, Turkmenistan, Uzbekistan, Kazakhstan and the Kyrgyz Republic. The key focus of the summit is likely to be regional security, Afghanistan issue and trade and connectivity, culture, development partnership and people-to-people ties. This will be the first such high-level engagement between India and the Central Asian countries.

Neeraj Chopra conferred Padma Shri

Tokyo Olympics Gold Medalist Neeraj Chopra was conferred the Padma Shri on January 26, 2022, the fourth-highest civilian award of India. The 24-year-old had created history by becoming the first Indian to win Olympic gold in athletics. He also got the Param Vishisht Seva Medal by the 4 Rajputana Rifles for his distinguished service. Chopra is a Subedar in the Indian Army.

ICC ODI Rankings: Virat Kohli, Rohit Sharma retain second, third spot

Indian batsmen Virat Kohli and Rohit Sharma retained their rankings on ICC Men’s ODI Player Rankings. South Africa’s wicketkeeper-batsman Quinton de Kock moved up four places and broke into the top five for the first time and batsman Rassie van der Dussen moved up 10 places to reach his career-best 10th rank after they helped their team achieve a memorable 3-10 whitewash in the ODI series against India.

Plinth construction starts at Ram Temple in Ayodhya, Uttar Pradesh

The third phase of the construction of the Ram Temple started at Ramjanmabhoomi in Ayodhya on January 24, 2022, with a laying of granite stones for the plinth. With an aim of achieving physical strength and other physical and chemical features and consequent longevity, the work of plinth with granite stone has begun. Digital instrumentation is also being used for monitoring the safety parameters of the temple and the data of these instruments will be used to study the behaviour of the structure in respect of earthquake, loading, etc. On the basis of the judgment of the Supreme Court on November 9, 2019, Shri Ram Janmabhoomi Teerth Kshetra Trust was entrusted to undertake the work of Ram Temple construction in Ayodhya, Uttar Pradesh.

Ministry of State for Culture released pictorial comic book ‘India’s Women Unsung Heroes’

The Minister of State for Culture Meenakshi Lekhi released the pictorial comic book ‘India’s Women Unsung Heroes’. The comic book has been prepared by the Ministry of Culture in partnership with Amar Chitra Katha. The latest comic book portrays the tales of valour of India’s forgotten women freedom fighter. It is a fitting tribute to them as it celebrates the lives of women who lit the flame of rebellion in the country. The Minister further informed that the book contains the stories of queens who had battled imperialism and also dedicated their lives to Maa Bharati.

External Affairs Minister S Jaishankar tests positive for COVID-19

The External Affairs Minister of India S Jaishankar has tested positive for COVID-19. The union minister while announcing the news also urged all those who came in close contact with him to take suitable precautions. EAM S. Jaishankar shared the latest news via Twitter and stated that he has tested positive for COVID. Earlier, he had taken part in a virtual event along with the Foreign Minister of France Jean-Yves Le Drian.

G Balasubramaniam is next High Commissioner of India to Nigeria

The Ministry of External Affairs announced on January 27, 2022, that G Balasubramaniam has been appointed as the next High Commissioner of India to Nigeria. Balasubramaniam has been currently serving as the Joint Secretary in the Ministry of External Affairs. G Balasubramaniam is expected to take up his latest assignment shortly.

INTERNATIONAL NEWS

North Korea fires two ballistic missiles in latest tests, says South Korea’s military

According to South Korea’s Joint Chiefs of Staff, it detected the launch of what has been presumed to be two ballistic missiles from around Hamhung, on the east coast of North Korea on January 27, 2022. This would be the sixth round of missile tests this month. The suspected missiles reportedly landed outside of Japan’s exclusive economic zone.

SpaceX Rocket Junk to crash into Moon in March: Experts

A chunk of a SpaceX rocket, which had blasted off seven years ago and was abandoned in space after completing its mission, is expected to crash into the Moon in March 2022. The rocket was launched in 2015 to put into orbit NASA’s Deep Space Climate Observatory (DSCOVR). The second stage of the rocket has been floating in space in a chaotic orbit, according to astronomers.

England ends face mask rules and COVID restrictions

England lifted the face mark rules and most of the COVID-19 restrictions on January 26, 2022. The move came after the British Government announced that its vaccine booster roll-out plan has successfully reduced serious illness and COVID-19 hospitalizations. Health officials in Britain have also been saying that they are planning a longer-term post-pandemic strategy that treats COVID-19 more like the flu. Earlier, the World Health Organisation had warned against the dangers of treating Coronavirus like the flu and dropping pandemic restrictions.

Latest Current Affairs 26 January 2022

NATIONAL NEWS

Supreme Court declines interim relief in plea to extend validity of expired FCRA licences of NGOs

The Supreme Court on Tuesday declined to pass an interim order directing the government to extend the validity of licences of NGOs under the Foreign Contribution Regulation Act (FCRA) which expired on September 30 last year, instead opting to pronounce its judgment first in a pending case challenging the very constitutionality of the amendments to the law on the flow of foreign funds into India. A Bench led by Justice A.M. Khanwilkar was hearing a plea made by a U.S.–based organisation, Global Peace Initiative, represented by senior advocate Sanjay Hegde, which challenged the expiry of the FCRA licences of nearly 6,000 NGOs. The organisation urged the court to let these NGOs continue with their licences until further orders. Countering the plea, Solicitor General Tushar Mehta said the government had extended the licences of 11,594 NGOs which applied within time. Mehta further questioned the locus standi of the petitioner, asking how an organisation based in Houston was concerned with the FCRA licences in India. The court refused to intervene in the issue though it allowed the petitioner to approach the authorities with a representation which would be considered on its merits. The court said the petition would be taken up after it had pronounced its judgment in the pending Noel Harper versus Union of India case on the validity of the amendments made to the FCRA in 2020. The apex court had reserved its verdict on the question of validity of the amendments on November 9, last year. The government, through the Ministry of Home Affairs, had maintained that the NGOs had no fundamental right to receive unbridled foreign contributions.

Supreme Court notice on parties’ promises of ‘irrational freebies’ before elections

The Supreme Court on Tuesday sought responses from the Union government and the Election Commission of India (ECI) on the continued ‘tamasha’ of political parties promising or distributing ‘irrational freebies’ using public funds. A Bench of Chief Justice of India N.V. Ramana, Justices A.S. Bopanna and Hima Kohli issued notice to the Centre and the top poll body on a petition filed by advocate Ashwini Kumar Upadhyay, represented by senior advocate Vikas Singh, to issue stringent guidelines to deregister the errant political parties and seize their election symbols. The ‘tamasha’ has been going on for decades. Promises always remain as promises. Most of them, except freebies, are not implemented, the petition said and contended that the offer of these freebies amounted to bribery and undue influence. The court, however, drew a skeptical note about how Upadhyay, in his petition, named only a few, select political parties and States. Upadhyay said he did not mean to target only a few parties and offered to make all political parties respondents in the petition. The court said it would start, for the time being, by issuing notice to the Centre and the ECI, which have been named respondents now. The court listed the case after four weeks. In the hearing, Singh submitted that parties, even in debt-ridden States, were promising/distributing these freebies to garner votes and to create an uneven playing field before the elections. Singh said the election commission’s guidelines on the freebies, issued after a Supreme Court judgment in the Subramaniam Balaji case, reported in 2013, were toothless. Promise/distribution of irrational freebies from public fund before election unduly influences the voters, shakes the roots of free-fair election, disturbs level playing field, vitiates the purity of election process and also violates Articles 14, 162, 266(3) and 282, the plea said.

U.P. Assembly polls: Polarisation suits both BJP and SP to consolidate vote bases, says Priyanka Gandhi

Alleging that polarisation suits both the BJP and the SP to consolidate their vote bases in Uttar Pradesh, Congress leader Priyanka Gandhi Vadra on Tuesday said the ruling party may end up being the largest beneficiary of this divisive rhetoric and therefore people need to be given a choice of another kind of politics that doesn’t divide society on religious or caste lines. Citing that farm laws and the Lakhimpur Kheri incident caused immense pain to farmers, she also said the government’s indifference’’ and hostile approach towards the farmers will play an important part in determining the outcome of the assembly polls in Uttar Pradesh’s western belt. In an exclusive interview to PTI, Priyanka Gandhi said her party will take a call on whether to forge a post-poll alliance once the election results are out and if and when such a situation should arise. With her party going to the polls with a focus on women and announcing that it will give 40% of tickets to them, she said women are 50% of the population and if they consolidate into a political and electoral force by recognising their own value and strength in political terms, they can change the politics of our nation. The saffron party, in turn, has accused the Akhilesh Yadav-led party SP of invoking Mohammad Ali Jinnah and Pakistan to vitiate the discourse. Priyanka Gandhi said people are suffering and they have to be made to connect this suffering to the lack of governance. Event management is not the same as effective governance. People have to be made to understand that, and demand good governance. Despite the crores it spends on advertising itself as one of the leading state governments in India, the truth is that the BJP government in UP does not know how to govern, she alleged.

In West Bengal, parents demand reopening of schools, colleges

A campaign is on in West Bengal in favour of reopening of educational institutions, with many angry parents demanding to know why it is always the students who are made to sit home whenever pandemic–related restrictions are imposed. Schools and colleges, which had reopened late last year, were to resume classes on January 2 after winter vacations but were shut again after the Omicron-driven third wave caused an explosion in the number of COVID-19 cases. As of now, they are to remain shut till January 31 but there is no official word yet on whether they will reopen after that date. The campaign is reflecting online, with demands for re–opening of institutions being made under the hashtag #openschoolcollegeuniversities. There was a time when the closure was a necessity. But now that we are trying to normalise ourselves, why are students being made to stay home? asked Sunetra Mitra, a professor of history at the Ramakrishna Sarada Mission Vivekananda Vidyabhavan in Kolkata. You see the young people go everywhere — on vacations, to malls, to restaurants, to pandals — to seem to be going everywhere except to their schools or colleges. Also, it is not possible for a vast majority of students to afford online classes. How many of them actually have access to a smartphone or laptop? Such students are eventually dropping out. Bandyopadhyay, who recently wrote in the letters-to-the-editor column of a leading Bengali daily calling for resumption of offline classes, said closure of educational institutions was necessary two years ago because no one was prepared for a pandemic but now schools and colleges must reopen with COVID protocols in place. Closure is not a solution. The biggest disadvantage of online teaching is I cannot see the faces of my students. I have no idea how receptive they are. The online mode also compromises on the assessment during exams — meritorious students are at a great disadvantage, Bandyopadhyay said.

Pfizer starts Omicron-specific COVID-19 vaccine trial Pfizer and its partner

BioNTech have begun enrolment for a clinical trial to test the safety and immune response of their Omicron-specific COVID-19 vaccine in adults aged up to 55, the companies said in a statement on January 25. Pfizer’s CEO Albert Bourla has previously said that the pharmaceutical giant could be ready to file for regulatory approval of the shot by March. The company’s head of vaccine research Kathrin Jansen said in a statement that while current data showed that boosters against the original COVID-19 strain continued to protect against severe outcomes with Omicron, the company was acting out of caution. We recognise the need to be prepared in the event this protection wanes over time and to potentially help address Omicron and new variants in the future, she said. Ugur Sahin, CEO of BioNTech, added that the protection of the original vaccine against mild and moderate COVID-19 appeared to wane rapidly against Omicron. Combo photo shows logos Pfizer and BioNTech. This study is part of our science-based approach to develop a variant-based vaccine. The trial will involve 1,420 people aged 18-55. A spokesperson for Pfizer said that it did not include people older than 55 because the goal of the study was to examine the immune response of participants dosed, rather than estimate vaccine efficacy. The trial is taking place across the United States and South Africa, and the first participant was dosed in North Carolina. The Pfizer-BioNTech vaccine was the first COVID-19 shot to be authorised in the West, in December 2020. Because it is based on messenger RNA technology, it is relatively easy to update to reflect the genetic code of new variants. Several countries have begun to emerge from their latest waves driven by Omicron, the most transmissible strain to date, even though global new cases are still rising. The coronavirus has killed some 5.6 million people since the outbreak emerged in China in December 2019.

INTERNATIONAL NEWS

NATO sends ships, fighter jets to eastern Europe as Russia continues troop build-up near Ukraine

NATO said Monday that it’s putting extra forces on standby and sending more ships and fighter jets to eastern Europe as Russia continues its troop build-up near Ukraine. It said that it’s beefing up its deterrence presence in the Baltic Sea area. A number of members of the 30-country military organisation have offered troops and equipment. Denmark is sending a frigate to the Baltic Sea and deploying F-16 war planes to Lithuania. Spain is sending ships to join NATO’s standing maritime force and considering sending fighter jets to Bulgaria. France stands ready to send troops to Bulgaria, NATO said. NATO will continue to take all necessary measures to protect and defend all Allies, including by reinforcing the eastern part of the Alliance. We will always respond to any deterioration of our security environment, including through strengthening our collective defence, NATO Secretary General Jens Stoltenberg said in a statement.

Julian Assange granted appeal in UK to fight extradition to US WikiLeaks founder Julian Assange’s battle to avoid extradition to the US will go to Britain’s Supreme Court after he was granted the right on Monday to appeal a lower court ruling. The High Court in London allowed Assange to appeal its decision that he could be sent to the US to stand trial on espionage charges. The decision is the latest step in Assange’s long battle to avoid trial on a series of charges related to WikiLeaks’ publication of classified documents more than a decade ago. Just over a year ago, a district court judge in London rejected a US extradition request on the grounds that Assange was likely to kill himself if held under harsh US prison conditions. US authorities later provided assurances that the WikiLeaks founder wouldn’t face the severe treatment his lawyers said would put his physical and mental health at risk. The High Court last month overturned the lower court’s decision, saying that the US promises were enough to guarantee Assange would be treated humanely. The court on Monday gave Assange permission to appeal that ruling to the Supreme Court.

Group opposes protection from caste discrimination in California Varsity’s faculty union.

A group of faculties in the California State University (CSU) system has written to the Board of Trustees asking that caste not be added as a ‘protected category’ to the system’s collective bargaining agreement (CBA), on the grounds that it would apply to Indian-origin faculty alone and single them out for targeted scrutiny. A protected category in the U.S., refers to a category that has specific protections against discrimination. The proposed changes to the agreement with the union follow from a change across the system’s 23 campuses announced on January 20, in which caste was specifically made part of the institutions’ anti-discrimination policy. The faculty letter, a copy of which was released by the Hindu American Foundation (HAF), was, according to the writers, written by over 80 CSU faculty (the list of names was withheld, so the number has not been verified by The Hindu). The letter requests that the CBA only be approved after caste, as a category, is taken out. Meetings to ratify the agreement between the CSU and the union (the California Faculty Association or CFA), are scheduled for Monday and Tuesday. The reason why caste oppressed people are asking for the category to be made explicit, is that when institutions make it explicit, they’re extending the existing rights more clearly, for caste oppressed people, she told The Hindu on Monday over the phone. Because once it’s listed, institutions then will build competency around it. The faculty letter alleges that Equality Labs is an anti-Hindu activist organization and that a member of the group was called in as a witness to the January 14 Union meeting.

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

Latest Current Affairs 25 January 2022

NATIONAL NEWS

Lok Sabha, Rajya Sabha to have staggered timing

Lok Sabha and Rajya Sabha are likely to function with staggered timing during the budget session of the Parliament, which is scheduled to start from January 31, 2022 amid rising number of COVID Cases in the country. While the Rajya Sabha is likely to meet in the first half of the day, the Lok Sabha is likely to meet in the second half of the day. President Ram Nath Kovind will address the joint sitting of the two Houses on January 31st. The budget will be presented on February 1st.

National Voters Day 2022

The 12th National Voters Day was observed today to commemorate the foundation day of the Election Commission of India. The Election Commission was set up on January 25, 1950. The National Voters Day aims to encourage the new voters to enroll themselves in the electoral process.

Air India likely to be handed over to Tata on January 27

National carrier Air India is likely to be handed over to the Tata Group on January 27, 2022. The government has decided to complete the disinvestment process by then, as per sources. Talace Pvt Ltd, which is a wholly-owned subsidiary of Tata Sons Pvt Ltd, had won the bid last year to acquire 100 per cent equity shareholding of government-owned Air India.

Health Minister to hold meeting with health ministries of 9 states/ Uts

The Union Health Minister Mansukh Mandaviya will hold virtual meeting with health ministers of nine states and union territories today over the COVID-19 situation. These states and Uts include Delhi, Haryana, Uttar Pradesh, Punjab, Himachal Pradesh, Jammu and Kashmir, Uttarakhand, Ladakh and Chandigarh.

President Kovind to address the nation on eve of 73rd Republic Day

President Ram Nath Kovind will address the nation on Tuesday on the eve of the 73rd Republic Day, a Rashtrapati Bhavan communique issued on Monday night said. The address will be broadcast from 7 pm on the entire national network of All India Radio (AIR) and telecast over all channels of Doordarshan in Hindi followed by the English version, it said.

Delhi HC to hear plea on PM’s security on April 30

The Delhi High Court on Monday posted for hearing on a petition on issue of safety and security of the Prime Minister on April 30. At the outset of the hearing, a Bench of Chief Justice D.N. Patel and Justice Jyoti Singh said petitioner Ashish Kumar could seek representation with the Central government on the issue. The Bench noted that the top court was awaiting the report of the committee appointed by it.

FCRA registration: SC to hear plea against Centre’s decision on Tuesday

The Supreme Court Monday said it would hear on Tuesday a petition which has sought quashing of the Centre’s alleged decision by which 5,789 entities lost their Foreign Contribution Regulation Act (FCRA) registration. The FCRA registration is mandatory for any association and NGO to receive foreign funding.

More restrictions in Kerala as COVID-19 cases continue to rise. As Kerala continues to register a steep rise in COVID-19 cases, the State government on Monday said the educational institutions which have less than 40%attendance for consecutive three days will be closed for two weeks. The COVID-19 evaluation meeting, chaired by Chief Minister Pinarayi Vijayan virtually from the USA where he is undergoing treatment, decided to declare the educational institutions with less than 40% attendance as clusters.

PM Modi to interact with BJP workers on Tuesday

Prime Minister Narendra Modi will interact with BJP workers from across the country via NaMo app on Tuesday. The interaction comes in the run-up to the assembly polls in five states, including Uttar Pradesh, with the Election Commission not allowing physical rallies by political parties due to the COVID-19 pandemic.

Houses of Parliament to work in shifts

During the upcoming Budget Session, Parliament will function in two shifts, with Rajya Sabha functioning from 10 a.m. to 3 p.m. and Lok Sabha from 4 p.m. till 9 p.m. The two Houses are sitting in shifts to enable the members to be seated across both chambers of Parliament to ensure social distancing.

Japan to widen virus measures and boost testing amid omicron

Japan’s government plans to put the majority of the country under pre-emergency status and extend COVID-19 restrictions as omicron cases have surged and threatened to disrupt basic services like hospitals and schools. Prime Minister Fumio Kishida said Monday that he will tighten anti-virus measures in 18 more prefectures, including Hokkaido in the north to Osaka and Kyoto in western Japan, until Feb 20. This will be in addition to areas where similar restrictions are already in place or to be further extended — including Tokyo, Okinawa, Yamaguchi, and Hiroshima.

Saina top attraction in Odisha Open beginning on Tuesday

London Olympics bronze medallist Saina Nehwal will be the star attraction in Odisha Open Super 100, the state’s first-ever international tournament under Badminton World Federation, which begins on Tuesday. Saina has been seeded first in the women’s singles while P Kashyap is the top seed in men’s singles of the tournament to be played at Jawaharlal Nehru Indoor Stadium. More than 300 players from 17 countries are participating in this tournament. The event begins with the qualifying round on Tuesday and will continue till January 30. Morning Filter will return tomorrow. Follow up on the day’s biggest stories and get concise analysis by The Hindu with the Evening Wrap newsletter. Today’s Top Picks Justice Ayesha Malik takes oath as first woman judge of Pakistan’s Supreme Court What you need to know about the 2022 Goa polls | Talking Politics with Nistula Hebbar ‘Emergency’ movie review: Carey Williams’ satire on racial politics is a knockout Lucknow IPL team to be called Lucknow Super Giants Copyright @ 2021, THG PUBLISHING PVT LTD. If you are facing any trouble in viewing this newsletter, please try hereIf you do not wish to receive such emails go here

INTERNATIONAL NEWS

Meta’s new AI supercomputer to be the world’s fastest by mid-2022

Meta, Facebook’s parent company, said recently that its new artificial intelligence supercomputer is expected to be the world’s fastest by the middle of this year. The company also stated that developing the next generation AI will require supercomputers capable of performing quintillions of operations per second.

US places 8,500 troops on ‘heightened alert’ over Russia-Ukraine standoff

The Pentagon informed on January 24, 2022 that US Defense Secretary Lloyd Austin has placed up to 8,500 troops on heightened alert to prepare them for deployment if needed amid fears of Russia invading Ukraine. This comes after Russia has amassed almost 100,000 soldiers along its border with Ukraine.

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 Chemical Engineering Previous Year Paper

GATE 2021 Chemical Engineering Previous Year Paper

General Aptitude (GA)

Chemical Engineering (CH)

Latest Current Affairs 27 January 2022

Latest Current Affairs 26 January 2022

GATE 2021 Civil Engineering Section-II Previous Year Paper

Latest Current Affairs 25 January 2022

GATE 2021 Civil Engineering Section-I Previous Year Paper

Civil Engineering

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

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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__________.