PM Modi to virtually inaugurate 25th National Youth Festivaled
A chemical leak was reported on January 11, 2022 in a fish processing plant in Baikampady, located on the outskirts of Mangaluru city in Karnataka. Around 20 employees were hospitalised out of the 80 present at the time of the accident after they developed breathing problems.
Union Minister Nitin Gadkari tests Covid positive
Union Minister Nitin Gadkari tested positive for Covid-19 on January 11, 2022. He tweeted saying that he has mild symptoms and has isolated himself following all the necessary protocols. The Minister is currently under home quarantine. Earlier, Defence Minister Rajnath Sing had also tested positive for Covid-19.
IPL Mega auction to be held on February 12-13
The IPL mega auction will take place in Bengaluru on February 12-13, 2022. The news was confirmed after the two new IPL teams- Ahmedabad and Lucknow- received formal clearance from the BCCI. Both teams have now been given a time frame to sign up players before the mega auction.
Republic Day celebrations to take place with stricter restrictions
The Republic Day celebrations will continue to take place amid the ongoing third wave of COVID-19 with stricter restrictions. The restrictions will be stricter than the ones imposed last year. The number of visitors allowed to witness the parade might be further limited. The route of the parade will also be shorter, similar to last year. The marching contingent will end at India Gate C instead of the Red Fort.
Lakshadweep achieves 100 percent COVID vaccination in the 15-18 age group
Lakshadweep has achieved 100 percent COVID-19 vaccination of children in the age group of 15-18 years. Lakshadweep has become the first among the states and the Union Territories to achieve the feat. According to the District Collector, the vaccination drive for children was launched by Administrator Praful Patel in Kavaratti as part of the nationwide campaign. The target of 3,492 children was achieved within a week after the launch of the vaccination drive through the various campaigns that were conducted in schools and the mobilization drives. Lakshadweep was also the first among the Uts and the states to have achieved 100% vaccination in other categories as well.
INTERNATIONAL NEWS
PCB Chairman to propose 4-nation T20I series involving India?
Pakistan Cricket Board (PCB) Chairman Ramiz Raja said on January 11, 2022 that he will make a proposal to ICC about holding a 4-nation T20I series comprising both India and Pakistan every year. He stated that he wants to see India, Pakistan, England and Australia face each other in the series every year. The matches can be hosted by the four nations on a rotation basis, as per the proposal.
Spinner Washington Sundar testes positive for COVID-19, out of SA ODIs
Washington Sundar, Team India off-spinner, has been ruled out of the forthcoming ODI series against South Africa after testing positive for Coronavirus. The All-India Senior Selection Committee has named Jayant Yadav as a replacement for Washington Sundar. Fast bowler Navdeep Saini has also been added by the Committee to the ODI squad as a back-up for Mohammed Siraj who is recovering from his hamstring injury. India and South Africa will lock horns in three ODIs starting from January 19, 2022, under the Captaincy of KL Rahul.
Oscars to have host after 3 years absence
Oscars 2022 which is scheduled to air on March 27, 2022, will be the first since the 2018 ceremony to have a host. Craig Erwich, ABC Entertainment, and Hulu Originals, has announced that the Oscars will return with a host, however, he did not elaborate on who that might be. Jimmy Kimmel had served as the last host of Oscars, having emceed the ceremony in 2017 and 2018. The Academy Awards went hostless in 2019 when the Academy at first announced Kevin Hart for hosting the gig. However, he was later dropped out after the organisation had asked him to apologize for years-old homophobic tweets.
Poet Maya Angelou becomes first Black Woman to feature on US Coin
Activist and Poet Maya Angelou has become the first black woman to appear on the US quarter, in a new version of the coin which was unveiled by the US Mint on January 10, 2022. The author of ‘I Know Why the Caged Birds Sings’, will also become the first figure commemorated through the American Women Quarters Program. It was signed into law in January 2021. As per the press release from the agency, the US Mint has started shipping the first coins with Maya Angelou’s likeness on the American Quarter, a 25-cent piece. Maya Angelou was born in Missouri in 1928. She was an essayist and poet who had worked with Martin Luther King Jr. and Malcolm X during the Civil Rights Movement.
GATE 2020 Metallurgical Engineering Previous Year Paper
GA – General Aptitude
Q1 – Q5 carry one mark each.
Q. 1He is known for his unscrupulous ways. He always sheds __________tears to deceive people.
(A)fox’s (B)crocodile’s (C)crocodile (D)fox
Q. 2 Jofra Archer, the England fast bowler, is __________than accurate.
(A) more fast (B) faster (C) less fast
(D) more faster
Q.No.3 Select the word that fits the analogy:
Build : Building :: Grow:
(A) Grown (B) Grew (C) Growth
(D) Growed
Q. 4 I do not think you know the case well enough to have opinions. Having said that, I agree with your other point. What does the phrase “having said that” mean in the given text?
(A) as opposed to what I have said (B) despite what I have said (C) in addition to what I have said
(D) contrary to what I have said
Q. 5 Define [x] as the greatest integer less than or equal to x, for each x € (-00,00). If y = [x], then area under y for x € [1,4] is
(A) 1 (B) 3 (C) 4
(D) 6
Q6 – Q10 carry two marks each.
Q. 6 Crowd funding deals with mobilisation of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.
Based on the above paragraph, which of the following is correct about crowd funding?
(A) Funds raised through unwilling contributions on web-based platforms. (B) Funds raised through large contributions on web-based platforms. (C) Funds raised through coerced contributions on web-based platforms.
(D) Funds raised through voluntary contributions on web-based platforms.
Q. 7 P, Q, R and S are to be uniquely coded using a and B. If P is coded as aa and Q as aß, then R and S, respectively, can be coded as
(A) Ba and aß (B) BB and ac (C) aß and BB
(D) Ba and BB
Q. 8 The sum of the first n terms in the sequence 8, 88,888, 8888, … is
Q. 9 Select the graph that schematically represents BOTH y = x” and y = x1/m properly in the interval OS X < 1, for integer values of m, where m > 1.
Q. 10 The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates in percentage) of these four schools is
(A) 58.5 % (B) 58.8% (C) 59.0 %
(D) 59.3%
MT: Metallurgical Engineering
Q1 – Q 25 carry one mark each.
Q. 1 The general solution to the following homogeneous ODE,
The values of λ1 and λ, are:
(A) -1 and -3 (B) -3 and -3 (C) 1 and -3
(D) 1 and 3
Q. 2 The number of independent elastic constants of an isotropic material is:
(A) 1 (B) 2 (C) 3
(D) 4
Q. 3 A slip system consists of a slip plane and a slip direction. Which one of the following is NOT a valid slip system in a FCC copper crystal?
(A) (111)[110] (B) (111)[011] (C) (111)[101]
(D) (111)[101]
Q. 4 A dielectric material is:
(A) Electrical conductor
(B) Metallic magnet
(C) Two coupled electrical conductors
(D) Electrical insulator
Q. 5 Which one of the following processes is an example of an electrolytic cell?
(A) Corrosion of a metal rod in ambient atmosphere
(B) Charging of a rechargeable battery
(C) Discharging of a rechargeable battery
(D) Sacrificial cathodic protection system
Q. 6 Which one of the following statements regarding selective leaching of a binary alloy is TRUE?
(A) The lower atomic weight element is leached.
(B) The element having higher diffusivity is leached.
(C) The more electronegative element is leached.
(D) The element with lower density is leached.
Q. 7 In green sand casting, which one of the following is NOT a part of the gating system?
(A) Runner
(B) Sprue
(C) Riser
(D) Pouring basin
Q. 8 For a material to exhibit superplasticity, one of the requirements is:
(A) Coarse-grained microstructure
(B) High strain-rate sensitivity
(C) Low strain-hardening exponent
(D) High modulus of elasticity
Q. 9 The dye penetrant test for detecting flaws is based on:
(A) Magnetism
(B) Sound propagation
(C) X-ray absorption
(D) Capillary action
Q. 10 When 1 mole of C3H8 at 300 K is burnt with a stoichiometric amount of oxygen at 300 K to form CO2 and H20, the adiabatic flame temperature is 5975 K. If C3Hg is burnt under the same conditions but with excess oxygen, the adiabatic flame temperature will be
(A) equal to 5975 K irrespective of the amount of excess oxygen.
(B) higher than 5975 K irrespective of the amount of excess oxygen.
(C) lower than 5975 K irrespective of the amount of excess oxygen.
(D) higher or lower than 5975 K depending on the amount of excess oxygen.
Q. No. 11 Two solid spheres X and Y of identical diameter are made of different materials having thermal diffusivities 100 x 10-6 m?s-1 and 25 x 10-6 ms-1 respectively. Both spheres are heated in a furnace maintained at 1000 K. If the center of the sphere X reaches 800 K in 1 hour, time required for the center of sphere Y to reach 800 K is
(A) 1 hour
(B) 2 hours.
(C) 4 hours.
(D) 16 hours.
Q. 12 Select the correct spectra (shown on a log-log scale in the figures) for emission from a gray surface and a black body, both maintained at 1000 K.
Q. 13 Given the three vectors X =-i-j+k, Y=-i+2j + k and Z= i + k, which one of the following statements is TRUE?
(A) X, Y and Z are mutually perpendicular.
(B) X, Y and Z are coplanar.
(C) X makes an angle of 30° with the normal to the plane containing Y and Z.
(D) Z makes an angle of 60° with the normal to the plane containing X and Y.
Q. 14 Angle between two neighboring tetrahedral bonds in Si having a diamond cubic structure is:
(A) 102.5°
(B) 109.50
(C) 1200
(D) 135.50
Q. 15 The sequence of precipitation during aging of Al – 4 wt% Cu alloy is:
Q. 16 The indenter used in Rockwell hardness measurements on C scale is
(A) diamond cone.
(B) 10 mm steel ball.
(C) diamond pyramid.
(D) 1/16-in. steel ball
Q. 17 For the function y=a*, the derivative, at x = 1 is:
Q. 19 The functions y = e* and y = e-* intersect at the point:
(A) (1,3) (B) (-2, 2) (C) (0, 1)
(D) (-1,-1)
Q. 20 A heavily cold-worked metal will
(A) yield a coarser recrystallized grain size. (B) possess a lower driving force for recrystallization. (C) have a higher energy barrier for nucleation of recrystallized grains.
(D) recrystallize at lower temperatures.
Q. 21 For the function f(x) given in the figure, the value of S(1 – f(x)) dx is_______(round off to one decimal place).
Q. 22 A component subjected to tensile stress in a mechanical device is monitored periodically for cracks by NDT. The NDT technique can only detect cracks (both surface and internal) which are larger than 1 mm. Keeping a 10% margin of safety, the maximum allowed tensile stress on the component will be______—–MPa (round off to the nearest integer).
Given, fracture toughness Kic=30 MPa m12 and assume crack geometry factor of unity.
Q. 23 An iron plate with a total exposed surface area of 50 cm2 undergoes atmospheric corrosion. If 200 g of weight is lost over a period of 10 years, then the corrosion rate is ________kg.m2 year” (round off to the nearest integer).
Q. 24 In cold-rolling, for the sheet to be drawn into rolls, the angle of contact (or angle of bite) should be less than or equal to _______degree (round off to one decimal place).
Given, the coefficient of friction between sheet and roll is 0.1
Q. 25 The number of atoms per unit area in (100) plane of Pb is _______(round off to the nearest integer).
Given, crystal structure and atomic radius of Pb are FCC and 0.175 nm respectively.
Q26 – Q55 carry two marks each.
Q. 26 In the edge dislocation configuration given in the figure, dislocations X and Y are fixed and separated by a distance 2h on the same slip plane. Dislocation Z is free to glide on a parallel slip plane. The two slip planes are separated by a distance h. Which one of the following statements is TRUE regarding the stability of dislocation Z at positions 1, 2 and 3?
Assume all dislocations have identical Burgers vector.
(A) Position 1: unstable equilibrium; Position 2: unstable; Position 3: unstable (B) Position 1: stable equilibrium; Position 2: unstable; Position 3: unstable (C) Position 1: unstable equilibrium; Position 2: stable; Position 3: unstable
(D) Position 1: stable equilibrium; Position 2: unstable; Position 3: stable
Q. 27 Which one of the following dislocation reactions is NOT feasible in a FCC crystal?
Q. 28 A galvanic cell is formed by connecting Zn (E2n2+/Zn = -0.76 V) and Fe (Efez+/Fe = -0.44 V) wires immersed in their respective ion solutions. The cell discharges spontaneously with a voltage of 0.5 V. The ratio of the concentration of [Fe2+] to [Zn2+] ions in the cell is of the order of:
Given, R = 8.314 J.mol-‘.K!, F = 96500 C.mol-‘, T = 298 K
(A) 10-6 (B) 10-5 (C) 106
(D) 107
Q. 29 The divergence of the vector field (x3 + y3)i + 3xy?j + 3zyak is:
Q. 30 Match the products in Column I with the manufacturing processes in Column II.
Q. 34 X-ray diffraction pattern from an elemental metal with a FCC crystal structure shows the first peak at a Bragg angle 0 = 24.650. The lattice parameter of this metal is ___________nm.
Given, the wavelength of the X-ray used is 0.1543 nm.
(A) 0.185 (B) 0.262 (C) 0.320
(D) 0.370
Q. 35 Match the materials in Column I with their common applications in Column II.
Q. 36 The Mg-Sn phase diagram exhibits two eutectics on either side of the high melting intermetallic line compound, Mg2Sn, as given below.
After the eutectic reaction has gone to completion and equilibrium has been attained at a temperature just below 561°C, the amount of eutectic constituent present in the alloy, Mg-50 wt.% Sn, is approximately ______________(in wt.%).
Given, atomic weight of Sn is 118.7 and Mg is 24.3
(A) 25 (B) 38 (C) 68
(D) 75
Q. 37 Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]
Assertion [a]: Low-alloy steels used for medium-temperature creep resistance often have additions of strong carbide-forming elements.
Reason [r]: During creep deformation, the particles with higher misfit with the matrix, lose coherency.
(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. 38 Determine the correctness or otherwise of the following Assertion [a] and the
Reason [r]
Assertion [a]: The rate of homogenization in a dilute substitutional solid solution of B in A is controlled by the diffusivity of B.
Reason [r]: Atomic migration cannot occur along dislocations and grain boundaries.
(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. 39 Match the elements in Column I with their electronic behaviour given in
Q. 40 Radius of the largest interstitial atom that can be accommodated in an octahedral void in BCC iron without distorting the lattice is_________nm (round off to three decimal places).
Assume hard sphere model and radius of Fe atom as 0.124 nm.
Q. 41 The production process of cylindrical pipes results in a statistical scatter in their diameter which is modelled by a normal distribution with a mean value of 10 mm. If the area under the normal curve between 9 mm and 10 mm is 0.35, then the probability of producing pipes of diameter greater than 11 mm is________(round off to two decimal places).
Q. 42 The solution (using trapezoidal rule) of the integral
by dividing the range 0 to 1 into two equal intervals is_______(round off to two decimal places).
Q. 43 Iron is corroding in fresh water which has dissolved oxygen concentration of 15 mM. The anodic current density at an overpotential of 120 mV is________A.cm2 (round off to three decimal places).
Given:
1. Anodic Tafel slope is 0.06 V.
2. Diffusion coefficient of oxygen is 2.42 x 10-5 cm2.s-1
3. Diffusion layer thickness is 0.06 cm.
Q. 44 A metal oxidizes at 1200 K with a parabolic rate constant of 3×10-6 g2.cm-4.s-1 Time taken for the oxide film to grow to a thickness of 2 um is_______s (round off to two decimal places).
Given, the density of oxide is 6.5 g.cm-3.
Q.No.45 Two plates of composition, Fe-10 wt.% Ni and Fe-20 wt.% Cr-5 wt% Ni are fusion-welded using a filler rod of composition 20 wt.% Ni-80 wt.% Cr. Contribution to dilution of the weld pool is 20% from each plate. The Ni content in the weld pool is________w t.% (round off to the nearest integer).
Q. 46 Figure shows schematic of a venturimeter. The cross sectional area is 100 mm at A and is 50 mm at B. If air is flowing through the venturimeter at a flow rate of 10-3 mos’, the height H in the air-over-water manometer is mm_____________ (round off to the nearest integer).
Assume:
1. Incompressible flow with no friction losses.
2. Density of air is 1 kg m-3.
3. Density of water is 1000 kg m-3.
4. Acceleration due to gravity is 9.8 m s-2.
Q. 47 For effective communication in a ball mill, it is desired that the balls travelling along the mill wall leave the wall at point C and travel freely in air along the path CDA, as shown in the figure. If ZBOC is 120°, the rotational speed of the mill is _____ rpm (rounded off to one decimal place) by performing suitable force balance at point C.
Assume:
1. There is no slip between the ball and mill wall.
2. O is the rotational axis of the mill and OB is parallel to the vector g.
3. Inner diameter of ball mill is 3.26 m.
4. Acceleration due to gravity g is 9.8 m s2.
Q. 48 If liquid copper is cooled to 1353 K, the magnitude of the driving force for liquid to transform to solid is_______J.mol-1 (round off to one decimal place).
Given, melting temperature and enthalpy of melting of copper are 1356 K and 13 kJ.mol-1 respectively.
Q. 49 1000 kg of liquid steel containing 0.03 wt.% S needs to be desulphurized using a slag to bring the sulphur content down to 0.015 wt.%. The quantity of slag needed is_________kg (round off to the nearest integer).
Assume:
1. Thermodynamic equilibrium
2. No sulphur in the slag prior to desulphurization treatment
Given the equilibrium sulphur partition ratio between slag and steel, is 50.
Q. 50 Zone refining of Si results in residual P content of 0.1 parts per billion by weight. The electrical conductivity of this zone refined Si is _________22.m-1 (round off to two decimal places).
Given:
1. Avogadro number is 6.02×1023.
2. Density of Si is 2.33 g.cm .
3. Atomic weight of P is 30.97.
4. Charge of electron is 1.6×10-19 A.S
5. Mobility of electron is 0.2 m2.Vol.s!
Q. 51 The steady state creep rate of a material increases by a factor of 20 when the temperature is increased from 890 K to 980 K. The creep rate at a temperature of______K (round off to the nearest integer) will be 5 times the creep rate at 890 K.
Q. 52 Crack growth is being continuously measured in a test specimen subjected to constant amplitude cyclic stress with a mean stress of zero. The crack growth rate is related to the stress intensity range, AK as
where, a is the crack length and N is the number of cycles. When the crack length increases by a factor of two, the crack growth rate will increase by a factor of_______(round off to one decimal place).
Q. 53 In a top gated mold, liquid metal enters the mold cavity as a freely falling stream under gravity from a height of 0.5 m. Ignore the fluid friction due to viscosity and the drag due to changes in the direction of flow. If the volume of the mold cavity is 10 m, then the time required to fill the mold is__________ (round off to nearest integer).
Given:
1. Acceleration due to gravity is 9.8 m.s2. 2. Cross-sectional area of the gate is 0.2 m2.
Q. 54 A Basic Oxygen Furnace operator, at the end of oxygen blow, measures the dissolved oxygen content in the steel as 0.03 wt.% and the steel temperature as 1800 K. The carbon content [C] in the steel is ___________wt.% (round off to two decimal places).
Assume:
1) Equilibrium between dissolved carbon (C), dissolved oxygen [O], and
CO (gas) at 1 atmosphere.
2) Henry’s law is valid for both [C] and [O]
Given:
[C]1 wt.% Henrian Std. State + [O]1 wt.% Henrian Std. State → (CO)1 atm. Std. State
△G° = -19840 – 40.65 T J
R= 8.314 J.mol-1.K-1
Q. 55 M and N are 3 x 3 matrices. If the det(M) is -9 and the det(N) is -14, then the det(NM) is ______________(round off to the nearest integer).
Delhi Chief Minister Arvind Kejriwal to address media at 12 pm today
Delhi Chief Minister Arvind Kejriwal is scheduled to address a press conference at 12 pm today. He is likely to introduce stricter COVID-19 restrictions in the wake of spiking COVID-19 cases in the capital city.
PM Modi to inaugurate 11 new medical colleges in Tamil Nadu on January 12th
Prime Minister Narendra Modi will inaugurate 11 new government medical colleges across the state of Tamil Nadu on January 12, 2022. He will also inaugurate the new campus of Central Institute of Classical Tamil, Chennai through video conferencing. The new medical colleges are being built at a cost of Rs 4000 crore, of which around Rs 2145 crore was provided by the centre and the rest by the state government.
UNESCO’s WHC to publish Hindi descriptions of India’s world heritage sites
UNESCO’s World Heritage Centre will publish Hindi descriptions of India’s UNESCO world heritage sites on its website. This was announced by World Heritage Centre’s Director on the occasion of World Hindi Day on January 10.
Contact testing not required unless high-risk people are involved: ICMR
The ICMR said in its latest guidelines issued on January 10, 2022 that those who have come in contact with an infected COVID-19 patient do not need to be tested unless any person is in the high-risk category. The asymptomatic individuals or patients discharged as per home isolation guidelines or those discharged from a covid-19 facility as per revised discharged policy need not be tested as well. However, individuals with symptoms like cough, fever, sore throat, loss of smell and taste or any respiratory symptom or breathlessness should be tested.
INTERNATIONAL NEWS
US closely monitoring India-China border dispute
The White House Press Secretary Jen Psaki informed on January 10, 2022 that the US is closely monitoring the India-China border dispute and is concerned by China’s attempts to intimidate its neighbours. Psaki said that the US will continue to support dialogue and peaceful resolution of these border disputes.
Russia has no intentions of attacking Ukraine: Russian Deputy FM
Russian Deputy Foreign Minister Sergey Ryabkov said on January 10, 2022 that Russia has no intentions to attack Ukraine. He stressed that there is no need to fear that there would be any kind of escalation of the situation. Russia and the US had security talks on January 20th in Geneva, which went on for almost 7.5 hours.
Pierre-Olivier Gourinchas appointed as Chief Economist of IMF
Pierre-Olivier Gourinchas, a French-born University of California-Berkley Economist, has been appointed as the next Chief Economist of the International Monetary Fund. He has replaced the Indian-Origin Gita Gopinath. Gourinchas will succeed Gita Gopinath who has been appointed as the First Deputy Managing Director of the International Monetary Fund. Gourinchas will begin his work as the new Chief Economist on January 24, 2022, initially on a part-time basis as he will conclude some prior teaching commitments. He will transition to full time on April 1. As per IMF, Pierre-Olivier will bring his expertise in analysing today’s most pressing economic problems. He is known for his agility in spotting emerging trends in the field of economics.
Chris Morris, South African all-rounder, announces retirement from all forms of cricket
Chris Morris, the South African all-rounder, announced his retirement from all forms of cricket on January 11, 2022. The cricketer thanked everyone who was part of his journey and also expressed excitement for his new role as a coach. Chris Morris had made his international debut in December 2012 against New Zealand and had played his first One Day Internationals in 2013. The all-rounder featured in four tests, 23 T2Ois and 42 ODIs for South Africa. He last played an international game in 2019.
Q. 1 Rajiv Gandhi Khel Ratna Award was conferred Mary Kom, a six-time world champion in boxing, recently in a ceremony the Rashtrapati Bhawan (the President’s official residence) in New Delhi. (A) with, (B) at on, (C) on, at (D) to, at
Q. 2 Despite a string of poor performances, the chances of K. L. Rahul’s selection in the team are
Q. 4 Hit by floods, the kharif (summer sown) crops in various parts of the country have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.
Which of the following statements can be inferred from the given passage?
(A) Officials declared that the food-grain production target will be met due to good rains. (B) Officials want the food-grain production target to be met by the November-February period. (C)Officials feel that the food-grain production target cannot be met due to floods. (D) Officials hope that the food-grain production target will be met due to a good rabi produce.
Q. 5 The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is _____________
(A) n2 (B) n2 + n (C) 2n2 – n (D) 2n2 +n
Q6 – Q10 carry two marks each.
Q. 6 Repo rate is the rate at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.
Which of the following statements can be inferred from the above passage?
(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks. (B) Increase in repo rate will decrease the cost of borrowing and increase lending byC commercial banks. (C) Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks. (D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.
Q. 7 P, Q, R, S, T, U, V, and W are seated around a circular table.
I. S is seated opposite to W.
II. U is seated at the second place to the right of R.
III. T is seated at the third place to the left of R.
IV. V is a neighbour of S.
Which of the following must be true?
(A) P is a neighbour of R. (B) Q is a neighbour of R. (C) P is not seated opposite to Q. (D) R is the left neighbour of S.
Q. 8 The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car How many kilometers the car Q had travelled when the cars crossed each other?
(A) 66.6 (B) 75.2 (C) 88.2 (D) 116.5
Q. No. 9 For a matrix M = [mij]; i, j = 1,2,3,4, the diagonal elements are all zero and mij = -mij: The minimum number of elements required to fully specify the matrix is______
(A) 0 (B) 6 (C) 12 (D) 16
Q. 10 The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013 – 2018 is
Company P Company Q
(A) 15:17 (B) 16:17 (C) 17:15 (D) 17:16
MN: Mining Engineering
Q1-Q25 carry one mark each.
Q. 1 The eigenvalues of the matrix are
(A)6,4 (B)4,5 (C)-2,5 (D)-4, 5
Q. 2 For the electric delay detonator shown in the figure, the components P, Q and R,
Q. 8 The “ratchet and pawl’ mechanism in a jack hammer drill
(A)forces down the piston (B)provides a twisting force to the drill steel (C)engages rifle bar with rifle nut (D)prevents reverse rotation of rifle bar
Q. 9 Post-pillar method of stoping is a variant of
(A) cut and fill stoping (B) sublevel stoping (C) vertical crater retreat method (D) sublevel caving
Q. 10 “Cross-measure borehole method is used for
(A) rock slope monitoring (B) methane drainage (C) connecting two drifts (D) subsidence monitoring
Q. 11 The dry and wet bulb temperatures at the inlet of the airstream are 30 °C and 25 °C, respectively. The corresponding values at the outlet of the airstream are 26 °C and 25 °C, respectively. The psychrometric process that occurs in the airstream is described as
(A) latent cooling
(B) sensible cooling
(C) condensation
(D) evaporative cooling
Q. 12 For a mixture of inflammable gases, the lower and upper explosibility limits can be computed using
(A) Dalton’s law
(B) Graham’s law
(C) Le Chatelier relation
(D) Boyle’s law
Q. 13 The code for the lowest category of mineral resources under United Nations Framework Classification (UNFC) system is
(A) 444 (B) 123 (C) 334 (D) 111
Q. 14 Match the following sampling patterns with the corresponding sampling types.
Q. 15 In the context of gas testing using flame safety lamp, the correct statement is
(A) Each accumulation test has to be necessarily followed by percentage test (B) Accumulation test is always done after percentage test (C) Either percentage test or accumulation test can be done first (D) Percentage test is done only in the event of accumulation test giving negative result
Q. 16 For x in the range of [-3, 3], the maximum value for the function
Q. 17 A rock sample has a coefficient of thermal diffusivity 1.282×10-6 m/s, specific heat 900 J/(kg °C) and density 2600 kg/m3. The coefficient of thermal conductivity of the rock sample in W/(m °C) is__________(round off to I decimal place).
Q. 18 A random variable X has the following probability mass function.
The expected value of the variable X is___________(round off to 1 decimal place).
Q. 19 A random sample has five observations as shown below.
The coefficient of variation of the sample is________(round off to 3 decimal places).
Q. 20 Rock strata has unit weight of 25 kN/m2 and Poisson’s ratio 1/3. At a depth of 200 m, the horizontal stress in MPa is_________(round off to 1 decimal place).
Q. 21 A shovel of bucket capacity 4.2 m3 makes 900 passes per day with a fill factor of 0.8. If the swell factor of the rock is 1.4, then in-situ volume handled by the shovel in a month of 24 working days in m3 is__________(round off to 1 decimal place).
Q. 22 A cylindrical sample of granular material has the following measurements:
Length: 10 cm
Diameter: 5 cm
Weight: 350 g
Assume the sample is completely dry with specific gravity of solid grains 2.8. The void ratio of the sample is__________(round off to 3 decimal places).
Q. 23 The following consecutive readings were taken at uniform intervals with a level and a levelling staff on continuously sloping ground.
The number of change points is___________.
Q. 24 The cost of a slurry pump is Rs. 50,000 and it has an estimated life of 7 years. If the salvage value is Rs. 8,000, the annual depreciation following straight-line depreciation method, in Rupees, is___________(round off to I decimal place).
Q. 25 In a mine bench, the shovel loading time follows exponential distribution with a mean loading time of 5 min per dumper. The arrival rate of dumpers that are identical in capacity, follows Poisson distribution with a mean arrival rate of 8 per hour. The probability that the shovel remains idle is___________(round off to 2 decimal places).
Q26 – Q55 carry two marks each.
Q. 26 For , the value of dw/dt is
Q. 27 For the differential equation y1-x2dy+x1-y2dx=0, assuming the constant of integration to be C, the general solution is
Q. 28 A belt-drive used for power transmission between two parallel shafts has a belt of mass 1.2 kg/m, and the maximum allowable belt tension is 2250 N. If the centrifugal tension is one third of the maximum allowable belt tension, the speed at which maximum power is transmitted by the belt, in m/s, is
(A) 46.48 (B) 38.73 (C) 25.00 (D) 35.36
Q.No.29 An air receiver of a compressor, having volume 0.5 m?, supplies air for charging ANFO in drill holes. During the charging process the absolute pressure of the air receiver falls from 900 kPa to 700 kPa. Assuming the entire process is isothermal, the volume of air supplied by the receiver at 100 kPa ambient pressure, in m is
(A) 1.00 (B) 0.39 (C) 0.64 (D) 4.48
Q. 30 A conveyor belt consumes 60 kW power while running at a speed of 3.0 m/s. The angle of lap is 180o and the coefficient of friction between belt and pulley is 0.2. The maximum tension (kN) in the belt is
(A) 21.7 (B) 61.7 (C) 82.9 (D) 42.9
Q. 31 A linear programming problem is stated below.
Maximize Z = 3x1 + 5x2
subject to, 2x1 + x2 8
6x1 + 8x2 30
x1, x2 0
The objective function has
(A) infinite number of solutions (B) unbounded solution (C) unique solution (D) infeasible solution
Q. 32 An explosive mixture has 80 g of ammonium nitrate (NH4NO3) and 14 g of fuel oil (C10H20). The oxygen balance in the mixture is
(A)surplus by 32 g (B)deficient by 24 g (C)surplus by 16 g (D)deficient by 32 g
Q. 33 A cylindrical sample of cross-sectional area A, length L, and Young’s Modulus E, is subjected to a constant uniaxial load P. Within the elastic limit of loading, the total strain energy stored is
Q. 34 A surface mine production system along with the reliability of the individual components is shown below. The system reliability is_______(round off to 3 decimal places).
Q. 35 The selling price of one rock bolt (in Rs.) is given as, S = (200 – 10n-0.5), where n is the number of bolts produced. The manufacturing cost of rock bolts has a fixed component of Rs. 15000, and a variable component of Rs. 100 per bolt. The minimum break-even production, in number of rock bolts, is______(round off to 1 decimal place).
Q. 36 Two underground mines are separated by a horizontal coal barrier of 60 m thickness. One mine is inundated, whereas the other mine has a blind heading of dimensions 4.0 m wide and 2.5 m height terminating at the barrier. The overall in-situ shear strength of the coal mass is 500 kPa. Assume that the failure mode is in shear. At a factor of safety of 10, the maximum water head that can be withstood by the coal barrier, in m, is____________(round off to 1 decimal place).
Q. 37 Air enters from ambient atmosphere into a level duct of uniform cross-section area 0.2 m- at a flow rate of 2.0 m3/s and density of 1.2 kg/m3. The entry shock loss factor is 1.0 and the resistance of the duct per meter length is 1.0 Ns2/m8. The static pressure measured at a distance of 20 m from the duct entrance in Pa, is___________(round off to 1 decimal place).
Q. 38 A sealed-off area air sample consists of 16.0% O2, 3.0% CO2, and the rest is N2. Assume that the standard composition of atmospheric air is 21.0% O2 and 79,0% N2. The percentage of blackdamp in the air sample is_______(round off to 2 decimal places).
Q. 39 A diesel loader produces 60 l/s of exhaust fumes containing 5000 ppm of CO. The incoming air has 10 ppm of CO. The minimum amount of air flow in m3/s that is needed at the loader to dilute Co to a permissible level of 50 ppm is___________(round off to 1 decimal place).
Q. 40 The equation for peak particle velocity (PPV) from blast induced ground vibration is given by , where k and B are site constants.
In a field study, the following readings are recorded.
The value of B is______________(round off to 3 decimal places).
Q. 41 An underground copper mine sends 2500 tonnes of ore per day to the concentrator plant having an average grade of 1.2% Cu. The plant produces concentrate of 25.0% Cu with a recovery of 93.0%. The solids portion of tailings generated from the plant per day in tonnes is_____________(round off to 1 decimal place).
Q. 42 A mine gallery is supported by regularly placed roof bolts of 100 kN allowable pull force per bolt, as shown below. Assuming unit weight of the immediate roof is 25 kN/m2, the factor of safety of the support system is______(round off to 2 decimal places).
Q. 43 The slip circle of radius 30.0 m in an overburden slope is shown with the centre of slip circle at point O. The tension crack is completely filled with water. For one meter width of the slope, the moment exerted by the force of water about O in kN-m is____________(round off to 1 decimal place).
Q. 44 The function values at four points of x are shown in the table. The area under the function, using trapezoidal method, is ______________(round off to 1 decimal place).
Q. 45 A particle starting from rest moves in a straight line such that after time, 1 (seconds), the acceleration becomes (6 – t/4) cm/s2. When the acceleration becomes zero, the velocity of the particle in cm/s is____________(round off to I decimal place).
Q. 46 A parallelepiped has edge vectors as shown below.
The volume of the parallelepiped is
(round off to 1 decimal place).
Q. 47 For a development heading, the blasting parameters are
Cross-section: 6.0 m × 5.0 m
Total number of holes: 72
Number of trimmer holes: 30
Depth of each hole: 3.5 m
Charge per hole (except trimmers): 3.5 kg
Charge per trimmer hole: 1.8 kg
Pull per round: 90% of hole depth
The powder factor for the development round in my/kg is_________(round off to 2 decimal places).
Q. 48 The following figure represents the observations from the level survey of an underground gallery.
If the reduced level of station A is 100.0 m, the reduced level of station D in m is___________(round off to 1 decimal place).
Q. 49 A tacheometer was setup at station P and the following readings were taken at two stations A and B with the staff held vertical and the line of sight horizontal.
The additive and multiplying constants of the tacheometer are 0 and 100, respectively. The length of AB in m is _____________ (round off to 1 decimal place).
Q. 50 The geometry of a simple planar curve (ADB) is shown below. The value of the mid-ordinate of the curve in m is_____________(round off to I decimal place).
Q. 51 A steel cube of side 50 mm is subjected to a uniform pressure of 200 MPa acting on each face. The Young’s modulus and Poisson’s ratio of the material are 200 GPa and 0.25, respectively. The decrease in the side of the cube in mm is (round off to 3 decimal places).
Q. 52 In the figure shown below, the friction coefficient between the block and the inclined plane is 0.2, and all the pulleys are weightless. The weight of the block is 10 N. The minimum force P in Newtons that is needed to slide the block up the inclined plane is____________(round off to 2 decimal places).
Q. 53 An assignment problem is given below with the cost of assignment as shown.
TL
If only one task can be assigned to one group, the minimum cost of assignment is ______.
Q. 54 A vertical stoping block of length 60.0 m, height 40.0 m, and average width 1.5 m has sharp boundary walls. However, the mining width of the stopping block is 2.0 m. The tonnage factors are 3.0 tonne/m2 for ore and 2.5 tonne/for wall rocks. The average grade of ore is 10.0%. The overall grade of ore mined on account of dilution in percentage is ____________ (round off to 2 decimal places).
Q. 55 A bauxite ore body has four boreholes as shown below. For each borehole, the grade of alumina, the thickness of the ore body, and the triangular area of influence are as shown.
The average grade of ore body in the region ABCD in percentage is_______(round off to 1 decimal place).
GATE 2020 Biomedical Engineering Previous Year Paper
GA – General Aptitude
Q1 – Q5 carry one mark each.
Q.No. 1 Rajiv Gandhi Khel Ratna Award was conferred Mary Kom, a six-time world champion in boxing, recently in a ceremony at the Rashtrapati Bhawan (the President’s official residence) in New Delhi.
(A) with, at
(B) on, in
(C)on, at
(D) to, at
Q.No. 2 Despite a string of poor performances, the chances of K. L. Rahul’s selection in the team are
Q.No.4 Hit by floods, the kharif (summer sown) crops in various parts of the country have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.
Which of the following statements can be inferred from the given passage?
(A) Officials declared that the food-grain production target will be met due to good rains. (B) Officials want the food-grain production target to be met by the November-February period. (C)Officials feel that the food-grain production target cannot be met due to floods. (D)Officials hope that the food-grain production target will be met due to a good rabi produce.
Q.No.5 The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is
(A) n2 – n (B) n2 + n (C) 2n2 – n (D) 2n2 + n
Q6 – Q10 carry two marks each.
Q.No. 6 Repo rate is the rate at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.
Which of the following statements can be inferred from the above passage?
(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks. (B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks. (C) Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks. (D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.
Q.No. 7 P, Q, R, S, T, U, V, and W are seated around a circular table.
I. S is seated opposite to W.
II. U is seated at the second place to the right of R.
III. T is seated at the third place to the left of R.
IV. V is a neighbour of S.
Which of the following must be true?
(A) P is a neighbour of R. (B) Q is a neighbour of R. (C) P is not seated opposite to Q. (D) R is the left neighbor of S.
Q.No. 8 The distance between Delhi and Agra is 233 km. A car P started traveling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were traveling at a constant speed. The speed of car P was 10 km/hr more than the speed of the car. How many kilometers the car Q had travelled when the cars crossed each other?
(A) 66.6 (B) 75.2 (C) 88.2 (D) 116.5
Q.No.9 For a matrix M = [mj]; i, j = 1,2,3,4, the diagonal elements are all zero and mij = -mji. The minimum number of elements required to fully specify the matrix is
(A) 0 (B) 6 (C) 12 (D) 16
Q.No. 10 The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013 – 2018 is Company P Company
(A) 15:17 (B) 16:17 (C) 17:15 (D) 17:16
BM: Biomedical Engineering
Q1 – Q25 carry one mark each.
Q. 1 m1 and m2 are the roots of the characteristic equation of a linear second-order physical system. Match the nature of the roots with the natural response of the system.
(A) P-L, Q-M, R-K
(B) P-M, Q-L, R-K
(C) P-L, Q-K, R-M
(D) P-M, Q-K, R-L
Q.No. 2 A person is sitting in a chair with feet on the ground. While rising up on his feet, the kinematic motion NOT occurring is
(A) Hip extension (B) Plantar flexion (C) Hip flexion (D) Knee extension
Q.No. 3 The equipment that measures elasticity of blood vessel in vivo is
Q.No.7 A 5 MHz ultrasound pulse is used to image a tumor at a depth of 2 cm in a soft tissue. It takes time t for the reflected echo from the tumor to come back to the receiver. Instead, if a 2.5 MHz wave is used, how long will it take for the echo from the same tumor to arrive at the receiver?
(A) t/2 (B) T (C) 2t (D) 4t
Q.No. 8 X(s) is the Laplace transform of a signal x(t).
The Laplace transform dx(t)/dt of love, assuming x(0) = 0, is
Q.No. 9 Which of the following are odd functions?
P: Sin(t)
Q: Cos(t)
R: Sin((t) + Cos(t)
S: Sin(t)Cos(t)
(A) Q and S (B) P and Q (C) P and S (D) R and Q
Q.No. 10 State-space model of a system is given as:
The conditions for the system to be controllable are
(A) a = 0, b ≠ 0 (B) a ≠ 0,b=0 (C) a ≠ 0,b ≠ 0 (D) a = 0, b = 0
Q.No. 11 In microprocessor systems with memory mapped I/O, which of the following is true?
(A) Only I/O devices with internal memory can be interfaced. (B) I/O devices can be accessed using IN and OUT instructions (C) Each I/O device can be addressed as a memory location
(D) Arithmetic and logic operations cannot be directly performed with the I/O data
Q.No. 12 The number of electrodes used in recording standard 12-lead Electrocardiogram (ECG) is
(A) 13 (B) 12 (C) 11 (D) 10
Q.No. 13 Which of the following is NOT a part of the knee joint?
(A) Patella (B) Tibia (C) Femur (D) Fibula
Q.No. 14 During a routine stethoscopic examination at the left midclavicular-5th intercostal space, murmurs were noted between first and second heart sound. The possible abnormality among the following could be
Q.No. 16 The value of the integral evaluated over the contour C:\z = 3/2 is
Q.No. 17 The eigenvalues of a 3 x 3 non-singular matrix P are 1, 2 and 3. The trace of matrix P. (rounded off to two decimal places) is ______________
Q.No. 18 The following recursion relation, when started from a finite positive non-zero value, converges to ___________________
Q.No. 19 In a nuclear imaging system, Sodium Iodide (Nal) crystals are used to detect gamma rays of 120 keV. The percentage (%) of gamma-rays that will pass through 1 cm of Nal crystal, assuming the Half-Value-Layer (HVL) of Nal as 0.2 cm, is________(rounded off to one decimal place).
Q.No. 20 The distal end of an endoscope is placed at a distance of 1 mm from the gastrointestinal wall. The refractive indices of the fiber core and cladding are 1.5 and 1.45, respectively.
The maximum field of view for the endoscope is_______degrees (rounded off to one decimal place).
Q.No. 21 Two inductors with the details given below are wound separately on two identical ring type ferromagnetic cores.The ratio L2/L, is
Q.No. 22 Two dyes X and Y having concentrations in the ratio 0.25 in identical cuvettes were subjected to absorption measurements in a spectrophotometer. The estimated ratio of their absorbance is 0.5. The ratio of their molar extinction coefficients is_________
Q.No. 23 Hydrolysis of one ATP molecule provides an energy of____kilo calories(correct up to one decimal place).
Q.No. 24 An 830 nm laser Doppler flow meter probe is oriented at an angle of 60° to the flow axis. If the average flow velocity is 3 cm/s, the magnitude of Doppler shift frequency (kHz) is ________(rounded off to one decimal place).
Q.No. 25 A 100 mA single current pulse from a pulse generator is used for artificial pacing of heart at the right ventricle. If the delivered energy does not exceed the fibrillation threshold of 300 uJ, the safe duration of the pulse that could be applied to the tissue mass having an impedance of 500ᘯ is________________us.
Q26 – Q55 carry two marks each.
Q.No.26 The resting potential of a mammalian nerve cell is – 80 mV. A certain drug administered to the body changes the intracellular K* concentration from 150 mmol/L to 55 mmol/L. The nearest value of cell membrane potential after the drug administration, assuming that the external equilibrium of K does not get changed during the event, is (Gas constant = 8.315 J/mol/K, core temperature = 37° C and Faraday constant = 96500 C/mol)
(A) -117 mV (B) -18.71 m V (C) -53.32 mV (D) -141.30 mV
Q.No. 27 The arrangement of four resistors of equal value in the diaphragm of a physiological pressure measurement catheter is shown below. The applied pressure is observed to cause an increase in length of resistors R2, R4 and an increase in cross sectional area in R1 and R3. The operation results in an equal change in the values of all four resistors. Which among the configurations given below should be used to connect the resistors to form a Wheatstone bridge so that bridge output voltage is proportional to the change in resistance of individual resistors’?
(A) I only (B) II only (C) Neither I nor II (D) Both I and II
Q.No. 28 For the given input voltage, Vin = 10 sin(2nt) to the functional circuit shown below, the output signal will be
Q.No. 29 During a non-invasive measurement of blood pressure, mean arterial pressure was observed to be 100 mm Hg. If systolic pressure is 150 mm Hg, the diastolic pressure would be
(A) 110 mm Hg (B) 75 mm Hg (C) 70 mm Hg (D) 50 mm Hg
Q.No.30 Two loads are connected to AC supply mains as depicted in the figure. One load draws 10 kW whereas the other load of 10 kVA is operated at 0.6 pf lagging. To achieve an overall power factor of 0.9544 lagging, the nearest kVAr rating of the capacitor bank needed to be connected across the supply mains is equal to
(A) 3 (B) 5 (C) 7 (D) 9
Q.No. 31 The nearest value of power dissipated in the 3 12 resistance in the circuit is
(A) 3W (B) 25/3 W (C) 12 W (D) 25/12 W
Q.No. 32 A second order low pass filter is being constructed by cascading two first order low pass filters with the following transfer functions
where w, and W2 are the respective 3dB cut off frequencies.
The undamped natural frequency wc of the resulting second order low pass filter is
Q.No. 33 Match the bridge type with the application given below:
(A) P-L, Q-K, R-N, S-M
(B) P-N, Q-K, R-L, S-M
(C)P-N, Q-L, R-M, S-K
(D) P-L, Q-M, R-N, S-K
Q.No. 34 For a non-unity feedback system with G(s) = 12/S+2, and H(s) = 2/S+3, the magnitude of steady-state error to a unit step-input is
(A) 0.50 (B) 0.45 (C) 0.25 (D) 0.20
Q.No. 35 Match the Boolean expression with its minimal realization
Q.No. 36 The glomerular filtration process of the kidney is modeled as a flat membrane with pores of radius 1 nm and length of pore 60 nm. The viscosity of the fluid is 0.002 Pa s. The aggregate area of the pores makeup 5% of the total surface area of the membrane. The average pressure on the blood side of the membrane is 8000 Pa and on the ultrafiltrate side is 6200 Pa. The total available area of the membrane is 1.5 m2. The nearest value of resulting filtration rate in cm/min is (A) 0.14 (B) 1.40 (C) 8.43 (D) 84.37
Q.No. 37 During resting state, the voltage outside the cell membrane compared to that inside the membrane is . Under such conditions, the intracellular and extracellular regions have and _concentrations, respectively.
(A) More positive, more Potassium [K+], more Sodium [Na+] (B) More negative, more Potassium [K+], more Sodium [Na+] (C) More negative, more Sodium [Na+], more Potassium [K+] (D) More positive, more Sodium [Na+], more Potassium [K+]
Q.No. 38 The tensile strength of a degradable suture used for a surgical procedure in the human body is observed to decrease exponentially from its original strength by 40% and 50% after 10 days and 20 days, respectively. The closest approximation of the time taken for the tensile strength to decay to 20% of its original value would be
(A) 35 days (B) 45 days (C) 60 days (D) 70 days
Q.No. 39 A 60 kg person is standing on one foot on a force plate. The ground reaction force is found to act 40 mm anterior to the ankle joint. The mass center of a foot is 60 mm from the Trochanter Knee Ankle (TKA) line. If the weight of the foot is 0.8 kg, the closest value of magnitude of moment acting on the ankle joint is
(A) 23 Nm (B) 48 Nm (C) 235 Nm (D) 466 Nm
Q.No. 40 The temperature of bone cement is increased from 37°C to 87°C during the femoral hip arthroplasty. The cement thickness is noted to be 20 mm. The stress developed due to exothermic reaction of bone cement during the polymerization process and shrinkage of the bone cement, respectively, are
Assume that
(i) bone, cement, and implant are modeled as a set of concentric cylinders
(ii) no direct adhesion takes place between bone and cement
(iii) temperature is uniform
Coefficient of thermal expansion of bone cement = 90 x 10-6/°C
Q.No. 41 A patient is initially imaged in a 1 Tesla MRI scanner and induced voltage is found to be equal to V). The expression for the magnitude of the received voltage in the RF coil is given below.
Vs: MR slice volume, Mo: Magnitude of resultant magnetic vector at equilibrium,
Yo: Larmor frequency, a: tip angle, BT: Magnetic field sensitivity of receive coil.
When the patient is shifted to a 3 Tesla MRI scanner that uses the same RF coil and the slice thickness is halved, the magnitude of the induced voltage was found to be equal to V2. The ratio V2/V1 is
(A) 1.5 (B) 3.0 (C) 4.5 (D) 6.0
Q.No. 42 A 3 MHz ultrasound transducer transmits a 3-cycle long pulse into a soft tissue at normal incidence to fat and liver interface. The axial resolution (mm) and the amplitude reflection coefficient at fat-liver interface, respectively, are
Q.No. 43 The forward biased current of a silicon (Si) diode is being calculated from the exponential model of the V-I characteristics. If the diode current Ip = 1 mA at a voltage drop Vo -0.7 V, the nearest value of Id when Vp -0.8 V is
Assume thermal voltage V1 = 25.3 m V for Si diode (A) 0.133 mA (B) 2 mA (C) 52 mA (D) 90 mA
Q.No.44 A continuous random variable x has a probability density function given by
where a is a real constant. The variance of x is __________(correct up to one decimal place).
Q.No. 45 The magnitude of the gradient of the function f(x,y) = x2 + y2 at the point (1,1) is_ (rounded off to two decimal places).
Q.No. 46 The value of following double integral is_________(correct up to three decimal places).
where R is the first quadrant of the circle with center at the origin and radius of one unit.
Q.No. 47 A gynaecologist recorded the blood pressure (BP) of patients as shown in the Table below. Using the Regression process, the diastolic BP of a 38 year old patient (mm Hg) is___________(rounded off to two decimal places).
Q.No. 48 A person in standing position first flexes the hip by 50° from the initial Trochanter knee ankle (TKA) line and then flexes knee by 20°. The distance of the ankle joint from the initial TKA line is (rounded off to the nearest integer).
(i) the distance between hip joint and knee joint is 400 mm
(ii) the distance between knee joint and ankle joint is 300 mm.
Q.No. 49 A chest radiograph of 36 cm x 48 cm is digitized. If we want to preserve details in the image to a spatial resolution of 6 cycles/mm, the approximate image data size in MB for an 8 bit quantization is__________(rounded off to two decimal places).
Q.No.50 An X-ray radiography scenario is shown in the figure. If the number of incident photons (Ni) is equal to 2 x 100 at 50 keV, the number of photons (Nd) that exit the tissue is ____________ X 106 (rounded off to two decimal places).
(use linear attenuation coefficient for soft tissue and blood at 50 keV as 0.4 cm! and 0.2 cm*’, respectively).
Q.No.51 The wavelength of an electron accelerated to a potential of 1V is (rounded off to two decimal places).
Mass of electron = 9.11×10-31 kg
Planck’s constant, h=6.63×10-34 Js
Charge of electron = 1.6 X10-19 C
Q.No. 52 In a permanent magnet moving coil (PMMC) instrument having following specifications, the angular deflection of the pointer for a coil current of 100 uA will be __________degrees (rounded off to one decimal place).
Magnetic flux density = 1.5 Tesla
Torsional spring constant = 2×10-6 Nm/deg
Cross sectional area of the coil = 2.5 cm?
Number of turns of the coil = 500
Q.No.53 Arterial blood extracted from a healthy adult showed an oxygen partial pressure value of 40 mm Hg. The total oxygen content in the arterial blood measured in %V/V is _______(rounded off to one decimal place).
Given: Solubility of oxygen in blood = 0.003 ml/mm Hg/dL
Hemoglobin oxygen saturation = 95%
Oxygen carrying capacity of Hb = 1.34 ml/g
Arterial blood hemoglobin concentration = 15g/dL
Q.No. 54 In the process of measuring blood flow from an artery using C-clamp magnetic flow probe, the voltage recorded across diametrically opposite sites of the artery is 3.75 nV. The blood flow rate through the artery is cm3/s (rounded off to two decimal places).
The inner diameter of the C-clamp = 0.5 cm,
The magnetic flux density = 1.5 x 10-5 Wb/mo.
Q.No. 55 A cell is injected with a current i(t) = u(t) to produce a change in the intracellular membrane voltage v (t). The cell-membrane is modeled as a linear system with impulse response h (t) = A e-t/t u(t). The cell membrane voltage output at 5 ms is________mV. Use A = -34 V/s; t = 3 ms.
COVID vaccine certificate to not carry PM Modi’s photo in 5 poll-bound states
Prime Minister Narendra Modi’s photo will not appear on the vaccine certificate in the five poll-bound states in compliance with the model code of conduct. The Health Ministry has applied filters to CoWIN software to ensure that it does not happen. The Assembly Polls will be held in seven phases in five states of Goa, Manipur, Punjab, Uttarakhand and Uttar Pradesh between February 10th and March 7, 2022. The result will be declared on March 10th.
Bharath Subramaniyam has become the 73rd Grandmaster of India, as per the All India Chess Federation on January 9, 2022. The 14-year-old teenager from Chennai completed his final GM Norm and crossed the requisite 2500 rating at Vergani Cup Open in Italy. He though finished seventh overall in the event by scoring 6.5 points from nine rounds. To get the Grandmaster title, a player has to secure three GM norms and cross the live rating of 2,500 Elo points.
Health Minister to chair COVID-19 review meet today
Union Health Minister Mansukh Mandaviya is scheduled to chair a virtual meeting today with the health ministers of five states and a union territory to review the COVID-19 situation in the states amid a sudden spike. PM Narendra Modi had also chaired a high-level review meeting to review the current COVID-19 pandemic situation in the country and the preparedness of the health infrastructure.
SC to hear plea seeking probe into the breach in PM Modi’s security in Punjab
The Supreme Court is expected to hear a plea today seeking a court-monitored probe into the breach in Prime Minister Narendra Modi’s security during his visit to Ferozepur, Punjab. A three-judge bench of the apex court is likely to take up the plea comprising Chief Justice NV Ramana and Justices Surya Kant and Hima Kohli.
Former RBI Governor Urjit Patel appointed as Vice-President of AIIB
The Former Governor of Reserve Bank of India Urjit Patel has been appointed as a Vice-President of the Asian Infrastructure Investment Bank. It is a Beijing-based multilateral development bank. Patel will succeed the outgoing Vice-President of AIIB DJ Pandian. He was in charge of sovereign and non-sovereign lending of the AIIB in South Asia, Southeast Asia, and the Pacific Islands. 58 years old Urjit Patil will join the new position on February 1, 2022, and will be one of the five Vice-Presidents of the AIIB with a tenure of three years. Patel had taken over as the Governor of Reserve Bank of India succeeding Raghuram Rajan in 2016 and had served the position till December 2018.
Noida ranked ‘Cleanest Medium City’ in India
Noida has bagged the Cleanest Medium City in Swachh Survekshan 2021. It is an annual survey of hygiene, cleanliness, and sanitation in India. The high rank achieved by Noida in Swachh Survekshan Survey 2021 is a miraculous victory as in the 2018 survey, the city was ranked at 324th. Noida has also achieved a 5-star garbage-free city rating which is a higher achievement from having received a 3-star garbage-free city rating in 2020.
INTERNATIONAL NEWS
Golden Globe Awards 2022 winners: ‘The Power of the Dog’ wins Best Picture Drama, Will Smith win Best Actor
The winners of the 79th Golden Globe awards were announced on January 9, 2022 by Hollywood Foreign Press Association in a private ceremony at Beverly Hilton. The event was not televised or live-streamed this year. The event did not also have the red carpet and no celebrity presenters and nominees were involved. Netflix’s ‘The Power of the Dog’ won Best Motion Picture -Drama, while ‘West Side Story’ won Best Motion Picture- Musical or Comedy. Will Smith won his first Golden Globe for Best Actor -Drama for his role of ‘Richard Williams’ in the 2021 movie ‘King Richard’ and Nicole Kidman won Best Actress-Drama for her role in ‘Being the Ricardos’.
Full House star Bob Saget passes away
Actor and comedian Bob Saget was found dead in his hotel room in Orlando, Florida on January 9, 2022. The 65-year-old had portrayed the popular character of Danny Tanner on the American TV show ‘Full House’. Saget, who is also a stand-up comedian was found unresponsive in his room while he was on a comedy tour.
Myanmar’s Aung San Suu Kyi sentenced to four more years in prison
Myanmar’s Court has sentenced ousted leader Aung San Suu Kyi to four years of imprisonment after finding her guilty of multiple charges. It includes the possession of illegally imported walkie-talkies and violation of COVID-19 restrictions. This is also the second round of verdicts against the former Myanmar State Counsellor.
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