Category: Coachings

GATE 2021 Ecology and Evolution 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.1The people               were at the demonstration were from all sections of society.
(A)whose
(B)which
(C)who
(D)whom

Q.2		A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like .


Q.3		For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

(A)
396

(B)
324

(C)
216

(D)
144

Q.4		Which one of the following numbers is exactly divisible by  (1113+1)?

(A)
1126+1

(B)
1133+1

(C)
1139+1

(D)
1152+1

Q.5		Oasis is to sand as island is to___________ Which one of the following options maintains a similar logical relation in the above sentence?
  (A)Stone
  (B)Land
  (C)Water
  (D)Mountain
  1. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Q.6		The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be counterproductive.Which one of the following statements is the CORRECT inference from the above passage?

(A)		Sleeping well alone is enough to prepare for an exam.  Studying has lesser benefit.
    (B)Students are efficient and are not wrong in thinking that sleep is a waste of time.
    (C)If a student is extremely well prepared for an exam, he needs little or no sleep.
  (D)To do well in an exam, adequate sleep must be part of the preparation.

Q.7

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm2 is:

(A)
12.50

(B)
6.25

(C)
3.125

(D)
1.5625

Q.8		Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01  for 0 ≤ X ≤ 100. The mean of X is ____________         

(A)
2.5

(B)
5.0

(C)
25.0

(D)
50.0

Q.9		 The number of students passing or failing in an exam for a particular subject are presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the exam in their second attempt.The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are                     .

A)
65 and 53

(B)
60 and 50

(C)
55 and 53

(D)
55 and 48

Q.10		Seven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to each other. R is parked to the immediate right of V. T is parked to the left of U.Based on the above statements, the only INCORRECT option given below is:

(A)
There are two cars parked in between Q and V.

(B)
Q and R are not parked together.

(C)
V is the only car parked in between S and R.

(D)
Car P is parked at the extreme end.

                              Ecology and Evolution (EY)

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

Q.1		Animal species can vary in whether dispersal is more likely among male offspring (male-biased), female offspring (female-biased), or similar between the sexes. Dispersal in birds and mammals is most commonly
(A)female-biased and male-biased, respectively.
(B)female-biased and similar between the sexes, respectively.
(C)male-biased and female-biased, respectively.
(D)similar between the sexes, and female-biased respectively.
Q.2Of the following, which one is the most direct measure of Darwinian fitness?
(A)Adult body size
(B)Lifetime reproductive success
(C)Lifespan
(D)Maximum sprint speed
Q.3The marginal value theorem in optimal foraging theory examines which one of the following foraging decisions?
(A)How long to stay in a patch of food
(B)How to allocate time to foraging versus reproduction
(C)How to minimise risk while foraging
(D)How to select between different food types within a patch
Q.4Which one of the following shows the highest degree of endemism?
(A)Birds of the Himalayas
(B)Mammals of central India
(C)Frogs of the Western Ghats
(D)Trees of the Gangetic basin
Q.5Which one of the following Mendelian disorders is influenced by diet?
(A)Cystic fibrosis
(B)Haemophilia
(C)Phenylketonuria
(D)Thalassemia
Q.6Which one of the following mammalian DNA regions exhibits the highest level of sequence variation?
(A)Homeobox transcription factor binding domain
(B)Hox genes
(C)Mitochondrial D-loop region
(D)Histone protein-encoding genes
Q.7Which one of the following makes a species most vulnerable to extinction?
(A)
Low density throughout a large geographic range and in several habitat types
(B)Locally common in a restricted geographic range and in several habitat types
(C)Low density throughout a large geographic range and in a specific habitat type
(D)Locally common in a restricted geographic range and in a specific habitat type
Q.8The frequency distributions of a trait in two populations, X and Y, are shown in the figure.
C:\Users\PC6~1\AppData\Local\Temp\ksohtml7596\wps105.pngWhich one of the following statements about the mean and standard deviation (SD) of the two populations is accurate?
(A)X has higher mean, and Y has higher SD.
(B)Y has higher mean, and X has higher SD.
(C)X has higher mean, and X has higher SD.
(D)Y has higher mean, and Y has higher SD.
Q.9Two sister species of bulbuls have non-overlapping distributions. One is distributed in India and the other in Sri Lanka. Which one of the following modes of speciation is the most parsimonious explanation for this pattern?
(A)Allopatric speciation
(B)Sympatric speciation
(C)Parapatric speciation
(D)Peripatric speciation
Q.10In an Arctic Ocean food chain, killer whales feed on sea otters, which feed on sea urchins, which in turn feed on kelp (a type of seaweed). An increase in the abundance of killer whales causes sea otter abundance to decline, leading to higher sea urchin densities, which in turn reduces the abundance of kelp. Which one of the following terms describes this phenomenon?
(A)Trophic cascade
(B)Prey switching
(C)Competitive exclusion
(D)Productivity-stability relationship
Q.11Listed below are hypotheses for the evolution of monogamy. Which one of these is NOT based on the concept of individual selection?
(A)Food provisioning by both parents is crucial for offspring survival.
(B)Biparental protection from predators is essential for offspring survival.
(C)Females are solitary and dispersed, therefore, males cannot effectively mate- guard more than one female at a time.
(D)Forming monogamous pairs allows individuals to regulate their reproductive output and ensure the survival of the species.

Q.12		Rising temperature due to global warming can stimulate decomposition of organic matter and release CO2 into the atmosphere. This is an example of

(A)
positive feedback.

(B)
negative feedback.

(C)
environmental heterogeneity.

(D)
environmental stochasticity.

Q.13		Ant-mimic spiders of the genus Myrmarachne are known for which one of the following evolutionary phenomena?

(A)
Aposematism

(B)
Aggressive mimicry

(C)
Batesian mimicry

(D)
Muellerian mimicry

Q.14		The probability of local extinction increases with body size when there is forest degradation, loss, and fragmentation. Consider the following hypotheses for the vulnerability of larger-bodied species:Larger-bodied species tend to have smaller population    sizes.Larger-bodied species require larger territories/home ranges.Larger-bodied species have higher absolute resource and energy requirements.Which one of the following options correctly lists all potential reasons for the vulnerability of larger-bodied species?

(A)
P and Q only

(B)
P only

(C)
P and R only

(D)
P, Q, and R

Q.15		Grazing by large mammalian herbivores can have a strong influence on ecosystem structure, and can cause ecosystems to transition between alternative states over decades. Which one of the following transitions can result from grazing?

(A)
Mangrove to coral reef

(B)
Terai grassland to alpine meadow

(C)
Savanna to grassland

(D)
Tropical rainforest to arid desert

Q.16		The effective population size of a sexually reproducing, diploid, animal species will be highest when the sex ratio (number of reproducing males / number of reproducing females) is

(A)
1

(B)
0.5

(C)
1.5

(D)
2

Q. 17 – Q. 22 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).


Q.17		The theory of evolution by natural selection was proposed by which one (or more) of the following?

(A)
Charles Darwin

(B)
Jean Baptiste Lamarck

(C)
Alfred Russel Wallace

(D)
Georges Cuvier
Q.18According to the MacArthur – Wilson equilibrium model of island biogeography, which one (or more) of the following factors affect(s) extinction rate on an island?
(A)Interspecific competition
(B)Island area
(C)Intraguild predation
(D)Species identity

Q.19		Which of the following is/are necessary condition(s) for natural selection to shape limb lengths in a population?

(A)
Individuals in a population vary in the length of their limbs.

(B)
Limb length increases in individuals with repeated use.

(C)
Offspring inherit the limb lengths of their parents.

(D)
Limb length influences running speed and thus, their ability to survive and reproduce.

Q.20		Which of the following is/are possible reason(s) for linkage disequilibrium between alleles at two loci?

(A)
Low recombination rate between loci

(B)
High recombination rate between loci

(C)
Natural selection

(D)
Polyploidy
Q.21Metabolism includes the processes of catabolism and anabolism. Select the anabolic process(es).
(A)Growth
(B)Storage
(C)Respiration
(D)Excretion

Q.22		SARS-CoV-2 is hypothesised to have jumped from bats to pangolins before infecting humans. Which one (or more) of the following methods can be effectively used for testing this hypothesis?

(A)
Comparative genomics

(B)
DNA fingerprinting

(C)
Phylogenetics

(D)
Transgenesis

Q. 23 – Q. 25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).


Q.23		A sample of heights of trees follows a normal distribution. In this sample, 68% of height measurements are expected to fall in the interval:mean ±          standard deviation. (Round off to the nearest integer.)

Q.24		A bird species has an annual survival probability of 0.30. While sampling the population of this species, the probability that any individual is captured in a given year is 0.40. A bird is captured, tagged and released in Year one. The probability that it is re-captured in Year two is     _________. (Round off to two decimal places.)

Q.25		Sex ratio at birth is biased towards females in a mongoose population. If the probability of having a daughter is 0.7 in this population, and if sex determination of each offspring is an independent event, then the probability that a female with a litter of four offspring has at least one son is____ . (Round off to two decimal places.)

Q.26 – Q.46 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).


Q.26		In a species of gecko, males are polymorphic such that some males are yellow and other males are white. A student hypothesises that body colour is a signal of aggression. To test this, he measures aggression in yellow and white males. He also measures body size in every individual he tests. He plots the data in the following way (yellow males: solid line and filled dots; white males: dashed line and open dots). Which one of the following statements is correct based on these data?                

(A)
All yellow males are more aggressive than white males.

(B)
Body size is correlated with aggression in all males.

(C)
Body size correlates with aggression in yellow males only.

(D)
Small yellow males are more aggressive than small white males.

Q.27		Homing pigeons can perceive the pattern of polarized light in the sky (which depends on the position of the sun relative to the earth). This enables homing pigeons to orient and navigate home if released in any location. One can reset their biological clock in captivity by artificially controlling the light conditions. If you acclimatize a pigeon to a new lighting cycle with “sunrise” at 6 PM and “sunset” at 6 AM, instead of 6 AM sunrise and 6 PM sunset that naturally occurs, the bird will be clock- shifted by 12 hours within a few days. Suppose you release two birds, a normal bird (N) and a 12-hr clock-adjusted bird (C), 30 km East of their home at 6 AM. In which direction will each bird fly?

(A)
Both birds will fly West.

(B)
Both birds will fly East.

(C)
Bird N will fly West, bird C will fly East.

(D)
Bird C will fly West, bird N will fly East.

Q.28		Demographic stochasticity introduces random variation in population growth because

(A)
changing weather conditions from year-to-year can result in good and bad years for reproduction.

(B)
the discrete nature of births and deaths introduces uncertainty in population parameters.

(C)
per capita birth rate in a population decreases with an increase in population density.

(D)
of predictable time lags between change in population size and reproduction.

Q.29		In an island chain, species richness (S) increases with island area (A) according to the equation, S=4.3A0.55.Which one of the following graphs best represents this equation?         

(A)
(i)

(B)
(ii)

(C)
(iii)

(D)
(iv)

Q.30		A researcher measures the abundance of a tree species in 10 plots in each of two habitats. She tests for differences in abundance between the two habitats using an ANOVA. The results from the ANOVA are as follows:Mean abundance in habitat A = 30 treesMean abundance in habitat B = 50 treesF-statistic (on 1 and 18 degrees of freedom) = 6.04P-value = 0.02Here, a P-value of 0.02 means that

(A)		repeating this study 100 times will provide a result of “no difference” in abundance between the two habitats with a probability of 0.02.
(B)there is a 2% chance that abundances differ between habitats.
  (C)the probability that an F-statistic with a value of 6.04 or greater falls within the F-distribution for 1 and 18 degrees of freedom is 0.02.

(D)		there is a very large difference in the abundance of the species between the two habitats because the P-value is less than 0.05.

Q.31		In the graph shown, the solid line represents the best fit from an ordinary least-squares regression, where X is the predictor variable and Y is the response variable. In this case, which one of the following assumptions of the linear regression is violated?        

(A)
Equal variances in Y across values of X

(B)
Normal distribution of residuals

(C)
Independence of data points

(D)
Linear relationship between X and Y

Q.32		Consider the following list of bacteria and the infections they cause in humans.Which one of the following combinations correctly matches these micro-organisms and the infections they cause in humans?
(A)P-2; Q-1; R-4; S-3
(B)P-2; Q-3; R-1; S-4
(C)P-3; Q-4; R-1; S-2
(D)P-3; Q-4; R-2; S-1
Q.33Which one of the following statements is INCORRECT with respect to the tree of life?

(A)
Ctenophora is more closely related to Cnidaria than it is to Echinodermata.

(B)
Porifera is more closely related to Ctenophora than it is to Echinodermata.

(C)
Arthropoda is more closely related to Tardigrada than it is to Annelida.

(D)
Arthropoda is more closely related to Mollusca than it is to Nematoda.

Q.34		Consider a population that shows logistic growth of the form C:\Users\PC6~1\AppData\Local\Temp\ksohtml7596\wps110.jpg where C:\Users\PC6~1\AppData\Local\Temp\ksohtml7596\wps111.jpg is the population growth rate, r is the instantaneous rate of increase, K is the carrying capacity and N is the population size.
For such a population (N > 0), which one of the following graphs shows the
correct relationship between per capita growth rate on the y-axis, and population size (N) on the x-axis?                        

(A)
(i)

(B)
(ii)

(C)
(iii)

(D)
(iv)

Q.35		Which one of the following represents the correct chronological order of geological periods (from oldest to most recent)?
(A)Devonian  Jurassic  Cambrian  Neogene
(B)Devonian  Cambrian  Neogene  Jurassic
(C)Cambrian  Devonian  Jurassic  Neogene
(D)Cambrian  Neogene  Devonian  Jurassic

Q.36		Soils undergo weathering over large time-scales (millions of years). Over time, concentration of phosphorus (P) declines monotonically (solid line), while nitrogen (N) shows a unimodal pattern (dotted line) as shown.
C:\Users\PC6~1\AppData\Local\Temp\ksohtml7596\wps114.pngBased on this pattern, which one of the following diagrams represents the likely trend in N:P ratio? 
(A)(i)
(B)(ii)
(C)(iii)
(D)(iv)

Q.37		A large forest area is fragmented into multiple smaller patches of different sizes. A researcher estimates the number of bird species in these forest fragments immediately following fragmentation, and then again 20 years later. The relationship between fragment size and species richness is shown in the graph for the two sampling events (immediately after fragmentation: closed circles and solid line; 20 years after fragmentation: open circles and dashed line). The best explanation for the differences in species richness with fragment size between the two sampling events is   

(A)
Allen’s rule.

(B)
K-selection.

(C)
extinction debt.

(D)
Bergmann’s rule.

Q.38		The table shows a list of analysis goals (i, ii, iii) and different statistical tests (P, Q, R).       Match the analysis goal to the most appropriate statistical test.

(A)
(i)-(P), (ii)-(R), (iii)-(Q)

(B)
(i)-(Q), (ii)-(P), (iii)-(R)

(C)
(i)-(Q), (ii)-(R), (iii)-(P)

(D)
(i)-(R), (ii)-(Q), (iii)-(P)

Q.39		Shifting cultivation is a form of agricultural practice in the hills of Northeast India, where a forest patch is cleared and cultivated for a few years, after which it is left fallow and allowed to regenerate. Succession occurs on such previously cultivated plots. Over time, the plant community should move towards which region in the graph?           

(A)
P

(B)
Q

(C)
R

(D)
S

Q.40		Consider 1000 terrestrial species that have geographical ranges of different shapes and sizes. If the Earth were entirely covered by land (no oceans), and the ranges of these species were overlaid on the surface of the Earth at random, which one of the following patterns is expected?
(A)Highest species richness per unit area in the tropics
(B)Highest species richness per unit area at higher latitudes
(C)Roughly equal species richness per unit area at all latitudes
(D)Geographically restricted species found only near the poles
Q.41The graph below shows how the lower limits of the elevational ranges of bird species on a tropical mountain have changed over 20 years (2000 to 2020) because of climate change. Each point below represents a bird species. Points would cluster on the dashed line if species had the same lower elevational range limits in 2000 and 2020. Given that the mountain summit is at an elevation of 3500 m (solid horizontal line), and assuming that the trend shown by the graph continues over the next 20 years, what would you expect in 2040?    
(A)Low-elevation species will become locally extinct.
(B)Mid-elevation species will become locally extinct.
(C)High-elevation species will become locally extinct.
(D)All species will return to their original elevational ranges.

Q.42		Behavioural ecologists exploring a newly discovered island find 20 new species of terrestrial lizards. Males of these species have a dorsal ridge that varies in size from large in some species to entirely lacking in others. The scientists hypothesise that dorsal ridges in males evolved by runaway sexual selection stemming from sensory bias in females. Which one of the following would provide the necessary evidence to support this hypothesis?

(A)
Females of species in which males lack this trait are attracted to males that have a large dorsal ridge artificially attached to them.

(B)
Males without a ridge are more likely to attract females of all species than males with a ridge.

(C)
Males with a larger dorsal ridge win more fights and get more mates than males with a smaller ridge.

(D)
Females of species whose males have a dorsal ridge do not show a preference for this trait.
Q.43The graph shows the relationship between a variable on the x-axis and genetic diversity on the y-axis. Each point represents a species and the trend line describes the relationship across species.
C:\Users\PC6~1\AppData\Local\Temp\ksohtml7596\wps120.pngSelect the most appropriate variable for the x-axis.
(A)Evolutionary age of species
(B)Abundance
(C)Body size
(D)Geographic range

Q.44		Hunting is a major source of mortality for large frugivorous birds. These birds disperse the seeds of forest trees and are the primary contributors to forest regeneration. The graphs show the distribution of different age- classes of a frugivore-dispersed tree species at two isolated sites.
C:\Users\PC6~1\AppData\Local\Temp\ksohtml7596\wps121.pngBased on the graphs, select the most likely conclusion.

(A)
Hunting is higher at site (i) than at site (ii).

(B)
Hunting is higher at site (ii) than at site (i).

(C)
Hunting is similar at both sites.

(D)
Frugivores are not hunted at either site.

Q.45		The following phylogeny shows how species P to T are related to each other. The branch lengths indicate the degree of evolutionary change.
C:\Users\PC6~1\AppData\Local\Temp\ksohtml7596\wps122.jpgThe species composition of three areas is given below   Area 1: PQR; Area 2: RST; Area 3: QRSGiven this information, the phylogenetic diversity of

(A)
Area 1 > Area 3 > Area 2

(B)
Area 1 = Area 2 = Area 3

(C)
Area 1 = Area 3 > Area 2

(D)
Area 1 < Area 3 < Area 2

Q.46		The IUCN Red List provides information on the conservation status of different species. Match the species to their status in the table below.

Species
Status

Tiger
Near threatened (NT)

Great Indian Bustard
Extinct (EX)

Passenger Pigeon
Critically endangered (CR)

Blackbuck
Endangered (EN)

(A)
Tiger: NT; Great Indian Bustard: EX; Passenger Pigeon: EN; Blackbuck: CR

(B)
Tiger: EN; Great Indian Bustard: CR; Passenger Pigeon: EX; Blackbuck: NT

(C)
Tiger: EN; Great Indian Bustard: CR; Passenger Pigeon: NT; Blackbuck: EX

(D)
Tiger: NT; Great Indian Bustard: EN; Passenger Pigeon: EX; Blackbuck: CR

Q.47 – Q.52 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).


Q.47		A gene duplication event in an organism results in two copies of a gene. Which one (or more) of the following outcomes is/are possible for the duplicated copy?

(A)
It retains the original function.

(B)
It acquires a new function.

(C)
It loses function.

(D)
It gets translated but not transcribed.

Q.48		The egg-laying mammal, platypus, is known for its ability to inject venom by stabbing with spurs on its hindlimbs. Which one (or more) of the following statements supports the hypothesis that venom in this species is used for intrasexual competition?

(A)
Only males produce venom.

(B)
Venom is secreted only during the breeding season.

(C)
Venom is only effective against invertebrates.

(D)
Venom is ineffective against conspecifics.

Q.49		All octopi dream every night, and sometimes change colour while dreaming. A student hypothesises that octopi change colour only when they dream about the food they ate that day. To test this hypothesis, the student conducts an experiment with two treatments that are randomly ordered, and separated by 2 days. In one treatment, she places 10 octopi in individual tanks in captivity and provides each one with a large crab to eat during the day. She then records the dream state colour of these octopi that night. Which one (or more) of the following would be an appropriate NEGATIVE control to test this hypothesis?

(A)
Provide the same 10 octopi with the same food source (crab), and then record their colour that night when they are dreaming.

(B)
Provide the same 10 octopi with a new food object (e.g. sea stars) and record the colour that night when they are dreaming.

(C)
Provide the same 10 octopi with a non-food object (e.g. rock), and record their colour that night when they are dreaming.

(D)
Provide 10 squid with the same food source (crab) and record the colour that night when they are dreaming.

Q.50		Which one (or more) of the following conservation actions would NOT benefit native species?

(A)
Planting Prosopis juliflora in the Thar desert to reduce erosion.

(B)
Stringing rope ladders across roads to connect the canopy for facilitating the movement of arboreal animals in the Western Ghats.

(C)
Increasing lights at night on beaches in Odisha to improve visibility for hatching sea turtles.

(D)
Growing native species in urban gardens of Bengaluru to attract pollinators.

Q.51		In cooperatively breeding animals, offspring from one year stay back and help their parents to rear offspring born in successive breeding episodes. Kin selection has been used to explain such helping behaviour. Which of the following result(s) support(s) the kin selection hypothesis?

(A)
Helpers provide more care in populations where extra-pair paternity is low, than in populations where extra-pair paternity is high.

(B)
Individuals who choose to stay and help are more likely to inherit their parents’ territory than individuals who stay but do not help.

(C)
Individuals who choose to disperse from their natal territory rather than stay and help have a lower survival because of predation during dispersal, when compared with individuals who stay and help.

(D)
Helpers whose parents continue to form the breeding pair provide more care than helpers whose parents are replaced by a new breeding pair.

Q.52		Which one (or more) of the following genetic processes is/are likely to be affected by the disruption of codon usage bias in highly expressed genes?

(A)
Translation rate

(B)
Translation accuracy

(C)
Transcription rate

(D)
Transcription accuracy

Q. 53 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).


Q.53		Male beetles are of two phenotypes: horned and hornless. Horned males mate with twice as many females compared with hornless males. But females mated to hornless males produce one-third more offspring. The reproductive success of a male (number of offspring fathered) is the number of females he mates with multiplied by the number of offspring each female produces. The reproductive success of horned males is_______times that of hornless males. (Round off to one decimal place.)

Q.54		A population shows exponential growth of the form C:\Users\PC6~1\AppData\Local\Temp\ksohtml7596\wps124.jpg where Nt is the population at time t, N0 is the initial population size and r is the rate of increase. If r = 0.1, then the doubling time for this population is _______. (Round off to two decimal places.)

Q.55		At a locus with two alleles A1 and A2, the genotype A1A1 produces white flowers, A2A2 produces red flowers, and A1A2 produces pink flowers. For a population in Hardy-Weinberg equilibrium, the frequency of red flowers is 0.25. If the white flowered plants are removed, and all pink and red flowered-plants in this population are randomly crossed amongst each other, the frequency of white flowered plants in the next generation will be______. (Round off to two decimal places.)

Answer Key

Q.No.AnsQ.No.AnsQ.No.AnsQ.No.AnsQ.No.AnsQ.No.AnsQ.No.Ans
1C 1A 11D 21A; B 31A 41C 51A; D 
2C 2B 12A 22A; C 32C 42A 52A; B 
3D 3A 13B 230.99 to 1.01 33D 43C 531.40 to 1.60 
4D 4C 14D 240.11 to 0.13 34A 44B 546.80 to 7.00 
5C 5C 15C 250.74 to 0.77 35C 45A 550.10 to 0.12 
6D 6C 16A 26C 36A 46B 
7C 7D 17A; C 27C 37C 47A; B; C 
8D 8D 18B 28B 38C 48A; B 
9D 9A 19A; C; D 29B 39B 49C 
10A 10A 20A; C 30C 40C 50A; C 

GATE 2021 Environmental Science and Engineering Previous Year Paper

GATE 2021 Environmental Science and Engineering Previous Year Paper

General Aptitude (GA) 

Q.1 The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?
(A) 9,92,500
(B) 9,95,006
(C) 10,00,000
(D) 12,51,506
Q.2 p and q are positive integers and
(A) 3
(B) 7
(C) 9
(D) 11
Q.3

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is________ 
(A) 4
(B) 3
(C) 6
(D) 7
Q.4 Nostalgia is to anticipation as_______is to________  Which one of the following options maintains a similar logical relation in the above sentence?
(A) Present, past
(B) Future, past
(C) Past, future
(D) Future, present
Q.5 Consider the following sentences:I woke up from sleep.I woked up from sleep.I was woken up from sleep.I was wokened up from sleep.Which of the above sentences are grammatically CORRECT?
(A) (i) and (ii)
(B) (i) and (iii)
(C) (ii) and (iii)
(D) (i) and (iv)
Q.6 Given below are two statements and two conclusions. Statement 1: All purple are green.Statement 2: All black are green. Conclusion I: Some black are purple. Conclusion II: No black is purple.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) Both conclusion I and II are correct.
Q.7 Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.Which of the following can be deduced from the above passage?Nowadays, computers are present in almost all places.Computers cannot be used for solving problems in engineering.For humans, there are both positive and negative effects of using computers.Artificial intelligence can be done without data.
(A) (ii) and (iii)
(B) (ii) and (iv)
(C) (i), (iii) and (iv)
(D) (i) and (iii)
Q.8 Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________ 
(A) π / 3
(B) 2π/3
(C) 3π/2
(D) 3π
Q.9

 

The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is
(A) 4
(B) 5
(C) 6
(D) 7
Q.10


Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is
(A) 2 : 3
(B) 3 : 4
(C) 4 : 5
(D) 5 : 6

Environmental Science and Engineering (ES)

Q.1 – Q.18 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

 
Q.1 A tangent is drawn on the curve of the function 𝒚 = 𝒙𝟐 at the point (𝒙, 𝒚) = (𝟑, 𝟗). The slope of the tangent is______.               
(A) 3
(B) 6
(C) 9
(D) 12
 
Q.2
(A) 0
(B) 1
(C) 2
(D) −1
Q.3 The table below shows the carbon content of four samples of powdered coal. If these four samples are mixed completely, what would be the resultant carbon percentage of the mixture by weight? 
(A) 58 %
(B) 86 %
(C) 87 %
(D) 90 %
Q.4 A sample of air is collected in the morning at an ambient temperature of 25 °C. The concentration of carbon monoxide (CO) in this sample is 30 ppmv (ppm by volume). The same sample is analysed later in the afternoon when the sample temperature is 35 °C. The analysis results will show the CO concentration as____ .
(A) < 29 ppmv
(B) > 30 ppmv
(C) = 30 ppmv
(D) = 29 ppmv
Q.5 In fluid statics, the line of action of the buoyant force always acts through the____________________.                                           
(A) centre of gravity of any submerged body
(B) centroid of the volume of any floating body
(C) centroid of the displaced volume of fluid by the body
(D) centroid of the volume of fluid vertically above the body
 
Q.6 What is the order of preference of the various elements in integrated waste management hierarchy (highest preference to lowest preference)?
(A) Reduce > Reuse & recycle > Energy recovery > Landfilling
(B) Reuse & recycle > Reduce > Energy recovery > Landfilling
(C) Reduce > Energy recovery > Reuse & recycle > Landfilling
(D) Reduce > Reuse & recycle > Landfilling > Energy recovery
 
Q.7 If d is the depth of an aquifer through which water is flowing, then the relationship between permeability K and transmissibility (also known as transmissivity) T is given by _________.
(A) 𝑇 = 𝐾𝑑
(B) 𝑇 = 𝐾/𝑑
(C) 𝑇 = √𝐾𝑑
(D) 𝐾 = √𝑇𝑑
 
Q.9 Which of the following causes ‘Type-I’ settling in a sedimentation tank?
(A) Agglomeration
(B) Compression
(C) Force of gravity
(D) Charge neutralization
 
Q.10 In the context of noise pollution, SPL is the sound pressure level in decibels (dB). The relationship between SPL, the root mean square (rms) sound pressure p, and the reference (hearing threshold) pressure p0 is expressed as_____________.
(A) SPL = 20 × log10
(B) SPL = 20 × log10
(C) SPL = 20 − log10
(D) SPL = 20 + log10
Q.11

The following block diagram highlights the typical phases of the life cycle of a product. In the figure, ‘P’, ‘Q’, and ‘R’ represent various possible scopes of analyses in life cycle assessment. Which of the following statements is true?
(A) ‘R’ represents cradle-to-grave analysis.
(B) ‘P’ represents cradle-to-gate analysis.
(C) ‘Q’ represents gate-to-grave analysis.
(D) ‘R’ represents gate-to-gate analysis.
 
Q.12 The United Nations Conference on Environment and Development was held in 1992 in Rio de Janeiro, Brazil. During this conference, several environmental management principles were adopted by many countries.Which one of the following principles allows the governments to take mitigation measures on the environmental issues having serious threats or irreversible damage, even if there is scientific uncertainty about such issues?
(A) Polluters pay principle
(B) Precautionary principle
(C) Extended producer responsibility
(D) Common but differentiated responsibilities
Q.13 Choose the correct order of biodegradability (highest to lowest) of the following municipal solid waste components.
(A) Food waste > Newspaper > Polyvinyl Chloride (PVC)
(B) Newspaper > Food waste > Polyvinyl Chloride (PVC)
(C) Food waste > Polyvinyl Chloride (PVC) > Newspaper
(D) Polyvinyl Chloride (PVC) > Food waste > Newspaper
 
Q.14 In proximate analysis, when a 10 kg moisture-free solid sample is heated in a furnace at 950 °C in the absence of air, its mass is reduced by 6 kg. If the same 10 kg moisture-free solid sample is heated in the furnace at the same temperature in the presence of air, its mass is reduced by 7 kg. The percentage of fixed carbon in the sample is__________.
(A) 20 %
(B) 60 %
(C) 10 %
(D) 30 %
 
Q.15 Chlorine is most effective as a water disinfectant at a pH of___________.
(A) 6
(B) 8
(C) 10
(D) 12
Q.16 The oxidation states of ‘𝐍’ in 𝐍𝐇𝟒+, 𝐍𝐎𝟐−, and 𝐍𝐎 are ________,respectively.
(A) +2, −3, and +3
(B) −3, +3, and +2
(C) −3, +3, and −4
(D) +4, −2, and +2
 
Q.17 What is the pH of a water sample having H+ concentration of 10 mg/L? The atomic weight of H is 1 g/mol.
(A) 2
(B) 4
(C) 6
(D) 8
 
Q.18 Which of the following pairing of nucleotide bases is present in double helix DNA?
(A) Thymine – Cytosine
(B) Adenine – Thymine
(C) Cytosine – Adenine
(D) Uracil – Thymine

Q.19 – Q.22 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

Q.19 Which of the following is/are both greenhouse gas(es) and ozone depleting substance(s)?
(A) CFC-11
(B) CO2
(C) HCFC-22
(D) N2O
 
Q.20 The ordinary differential equation . has y as the dependent variable and x as the independent variable. Which of the following classification(s) is/are applicable to the equation?
(A) Linear
(B) Non-linear
(C) First order
(D) Second order
 
Q.21 Consider the following equation:𝒙𝟑 − 𝟏𝟎𝒙𝟐 + 𝟑𝟏𝒙 − 𝟑𝟎 = 𝟎Which of the following is/are the root(s) of the above equation?
(A) 1
(B) 2
(C) 3
(D) 4
Q.22 A wind rose is a representation of meteorological conditions. Which of the following is/are included in this representation?
(A) Mixing height
(B) Wind speed
(C) Wind direction
(D) Percentage of time

Q.23 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

Q.23 A flocculation tank used for water treatment has a velocity gradient (G) of 800 s-1. The volume of the tank is 40 m3. The dynamic viscosity of water is 9×10-4 N·s/m2. The theoretical power required to maintain the given velocity gradient is _________kW (rounded off to the nearest integer).
   
Q.24 In a sample, the growth of microbial cells started with an initial concentration of 5×104 cells per millilitre (mL) of the sample. After a certain time period, the cell concentration was found to be 1280×104 cells per mL of the sample. Assuming binary fission of cells and no cell death, the number of generations of cell growth occurred in this time period is_____________(answer in integer).
   
Q.25 A water jet discharging from a 4 cm diameter orifice has a diameter of 3.5 cm at its vena contracta. The coefficient of velocity is defined as the ratio of the actual velocity of the jet at vena contracta to the theoretical velocity of the jet. If the coefficient of velocity is 0.98, the coefficient of discharge for the orifice will be_________ (rounded off to two decimal places).

Q.26 The 2×2 matrices P and Q satisfy the following relations:The matrix Q is equal to____________.

(A)

(B)

(C)

(D)

 

Q.27 A biased die has six faces numbered as k = 1, 2, 3, 4, 5, and 6. On rolling the die, the probability of the number k appearing is proportional to k2. What is the probability that an even number will appear on rolling the die?

(A) 35/91

(B) 56/91

(C) 12/21

(D) 9/21

Q.28

Match the entries in Column I with the correct entries in Column II.

 
(A) P-(iii), Q-(ii), R-(i)
(B) P-(ii), Q-(i), R-(iii)
(C) P-(i), Q-(iii), R-(ii)
(D) P-(ii), Q-(iii), R-(i)
Q.29

Which of the following international multilateral agreements (conventions, protocols) from Column I match with the entries in Column II?

  
(A) P-(iv), Q-(iii), R-(ii), S-(i)
(B) P-(iv), Q-(ii), R-(iii), S-(i)
(C) P-(iii), Q-(i), R-(ii), S-(iv)
(D) P-(i), Q-(iii), R-(iv), S-(ii)
Q.30 An ideal PFR or an ideal CFSTR may be used to degrade a pollutant with first order reaction kinetics. Both the reactors are fed with the same inlet concentration and the same volumetric flow rate, and are designed to achieve the same outlet concentration.Which of the following statements is true when comparing PFR with CFSTR?PFR is Plug Flow Reactor.CFSTR is Continuous Flow Stirred Tank Reactor (also referred to as CSTR).
(A) PFR will always require less reactor volume than CFSTR.
(B) PFR will require the same reactor volume as CFSTR.
(C) CFSTR will always require less reactor volume than PFR.
(D) CFSTR can sometimes require less reactor volume than PFR.
 
Q.31 A 200 mL sample of water has an initial pH = 9. In order to determine alkalinity, the sample was titrated using 0.02 N H2SO4 acid to an end point of pH = 4.5. In the titration, 25 mL of 0.02 N H2SO4 acid was required. What is the total alkalinity of the sample in ‘mg/L as NaHCO3’?[Atomic weight (g/mol): Ca = 40, Na = 23, H = 1, C = 12, S = 32, and O = 16]
(A) 20
(B) 125
(C) 210
(D) 305
Q.32 A sewage treatment plant (STP) receives sewage at a flow rate of 20000 m3 per day. The sewage has 200 mg/L of suspended solids. Assume 60 % suspended solids are removed in the primary clarifier. The underflow (i.e. sludge) removed from the clarifier contains 5 % solids (by weight).The daily volume of the sludge generated will be ______m3 per day.Assume sludge density = 1000 kg/m3.
(A) 48
(B) 80
(C) 480
(D) 800
Q.33 In context of municipal solid waste treatment, match the equipment in List I with their function in List II. 
(A) P-(iii), Q-(iv), R-(i), S-(ii)
(B) P-(iii), Q-(ii), R-(iv), S-(i)
(C) P-(i), Q-(iv), R-(iii), S-(ii)
(D) P-(iv), Q-(ii), R-(i), S-(iii)
Q.34 The characteristics of a water sample are as follows: Na+ = 92 mg/L, K+ = 19.5 mg/L, Ca2+ = 40 mg/L, and Mg2+ = 24 mg/L. What is the sodium adsorption ratio (SAR) of the water sample which may be considered for irrigation purposes?[Atomic weight (g/mol): Na = 23, K = 39, Ca = 40, and Mg = 24]
(A) 2.83
(B) 1.94
(C) 2.00
(D) 4.00

Q.35 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

Q.35 Which of the following is true for the nitrifying bacteria belonging to genus Nitrobacter?
(A) They are autotrophs.
(B) They are eukaryotes.
(C) They convert chemical energy to cellular energy using mitochondria.
(D) They convert NO3− to NO2−.
Q.36 Which of the following is/are the dominant mechanism(s) for the removal of spherical particles with diameter less than 10 µm from a gas stream using a fabric filter?
(A) Impaction
(B) Gravitation
(C) Interception
(D) Diffusion
 
Q.37 In air pollution, which of the following is/are classified as primary pollutants?
(A) Carbon monoxide (CO)
(B) Sulphur dioxide (SO2)
(C) Ozone (O3)
(D) Nitrogen dioxide (NO2)
Q.38 Which of the following is/are correct for the process of glycolysis?
(A) There is net decrease in standard Gibbs free energy.
(B) The end product is glyceraldehyde 3-phosphate.
(C) First phase includes the phosphorylation of the glucose molecule.
(D) It results in the net gain of NADH.
 
Q.39 In the context of water quality, which of the following is/are correct for the most probable number (MPN) of a water sample?
(A) The estimated organisms are gram negative.
(B) It is based on the assumption of Poisson distribution.
(C) It measures the exact number of microorganisms present in the sample.
(D) It includes the quantification of pathogenic virus.
 
Q.40 For any particular location, which of the following would influence the solar radiation incident on a rooftop solar water heater?
(A) Heater surface temperature
(B) Day of the year
(C) Hot water temperature
(D) Sky clearness

Q.41 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

 
Q.41 If 𝒇(𝒙) + 𝟑𝒇(𝒈(𝒙)) = 𝒙 − 𝟐,where 𝒈(𝒙)= then the value of the ratiois_____________(answer in integer).
   
Q.42 Consider a function 𝒚 = 𝒇(𝒙) which satisfies the following equation: As 𝒙 → −∞, 𝒚 = 𝟏, and at 𝒙 = 𝟎, 𝒚 = 𝟐.The value of at 𝒙 = 𝟎 is_______ (answer in integer).
   
Q.43 The concentration of NO2 in the air at NTP is reported as 0.30 ppmv (ppm by volume). The concentration of NO2 in µg/m3 is____________(rounded off to the nearest integer).[At NTP, temperature = 298 K, pressure = 1 atm, and one mole of ideal gas occupies 24.45 L][Molecular weight of NO2 = 46 g/mol]
Q.44 In open channel flow, the specific energy is the total energy per unit weight of a liquid, where the component potential energy is measured from the bed of the channel as the datum.A rectangular channel of 10 m width carries 20 m3/s of water. The depth of flowing water is 1 m. The specific energy for this flow condition is_________m (rounded off to one decimal place).Consider acceleration due to gravity (g) = 10 m/s2.
Q.45 Two reservoirs are connected by a pipeline consisting of two pipes ‘A’ and ‘B’ in series. The two pipes are of same length and have the same Darcy friction factor. If the internal diameter of pipe ‘B’ is twice as large as the internal diameter of pipe ‘A’, the ratio of the head loss in pipe ‘A’ to that in pipe ‘B’ is__________(answer in integer). Neglect all minor losses.
   
Q.46 In a field test of a geological formation of permeable soil (porosity = 20 %), the hydraulic gradient was found to be 2 %. The actual seepage velocity of the flow was found to be 0.0025 m/s. Assume that the flow is in the laminar regime. The permeability (K) of the aquifer is_____m/s (rounded off to three decimal places).
   
Q.47 An underground hazardous waste storage tank is leaking. The contaminant concentration directly beneath the site is 0.5 mg/L. The contaminant is travelling at an effective rate of 0.4 m per day towards a water well which is 2 km away.Assume that the degradation of the contaminant follows a first order reaction, and the initial concentration of the contaminant becomes half in 10 years.In this case, the contaminant concentration expected at the well under steady state conditions is__________mg/L (rounded off to two decimal places).
   
Q.48 The net profit expected from a manufacturing unit is ₹ 6000 per year. The operational life of the unit is 15 years. Assuming a fixed discount rate of 8 % per annum, the net present worth of the profit earned over the operational life is ₹_____________(answer in integer).
   
Q.49 A 900 mm internal diameter sewer is laid at a slope of 0.004 and has an actual flow of 0.15 m3/s. Assuming Manning’s roughness coefficient to be 0.013, the ratio of the actual flow to the flow when the sewer is running full is___________(rounded off to two decimal places).Take π = 3.14.
   
Q.50 A 10 million litres per day (MLD) sewage treatment plant (STP) is based on the Activated Sludge Process (ASP). First, the sewage undergoes primary treatment and the resulting treated sewage has BOD5 of 140 mg/L concentration. This is further passed through a 1500 m3 capacity aeration tank (in ASP), where the mixed liquor volatile suspended solids (MLVSS) concentration is maintained at 3000 mg/L. The concentration of BOD5 of the treated sewage is5 mg/L.The Food to Microorganisms ratio (F/M) of the ASP is ________day-1 (rounded off to two decimal places).
Q.51 The municipal solid waste (MSW) generated in a community (population = 100000) is disposed on a 12×104 m2 landfill site, which can be filled to a total depth of 25 m (including soil cover). Assume that MSW is generated at a rate of 2.5 kg per person per day and its compacted density is 800 kg/m3. If the volumetric ratio of MSW and soil cover is 5:1, the useful life of the landfill site is_________years (rounded off to the nearest integer).
   
Q.52 A mechanized stationary container system is proposed for waste collection from a commercial area. The container unloading time is 0.1 hours per container. There are two containers at each location and the drive time between the two locations is 0.2 hours. The maximum waste ‘pick-up time’ is 2.4 hours per trip.The ‘pick-up time’ starts at the instant the truck arrives at the first pick-up location and ends when the last container on the route is emptied. The maximum number of locations which can be covered in a trip by the collection vehicle are__________(answer in integer).
Q.53 The molar concentrations (M, i.e. mol/L) of some ionic species in a water sample were estimated as follows:𝐍𝐚+ = 𝟎. 𝟐𝟓 𝐌; 𝐂𝐚𝟐+ = 𝟎. 𝟏𝟐 𝐌; 𝐂𝐥− = 𝟎. 𝟑𝟐 𝐌; 𝐇𝐂𝐎𝟑− = 𝟎. 𝟎𝟓 𝐌.The ionic strength of this water sample is_______M (correct up to two decimal places).
   
Q.54 Excess amount of solid calcium sulphate (𝐂𝐚𝐒𝐎𝟒) was added to a pure water sample (pH = 7) so that some solids remain undissolved at the equilibrium. The solubility product of 𝐂𝐚𝐒𝐎𝟒 is 2×10-5mol2/L2. The molar concentration of 𝐒𝐎𝟒𝟐− in this water sample atequilibrium will be_________mol/L (rounded off to three decimal places).
   
Q.55 A facultative pond system for sewage treatment consists of two ponds in series. The hydraulic retention time (HRT) of each pond is 6 days. The total BOD5 reduction through the entire pond system is 90 %. If the ponds are considered to be completely mixed, then the rate constant describing the BOD5 removal is_____ day-1 (rounded off to two decimal points). Assume that the rate constant is same for both the ponds.

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 B  11 A  21 B; C  31 C  41 5 to 5  51 21 to 22 
2 B  2 A  12 B  22 B; C; D  32 A  42 1 to 1  52 6 to 6 
3 C  3 B  13 A  23 23 to 23  33 A  43 562 to 566  53 0.50 to 0.68 
4 C  4 C  14 C  24 8 to 8  34 A  44 1.1 to 1.3  54 0.004 to 0.006 
5 B  5 C  15 A  25 0.74 to 0.76  35 A  45 32 to 32  55 0.34 to 0.38 
6 C  6 A  16 B  26 A  36 A; C; D  46 0.024 to 0.026     
7 D  7 A  17 A  27 B  37 A; B; D  47 0.18 to 0.20     
8 A  8 C  18 B  28 D  38 A; C; D  48 49200 to  53300     
9 C  9 C  19 A; C OR A; C;  D  29 A  39 A; B  49 0.12 to 0.14     
10 A  10 A  20 A; C  30 A  40 B; D  50 0.25 to 0.35     

GATE 2021 Electrical Engineering Previous Year Paper

GATE 2021 Electrical 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 people __________were at the demonstration were from all sections of society.
(A) whose
(B) which
(C) who
(D) whom
Q.2

A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like .
Q.3 For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:
(A) 396
(B) 324
(C) 216
(D) 144
 
Q.4 Which one of the following numbers is exactly divisible by  (1113 +1)?
(A) 1126 +1
(B) 1133 +1
(C) 1139 -1
(D) 1152 -1
 
Q.5 Oasis is to sand as island is to _________Which one of the following options maintains a similar logical relation in the above sentence?
(A) Stone
(B) Land
(C) Water
(D) Mountain

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

Q.6 The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be counterproductive.Which one of the following statements is the CORRECT inference from the above passage?
(A) Sleeping well alone is enough to prepare for an exam. Studying has lesser benefit.
(B) Students are efficient and are not wrong in thinking that sleep is a waste of time.
(C) If a student is extremely well prepared for an exam, he needs little or no sleep.
(D) To do well in an exam, adequate sleep must be part of the preparation.
Q.7


In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm2 is:
(A) 12.50
(B) 6.25
(C) 3.125
(D) 1.5625
Q.8 Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01  for 0 ≤ X ≤ 100.The mean of X is ___________            
(A) 2.5
(B) 5.0
(C) 25.0
(D) 50.0
Q.9

         

The number of students passing or failing in an exam for a particular subject are presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the exam in their second attempt.The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are  ____________.
A) 65 and 53
(B) 60 and 50
(C) 55 and 53
(D) 55 and 48
Q.10 Seven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to each other. R is parked to the immediate right of V.  T is parked to the left of U.Based on the above statements, the only INCORRECT option given below is:
(A) There are two cars parked in between Q and V.
(B) Q and R are not parked together.
(C) V is the only car parked in between S and R.
(D) Car P is parked at the extreme end.
Electrical Engineering 
  1. – Q.12 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
Q.1 Let p and q be real numbers such that p2 + q2 = 1. The eigenvalues of the matrix are
(A) 1 and 1
(B) 1 and -1
(C) j and – j
(D) pq and – pq 
Q.2 Let p(Z) = Z3 +(1+ j)Z2 +(2+ j) Z  +3, where Z is a complex number. Which one of the following is true?
(A) conjugate{ p(Z)} = p(conjugate{Z}) for all z
(B) The sum of the roots of p (Z) = 0 is a real number
(C) The complex roots of the equation p (Z) = 0 come in conjugate pairs
(D) All the roots cannot be real
Q.3 Let f (x) be a real-valued function such that f ‘(x0 ) =0 for some x0 є(0, 1), and f ”(x) > 0 for all x є (0, 1). Then f (x) has
(A) no local minimum in (0, 1)
(B) one local maximum in (0, 1)
(C) exactly one local minimum in (0, 1)
(D) two distinct local minima in (0, 1)
 
Q.4

For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘ab’ is

      
(A) 10 V in series with 12 Ω
(B) 65 V in series with 15 Ω
(C) 50 V in series with 2 Ω
(D) 35 V in series with 2 Ω
 
Q.5 Which one of the following vector functions represents a magnetic field B? ( xˆ, yˆ, and ˆz are unit vectors along x-axis, y-axis, and z-axis, respectively)
(A) 10 x xˆ + 20 y yˆ – 30 Z zˆ
(B) 10 y xˆ + 20 x yˆ -10 Z zˆ
(C) 10Z xˆ + 20 y yˆ -30 x zˆ
(D) 10 x xˆ – 30 Z yˆ+ 20 y zˆ
Q.6 If the input x(t) and output y(t) of a system are related asy(t) = max(0, x(t)) , then the system is
(A) linear and time-variant
(B) linear and time-invariant
(C) non-linear and time-variant
(D) non-linear and time-invariant
 
Q.7 Two discrete-time linear time-invariant systems with impulse responsesh 1[n] = δ [n -1] + δ [n +1] and h2[n] = δ[n]= δ[n -1] are connected in cascade, where δ [n] is the Kronecker delta. The impulse response of the cascaded system is
(A) δ [n – 2]+δ[n +1]
(B) δ[n -]δ[n]+δ[n+1]δ[n -1]
(C) δ[n – 2]+δ[n -1]+δ[n]+δ[n +1]
(D) δ[n]δ[n -1]+δ[n – 2]δ[n +1]

Q.8

Consider the table given:

 

The correct combination that relates the constructional feature, machine type and mitigation is
(A) P-V-X, Q-U-Z, R-T-Y
(B) P-U-X, Q-S-Y, R-V-Z
(C) P-T-Y, Q-V-Z, R-S-X
(D) P-U-X, Q-V-Y, R-T-Z

Q.9

Consider a power system consisting of N number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is NL. The balanced Newton-Raphson method is used to carry out load flow study in polar form. H, S, M, and R are sub-matrices of the Jacobian matrix J as shown below:

 

The dimension of the sub-matrix M is
(A) NL x (N -1)
(B) (N -1) x (N -1- NL )
(C) NL x (N -1+ NL )
(D) (N -1)x (N -1+ NL )
Q.10

Two generators have cost functions F1 and F2.Their incremental-cost characteristics are

They need to deliver a combined load of 260 MW. Ignoring the network losses, for economic operation, the generations P1 and P2   (in MW) are
(A) P1 =P2 = 130
(B) P1 = 160, P2 =100
(C) P1 = 140, P2 =120
(D) P1 = 120, P2 =140
 
Q.11

For the closed-loop system shown, the transfer function E(s)/R(s) is

   

(A) G / 1+GH

(B) GH / 1+GH

(C) 1 / 1+GH

(D) 1 / 1+G
Q.12 Inductance is measured by
(A) Schering bridge
(B) Maxwell bridge
(C) Kelvin bridge
(D) Wien bridge

Q.13 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

 

Q.13		 Suppose the circles x2 + y2 =1 and (x -1)2 + ( y -1)2 = r2 intersect each other orthogonally at the point (u,v) . Then u +v = ______________.
   

Q.14		 In the given circuit, the value of capacitor C that makes current I= 0 is __________ µF.         
   

Q.15		 Two single-core power cables have total conductor resistances of 0.7 Ω and 0.5 Ω, respectively, and their insulation resistances (between core and sheath) are 600 MΩ and 900 MΩ, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is __________×106.
   

Q.16		 In the given circuit, for voltage Vy to be zero, the value of β should be ___________. (Round off to 2 decimal places).

Q.17		 A 1 μC point charge is held at the origin of a cartesian coordinate system. If a second point charge of 10 μC is moved from (0, 10, 0) to (5, 5, 5) and subsequently to (5, 0, 0), then the total work done is  __________mJ.(Round off to 2 decimal places).Take 1/ 4πEO= 9×109 in SI units. All coordinates are in meters.
   

Q.18		 The power input to a 500 V, 50 Hz, 6-pole, 3-phase Induction motor running at 975 RPM is 40 kW. The total stator losses are 1 kW. If the total friction and windage losses are 2.025 kW, then the efficiency is___%.
   

Q.19		 An alternator with internal voltage of 1∠δ1 p.u and synchronous reactance of 0.4 p.u is connected by a transmission line of reactance 0.1 p.u to a synchronous motor having synchronous reactance 0.35 p.u and internal voltage of 0.85∠δ2 p.u. If the real power supplied by the alternator is 0.866 p.u, then (δ1 – δ2 ) is       degrees. (Round off to 2 decimal places.)(Machines are of non-salient type. Neglect resistances.)
   

Q.20

The Bode magnitude plot for the transfer function V0(s) / Vi(s) of the circuit is as shown. The value of R is ___Ω.(Round off to 2 decimal places.)

Q.21		 A signal generator having a source resistance of 50 Ω is set to generate a 1 kHz sinewave. Open circuit terminal voltage is 10 V peak-to-peak.Connecting a capacitor across the terminals reduces the voltage to 8 V peak-to-peak. The value of this capacitor is  ______F. (Round off to 2 decimal places.)
   

Q.22		 A 16-bit synchronous binary up-counter is clocked with a frequency fCLK . The two most significant bits are OR-ed together to form an output Y. Measurements show that Y is periodic, and the duration for which Y remains high in each period is 24 ms. The clock frequency fCLK is____ MHz. (Round off to 2 decimal places.)
   

Q.23		 In the BJT circuit shown, beta of the PNP transistor is 100. Assume VBE =- 0.7 V. The voltage across RC will be 5 V when R2 is  _______kΩ. (Round off to 2 decimal places.)   

Q.24		 In the circuit shown, the input Vi is a sinusoidal AC voltage having an RMS value of 230V± 20% . The worst-case peak-inverse voltage seen across any diode is_________V. (Round off to 2 decimal places.)  
   

Q.25

In the circuit shown, a 5 V Zener diode is used to regulate the voltage across load R0. The input is an unregulated DC voltage with a minimum value of 6 V and a maximum value of 8 V. The value of Rs is 6 Ω. The Zener diode has a maximum rated power dissipation of 2.5 W. Assuming the Zener diode to be ideal, the minimum value of R0 is ______Ω.

 

                    

Q.26 – Q.37 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).


Q.26		 In the open interval (0, 1) , the polynomial p(x) = x4 – 4x3 + 2 has
(A) two real roots
(B) one real root
(C) three real roots
(D) no real roots

Q.27		 Suppose the probability that a coin  toss shows “head” is p , where 0 < p <1. The coin is tossed repeatedly until the first “head” appears. The expected number of tosses required is
(A) p / (1- p)
(B) (1 – p) / p
(C) 1/ p
(D) 1/ p2

Q.28		 Let (-1- j), (3- j), (3+ j) and (-1+ j ) be the vertices of a rectangle C in the complex plane. Assuming that C is traversed in counter-clockwise direction, the value of the contour integral is
(A) jπ/2 
(B) 0
(C) – jπ /8 
(D) jπ /16
Q.29

In the circuit, switch ‘S’ is in the closed position for a very long time. If the switch is opened at time t =0 , then iL (t) in amperes, for t ≥0 is

 
(A) 8 e-10 t
(B) 10
(C) 8+ 2e-10 t
(D) 10(1- e-2t )
 
Q.30

The input impedance, Zin(s), for the network shown is

           
(A)
(B) 6s + 4
(C) 7s + 4
(D)
Q.31 The causal signal with z-transformZ2(Z–a)-2 is ( u[n] is the unit step signal)
(A) a2nu[n]
(B) (n +1) anu[n]
(C) n-1anu[n]
(D) n2anu[n]
 
Q.32

Let f (t) be an even function, i.e. f (-t) = f (t) for all t. Let the Fourier transform of f (t) be defined as F (ω) = .

Suppose=-ωF(ω) for all ω, and F(0) =1. Then
(A) f (0) < 1
(B) f (0) > 1
(C) f (0) = 1
(D) f (0) = 0
 
Q.33 In a single-phase transformer, the total iron loss is 2500 W at nominal voltage of 440 V and frequency 50 Hz. The total iron loss is 850 W at 220 V and 25 Hz. Then, at nominal voltage and frequency, the hysteresis loss and eddy current loss respectively are
(A) 1600 W and 900 W
(B) 900 W and 1600 W
(C) 250 W and 600 W
(D) 600 W and 250 W
Q.34

In the figure shown, self-impedances of the two transmission lines are 1.5j p.u each, and Zm = 0.5j p.u is the mutual impedance. Bus voltages shown in the figure are in p.u. Given that δ>0, the maximum steady-state real power that can be transferred in p.u from Bus-1 to Bus-2 is

 
(A)
(B)
(C)
(D)

Q.37		 A counter is constructed with three D flip-flops. The input-output pairs are named (D0, Q0), (D1, Q1), and (D2, Q2), where the subscript 0 denotes the least significant bit. The output sequence is desired to be the Gray-code sequence 000, 001, 011, 010, 110, 111, 101, and 100, repeating periodically. Note that the bits are listed in the Q2 Q1 Q0 format. The combinational logic expression for D1 is
(A) Q2Q1Q0
(B) Q2Q0 + Q1Q0
(C) Q2Q0 + Q1Q0
(D) Q2Q1 + Q2Q1

Q.38 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

 

Q.38		 Let A be a 10 x 10 matrix such that A5 is a null matrix, and let I be the 10 x 10 identity matrix. The determinant of A + I is  ___________ .
   

Q.39		 A three-phase balanced voltage is applied to the load shown. The phase sequence is RYB. The ratioIB/IR is___.
   

Q.40

In the given circuit, for maximum power to be delivered to RL, its value should be _________ Ω.(Round off to 2 decimal places.)

 

Q.41		 One coulomb of point charge moving with a uniform velocity 10 xˆ m/s enters the region x ≥ 0 having a magnetic flux densityB =(10 y xˆ  + 10 x yˆ + 10zˆ) T. The magnitude of force on the charge at x = 0+ is _________ N.( xˆ,  yˆ,  and zˆ are unit vectors along x-axis, y-axis, and z-axis, respectively.)
   

Q.42		 Consider a large parallel plate capacitor. The gap d between the two plates is filled entirely with a dielectric slab of relative permittivity 5. The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field E2 in the gap to the original electric field E1is__ .
   

Q.43		 Consider a continuous-time signal x(t) defined by x(t) = 0 for | t | >1,and x(t) =1- | t | for|t|≤1. Let the Fourier transform of x(t) be defined as . The maximum magnitude of X (ω) is_________.
   

Q.44		 A belt-driven DC shunt generator running at 300 RPM delivers 100 kW to a 200 V DC grid. It continues to run as a motor when the belt breaks, taking 10 kW from the DC grid. The armature resistance is 0.025 Ω, field resistance is 50 Ω, and brush drop is 2 V. Ignoring armature reaction, the speed of the motor is  _____RPM. (Round off to 2 decimal places.)

Q.45		 An 8-pole, 50 Hz, three-phase, slip-ring induction motor has an effective rotor resistance of 0.08 Ω per phase. Its speed at maximum torque is 650 RPM. The additional resistance per phase that must be inserted in the rotor to achieve maximum torque at start is ______Ω. (Round off to 2 decimal places.) Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.
   

Q.46

Consider a closed-loop system as shown. Gp(s) =14.4 / s(1+0.1s) is the plant transfer function and Gc (s) = 1 is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is_______rad/s. (Round off to 2 decimal places.)

 

  

Q.47		 In the given figure, plant Gp(s) = 2.2 /(1+0.1s)(1+0.4s)(1+1.2s)and compensator Gc(s) =. The external disturbance input is D(s). It is desired that when the disturbance is a unit step, the steady-state error should not exceed 0.1 unit. The minimum value of K is_____.(Round off to 2 decimal places.) 
   

Q.48

The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the RMS value of the full- wave rectified waveform to the RMS value of the clipped waveform is____________.(Round off to 2 decimal places.)

 
Q.49 The state space representation of a first-order system is given asx =-x+u y = xwhere, x is the state variable, u is the control input and y is the controlled output. Let u =-K x be the control law, where K is the controller gain. To place a closed-loop pole at -2, the value of K is_____________.
   

Q.50		 An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance M between the windings of the transformer is _________μH.(Round off to 2 decimal places.)
   
Q.51 A 100 Hz square wave, switching between 0 V and 5 V, is applied to a CR high-pass filter circuit as shown. The output voltage waveform across the resistor is 6.2 V peak-to-peak. If the resistance R is 820 Ω, then the value C is________μF.(Round off to 2 decimal places.)
Q.52

A CMOS Schmitt-trigger inverter has a low output level of 0 V and a high output level of 5 V. It has input thresholds of 1.6 V and 2.4 V. The input capacitance and output resistance of the Schmitt-trigger are negligible.The frequency of the oscillator shown is_______Hz.(Round off to 2 decimal places.)

 

     
   
Q.53

Consider the boost converter shown. Switch Q is operating at 25 kHz with a duty cycle of 0.6. Assume the diode and switch to be ideal. Under steady- state condition, the average resistance Rin as seen by the source is___________Ω.(Round off to 2 decimal places.)

 
Q.54 Consider the buck-boost converter shown. Switch Q is operating at 25 kHz and 0.75 duty-cycle. Assume diode and switch to be ideal. Under steady- state condition, the average current flowing through the inductor is______A.
   
Q.55

A single-phase full-bridge inverter fed by a 325 V DC produces a symmetric quasi-square waveform across ‘ab’ as shown. To achieve a modulation index of 0.8, the angle θ expressed in degrees should be_________.(Round off to 2 decimal places.)(Modulation index is defined as the ratio of the peak of the fundamental component of Vab to the applied DC value.)

 

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 B  11 C  21 2.30 to 2.50  31 B  41 100 to 100  51 12.30 to 12.60 
2 C  2 D  12 B  22 2.00 to 2.10  32 A  42 5 to 5  52 3150.00 to 3170.00 
3 D  3 C  13 1 to 1  23 16.70 to 17.70  33 B  43 1 to 1  53 1.55 to 1.65 
4 D  4 B  14 20.00 to 20.00  24 389 to 391  34 A  44 273.00 to 277.00  54 24 to 24 
5 C  5 A  15 300 to 300  25 29.00 to 31.00  35 C  45 0.50 to 0.54  55 50.00 to 52.00 
6 D  6 D  16 -3.30 to -3.20  26 B  36 D  46 10.80 to 11.00     
7 C  7 C  17 8.90 to 9.10  27 C  37 C  47 9.50 to 9.60     
8 D  8 B  18 89.50 to 90.50  28 C  38 1 to 1  48 1.20 to 1.23     
9 D  9 A  19 59.00 to 61.00  29 C  39 1 to 1  49 1 to 1     
10 A  10 B  20 0.09 to 0.11  30 A  40 1.40 to 1.42  50 50.00 to 52.00     

GATE 2021 Electronics and Communication Engineering Previous Year Paper

GATE 2021 Electronics and Communication 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 current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its

population 2 years ago?
(A) 9,92,500
(B) 9,95,006
(C) 10,00,000
(D) 12,51,506
Q.2
(A) 3
(B) 7
(C) 9
(D) 11
Q.3

                                                            

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is _________ 
(A) 4
(B) 3
(C) 6
(D) 7
Q.4 Nostalgia is to anticipation as is to________ Which one of the following options maintains a similar logical relation in the above sentence?
(A) Present, past
(B) Future, past
(C) Past, future
(D) Future, present
Q.5 Consider the following sentences:I woke up from sleep.I woked up from sleep.I was woken up from sleep.I was wokened up from sleep.Which of the above sentences are grammatically CORRECT?
(A) (i) and (ii)
(B) (i) and (iii)
(C) (ii) and (iii)
(D) (i) and (iv)

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

Q.6

Given below are two statements and two conclusions.

Statement 1: All purple are green.

Statement 2: All black are green. 

Conclusion I: Some black are purple. 

Conclusion II: No black is purple.

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) Both conclusion I and II are correct.
Q.7 Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.Which of the following can be deduced from the above passage?Nowadays, computers are present in almost all places.Computers cannot be used for solving problems in engineering.For humans, there are both positive and negative effects of using computers.Artificial intelligence can be done without data.
(A) (ii) and (iii)
(B) (ii) and (iv)
(C) (i), (iii) and (iv)
(D) (i) and (iii)
Q.8 Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is__________
(A) 𝜋/3
(B) 2𝜋/3
(C) 3𝜋 / 2
(D) 3π
Q.9

 

The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is
(A) 4
(B) 5
(C) 6
(D) 7
Q.10


Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is
(A) 2 : 3
(B) 3 : 4
(C) 4 : 5
(D) 5 : 6
Electronics and Communication Engineering (EC)

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

Q.1

The vector function 𝐅 (𝐫) = −𝒙 𝒊̂ + 𝒚 𝖩̂ is defined over a circular arc C shown in the figure. The line integral of ∫𝑪 𝐅 (𝐫) 𝒅𝐫 is.

                  
(A) 1/2
(B) 1/4
(C) 1/6
(D) 1/3
Q.2

Consider the differential equation given below.           

The integrating factor of the differential equation is
(A) (1 − 𝑥2)−3⁄4
(B) (1 − 𝑥2)−1⁄4
(C) (1 − 𝑥2)−3⁄2
(D) (1 − 𝑥2)−1⁄2
Q.3 Two continuous random variables 𝑿 and 𝒀 are related as  𝒀 = 𝟐𝑿 + 𝟑 Let 𝝈𝟐𝑿 and 𝝈𝟐𝒀 denote the variances of 𝑿 and 𝒀, respectively. The variances are related as
(A) 𝜎2𝑌 = 2 𝜎2𝑋
(B) 𝜎2𝑌 = 4 𝜎2𝑋
(C) 𝜎2 𝑌 = 5 𝜎2𝑋
(D) 𝜎2𝑌 = 25 𝜎2𝑋
 
Q.4

Consider a real-valued base-band signal (𝒕), band limited to 𝟏𝟎 kHz. The Nyquist rate for the signal 

𝒚(𝒕) = 𝒙(𝒕) 𝒙 ( 𝟏 + t/2) is
(A) 15 kHz
(B) 30 kHz
(C) 60 kHz
(D) 20 kHz
Q.5 Consider two 𝟏𝟔-point sequences [𝒏] and 𝒉[𝒏]. Let the linear convolution of 𝒙[𝒏] and 𝒉[𝒏] be denoted by 𝒚[𝒏], while 𝒛[𝒏] denotes the 𝟏𝟔-point inverse discrete Fourier transform (IDFT) of the product of the 𝟏𝟔-point DFTs of [𝒏] and 𝒉[𝒏]. The value(s) of 𝒌 for which 𝒛[𝒌] = 𝒚[𝒌] is/are
(A) 𝑘 = 0, 1, 2, … , 15
(B) 𝑘 = 0
(C) 𝑘 = 15
(D) 𝑘 = 0 and 𝑘 = 15
Q.6 A bar of silicon is doped with boron concentration of 𝟏𝟎𝟏𝟔 𝐜𝐦−𝟑 and assumed to be fully ionized. It is exposed to light such that electron-hole pairs are generated throughout the volume of the bar at the rate of 𝟏𝟎𝟐𝟎 𝐜𝐦−𝟑𝐬−𝟏. If the recombination lifetime is 𝟏𝟎𝟎 µs, intrinsic carrier concentration of silicon is 𝟏𝟎𝟏𝟎 𝐜𝐦−𝟑 and assuming 𝟏𝟎𝟎% ionization of boron, then the approximate product of steady-state electron and hole concentrations due to this light exposure is
(A) 1020cm−6
(B) 2 × 1020 cm−6
(C) 1032 cm−6
(D) 2 × 1032 cm−6
Q.9

For the circuit with an ideal OPAMP shown in the figure, VREF is fixed.            

 If VOUT = 𝟏 volt for VIN = 𝟎. 𝟏 volt and VOUT = 𝟔 volt for VIN = 𝟏 volt, where VOUT is measured across RL connected at the output of this OPAMP, the value of 𝐑𝐅⁄𝐑𝐈𝐍 is
(A) 3.285
(B) 2.860
(C) 3.825
(D) 5.555

Q.10

Consider the circuit with an ideal OPAMP shown in the figure.

             

Assuming |𝐕𝐈𝐍| ≪ |𝐕𝐂𝐂| and |𝐕𝐑𝐄𝐅| ≪ |𝐕𝐂𝐂|, the condition at which VOUT equals to zero is
(A) VIN = VREF
(B) VIN = 0.5 VREF
(C) VIN = 2 VREF
(D) VIN = 2 + VREF
Q.11 If (𝟏𝟐𝟑𝟓)𝒙 = (𝟑𝟎𝟑𝟑)𝒚, where 𝒙 and 𝒚 indicate the bases of the corresponding numbers, then
(A) 𝑥 = 7 and 𝑦 = 5
(B) 𝑥 = 8 and 𝑦 = 6
(C) 𝑥 = 6 and 𝑦 = 4
(D) 𝑥 = 9 and 𝑦 = 7
Q.12 Addressing of a 𝟑𝟐K × 𝟏𝟔 memory is realized using a single decoder. The minimum number of AND gates required for the decoder is
(A) 28
(B) 232
(C) 215
(D) 219
Q.14

The complete Nyquist plot of the open-loop transfer function (𝒔)𝑯(𝒔) of a feedback control system is shown in the figure.

 

                   

If 𝑮(𝒔)𝑯(𝒔) has one zero in the right-half of the 𝒔-plane, the number of poles that the closed-loop system will have in the right-half of the 𝒔-plane is
(A) 0
(B) 1
(C) 4
(D) 3
Q.15 Consider a rectangular coordinate system (x, y, z) with unit vectors ax, ay, and az. A plane wave traveling in the region 𝒛 ≥ 𝟎 with electric field vector 𝐄 = 𝟏𝟎 𝐜𝐨(𝟐 × 𝟏𝟎𝟖𝒕 + 𝖰𝒛)𝐚𝒚 is incident normally on the plane at 𝒛 = 𝟎, where β is the phase constant. The region 𝒛 ≥ 𝟎 is in free space and the region 𝒛 < 𝟎 is filled with a lossless medium (permittivity 𝗌 = 𝗌𝟎, permeability 𝝁 = 𝟒𝝁𝟎, where 𝗌𝟎 = 𝟖. 𝟖𝟓 × 𝟏𝟎−𝟏𝟐 F/m and 𝝁𝟎 = 𝟒𝝅 ×𝟏𝟎−𝟕 H/m). The value of the reflection  coefficient is
(A) 1/3
(B) 3/5
(C) 2/5
(D) 2/3

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

 
Q.16 If the vectors (𝟏. 𝟎, −𝟏. 𝟎, 𝟐. 𝟎), (𝟕. 𝟎, 𝟑. 𝟎, 𝒙) and (𝟐. 𝟎, 𝟑. 𝟎, 𝟏. 𝟎) in ℝ𝟑are linearly dependent, the value of 𝒙 is ______________
Q.17 Consider the vector field 𝐅 = 𝐚x(𝟒𝒚 − 𝒄𝟏𝒛) + 𝐚𝒚(𝟒𝒙 + 𝟐𝒛) + 𝐚𝒛(𝟐𝒚 + 𝒛) in a rectangular coordinate system (x, y, z) with unit vectors ax, ay, and az. If the field F is irrotational (conservative), then the constant 𝒄𝟏 (in integer) is___________
   
   
Q.18

Consider the circuit shown in the figure.

                        

The current I flowing through the 7 Ω resistor between P and Q (rounded off to one decimal place) is   _________A.
Q.19

Consider the circuit shown in the figure.

                       

The value of v0 (rounded off to one decimal place) is   _________ V.
   
Q.20 An 𝟖-bit unipolar (all analog output values are positive) digital-to-analog converter (DAC) has a full-scale voltage range from 𝟎 V to 𝟕. 𝟔𝟖 V. If the digital input code is 10010110 (the leftmost bit is MSB), then the analog output voltage of the DAC (rounded off to one decimal place) is _______V.
Q.21

The autocorrelation function 𝑹(𝑟) of a wide-sense stationary random process 𝑿(𝒕) is shown in the figure.              

The average power of 𝑿(𝒕) is_______
   
Q.22 Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of 𝟓𝟎%. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is __________________
   
Q.23 A speech signal, band limited to 𝟒 kHz, is sampled at 𝟏. 𝟐𝟓 times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range −𝟓 V to +𝟓 V, are subsequently quantized in an 𝟖-bit uniform quantizer and then transmitted over a voice- grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 𝟐𝟔 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is ___________ kHz.
   
Q.24 A 𝟒 kHz sinusoidal message signal having amplitude 𝟒 V is fed to a delta modulator (DM) operating at a sampling rate of 𝟑𝟐 kHz. The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is ____________V.
   
Q.25 The refractive indices of the core and cladding of an optical fiber are 𝟏. 𝟓𝟎 and 𝟏. 𝟒𝟖, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is  ____________________  degree.

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

Q.27 A box contains the following three coins. I. A fair coin with head on one face and tail on the other face. II. A coin with heads on both the faces. III.A coin with tails on both the faces.A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head, the probability of getting a head in the second toss is
(A) 2/5
(B) 1/3
(C) 1/2
(D) 2/3
Q.29

Consider the two-port network shown in the figure.

   

The admittance parameters, in siemens, are
(A) 𝑦11 = 2, 𝑦12 = −4, 𝑦21 = −4, 𝑦22 = 2
(B) 𝑦11 = 1, 𝑦12 = −2, 𝑦21 = −1, 𝑦22 = 3
(C) 𝑦11 = 2, 𝑦12 = −4, 𝑦21 = −1, 𝑦22 = 2
(D) 𝑦11 = 2, 𝑦12 = −4, 𝑦21 = −4, 𝑦22 = 3
Q.30 For an n-channel silicon MOSFET with 𝟏𝟎 nm gate oxide thickness, the substrate sensitivity (𝝏𝑽𝑻⁄𝝏|𝑽𝑩𝑺|) is found to be 𝟓𝟎 mV/V at a substrate voltage|𝑽𝑩𝑺| = 𝟐 𝑽, where 𝑽𝑻 is the threshold voltage of the MOSFET. Assume that, |𝑽𝑩𝑺| ≫ 𝟐𝚽𝑩, where 𝐪𝚽𝑩 is the separation between the Fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given areElectron charge (q) = 𝟏. 𝟔 × 𝟏𝟎−𝟏𝟗 CVacuum permittivity (𝗌𝟎) = 𝟖. 𝟖𝟓 × 𝟏𝟎−𝟏𝟐 F/m Relative permittivity of silicon (𝗌𝐒𝐢) = 𝟏𝟐 Relative permittivity of oxide (𝗌𝐨𝐱) = 𝟒The doping concentration of the substrate is
(A) 7.37 × 1015 cm−3
(B) 4.37 × 1015 cm−3
(C) 2.37 × 1015 cm−3
(D) 9.37 × 1015 cm−3
Q.31

The propagation delays of the XOR gate, AND gate and multiplexer (MUX) in the circuit shown in the figure are 4ns, 2 ns and 1 ns, respectively.

                     

If all the inputs P, Q, R, S and T are applied simultaneously and held constant, the maximum propagation delay of the circuit is
(A) 3 ns
(B) 5 ns
(C) 6 ns
(D) 7 ns
Q.32 The content of the registers are R1 = 𝟐𝟓H, R2 = 𝟑𝟎H and R3 = 𝟒𝟎H. The following machine instructions are executed.PUSH{R1} PUSH{R2} PUSH{R3} POP{R1} POP{R2} POP{R3}After execution, the content of registers R1, R2, R3 are
(A) R1 = 40H, R2 = 30H,   R3 = 25H
(B) R1 = 25H, R2 = 30H,   R3 = 40H
(C) R1 = 30H, R2 = 40H,   R3 = 25H
(D) R1 = 40H, R2 = 25H,   R3 = 30H
Q.33

The electrical system shown in the figure converts input source current 𝒊𝒔(𝒕) to output voltage vo (t).            

 Current iL (t ) in the inductor and voltage vC (t )across the capacitor are taken as the state variables, both assumed to be initially equal to zero, i.e., iL (0)= 0 and vC (0) = 0. The system is
(A) completely state controllable as well as completely observable
(B) completely state controllable but not observable
(C) completely observable but not state controllable
(D) neither state controllable nor observable
Q.34 A digital transmission system uses a (𝟕, 𝟒) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this code ( 𝐦𝒊 ; 𝐜𝒊 ), where 𝐜𝒊 is the codeword corresponding to the ith        message      𝐦𝒊,     are     known     to     be     ( 𝟏 𝟏 𝟎 𝟎 ; 𝟎 𝟏 𝟎 𝟏 𝟏 𝟎 𝟎 ), ( 𝟏 𝟏 𝟏 𝟎 ; 𝟎 𝟎 𝟏 𝟏 𝟏 𝟏 𝟎 ) and (𝟎 𝟏 𝟏 𝟎 ; 𝟏 𝟎 𝟎 𝟎 𝟏 𝟏 𝟎 ), then which of the following is a valid codeword in this code?
(A) 1 1 0 1 0 0 1
(B) 1 0 1 1 0 1 0
(C) 0 0 0 1 0 1 1
(D) 0 1 1 0 1 0 0

Q.35

The impedance matching network shown in the figure is to match a lossless line having characteristic impedance 𝒁𝟎 = 𝟓𝟎 Ω with a load impedance 𝒁𝐋. A quarter-wave line having a characteristic impedance 𝒁𝟏 = 𝟕𝟓 Ω is connected to 𝒁𝐋. Two stubs having characteristic impedance of 𝟕𝟓 Ω each are connected to this quarter-wave line. One is a short-circuited (S.C.) stub of length 𝟎. 𝟐𝟓𝝀 connected across PQ and the other one is an open-circuited (O.C.) stub of length 𝟎. 𝟓𝝀 connected across RS.The impedance matching is achieved when the real part of 𝒁𝐋 is

                        
(A) 112.5 Ω
(B) 75.0 Ω
(C) 50.0 Ω
(D) 33.3 Ω

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

 
Q.36

A real 𝟐 × 𝟐 non-singular matrix 𝐀 with repeated eigenvalue is given as where 𝒙 is a real

positive number. The value of 𝒙 (rounded off to one decimal place) is ____________ 
   
Q.37

For a vector field 𝐃 = 𝝆 𝐜𝐨𝐬𝟐 𝝋 𝐚𝝆 + 𝒛𝟐 𝐬𝐢𝐧𝟐 𝝋 𝐚𝝋 in a cylindrical coordinate system (𝝆, 𝝋, 𝒛) with unit vectors 𝐚𝝆, 𝐚𝝋 𝐚𝐧𝐝 𝐚𝒛, the net flux of 𝐃 leaving the closed surface of the cylinder (𝝆 = 𝟑, 𝟎 ≤ 𝒛 ≤ 𝟐) (rounded off to two

decimal places) is_____________
   
Q.38

In the circuit shown in the figure, the switch is closed at time 𝒕 = 𝟎, while the capacitor is initially charged to −𝟓 V(i.e., vc(𝟎) = −𝟓 V).

        

The time after which the voltage across the capacitor becomes zero (rounded off to three decimal places) is_____________ms.
Q.39 The exponential Fourier series representation of a continuous-time periodic signal 𝒙(𝒕) is defined as            ∞𝒙(𝒕) =  ∑   𝒂𝒌 𝒆𝒋𝒌𝑚𝟎𝒕           𝒌 = −∞where 𝑚𝟎 is the fundamental angular frequency of 𝒙(𝒕) and the coefficients of the series are 𝒂𝒌. The following information is given about (𝒕) and 𝒂𝒌.𝒙(𝒕) is real and even, having a fundamental period of 𝟔The average value of 𝒙(𝒕) is 𝟐The average power of the signal 𝒙(𝒕) (rounded off to one decimal place) is___________
   
Q.40 For a unit step input [𝒏], a discrete-time LTI system produces an output signal ( 𝟐𝜹[𝒏 + 𝟏] + 𝜹[𝒏] + 𝜹[𝒏 − 𝟏] ). Let 𝒚[𝒏] be the output of the system for an input 𝒖[𝒏]). The value of 𝒚[𝟎] is_________  
Q.41

Consider the signals [𝒏] = 𝟐𝒏−𝟏 𝒖[−𝒏 + 𝟐] and 𝒚[𝒏] = 𝟐−𝒏+𝟐 𝒖[𝒏 + 𝟏], where 𝒖[𝒏] is the unit step sequence. Let (𝒆𝒋𝑚) and 𝒀(𝒆𝒋𝑚) be the discrete- time Fourier transform of 𝒙[𝒏] and 𝒚[𝒏], respectively. The value of the integral                       

(rounded off to one decimal place) is___________.
Q.42

A silicon P-N junction is shown in the figure. The doping in the P region is 𝟓 × 𝟏𝟎𝟏𝟔 cm−3 and doping in the N region is 𝟏𝟎 × 𝟏𝟎𝟏𝟔 cm−3. The parameters given areBuilt-in voltage (𝚽𝐛𝐢) = 0.8 V Electron charge (𝐪) = 𝟏. 𝟔 × 𝟏𝟎−𝟏𝟗 CVacuum permittivity (𝗌𝟎) = 𝟖. 𝟖𝟓 × 𝟏𝟎−𝟏𝟐 F/m Relative permittivity of silicon (𝗌𝐒𝐢) = 𝟏𝟐          

The magnitude of reverse bias voltage that would completely deplete one of the two regions (P or N) prior to the other (rounded off to one decimal place) is__________ V.
Q.43

An asymmetrical periodic pulse train vin of 𝟏𝟎 V amplitude with on-time TON = 1 ms and off-time TOFF = 1 µs is applied to the circuit shown in the figure. The diode D1 is ideal.The difference between the maximum voltage and minimum voltage of the output waveform vo (in integer) is __________ V.
Q.44 For the transistor M1 in the circuit shown in the figure, µ𝒏𝑪𝐨𝐱 = 𝟏𝟎𝟎 µ𝐀/𝐕𝟐 and (𝑾⁄𝑳) = 𝟏𝟎, where µ𝒏 is the mobility of electron, 𝑪𝐨𝐱 is the oxide capacitance per unit area, 𝑾 is the width and 𝑳 is the length.                                   
The channel length modulation coefficient is ignored. If the gate-to-source voltage 𝑽𝐆𝐒 is 1 V to keep the transistor at the edge of saturation, then the threshold voltage of the transistor (rounded off to one decimal place) is ___________V.
Q.45

A circuit with an ideal OPAMP is shown in the figure. A pulse 𝐕𝐈𝐍 of 𝟐𝟎 m𝐬 duration is applied to the input. The capacitors are initially uncharged.

         

The output voltage 𝐕𝐎𝐔𝐓 of this circuit at 𝒕 = 𝟎+ (in integer)  is______ V.
   
Q.46

The propagation delay of the exclusive-OR (XOR) gate in the circuit in the figure is 3 ns. The propagation delay of all the flip-flops is assumed to be zero. The clock (Clk) frequency provided to the circuit is 500 MHz.           

Starting from the initial value of the flip-flop outputs 𝐐𝟐𝐐𝟏𝐐𝟎 = 𝟏 𝟏 𝟏 with𝐃𝟐 = 𝟏, the minimum number of triggering clock edges after which the flip- flop outputs 𝐐𝟐𝐐𝟏𝐐𝟎 becomes 1 0 0 (in integer) is  
Q.47

The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time𝒕 = 𝟎.

 

 

Initially, when the switch is open, the capacitor is discharged and the ammeter reads zero ampere. After the switch is closed, the ammeter reading keeps fluctuating for some time till it settles to a final steady value. The maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is_____A.

Q.48

A unity feedback system that uses proportional-integral (PI) control is shown in the figure.   

The stability of the overall system is controlled by tuning the PI control parameters 𝑲𝑷 and 𝑲𝑰. The maximum value of 𝑲𝑰 that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is____________
   
Q.49 A sinusoidal message signal having root mean square value of 𝟒 V and frequency of 𝟏 kHz is fed to a phase modulator with phase deviation constant𝟐 rad/volt. If the carrier signal is 𝒄(𝒕) = 𝟐 𝐜𝐨𝐬(𝟐𝝅𝟏𝟎𝟔𝒕), the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is _______Hz.
   
Q.50 Consider a superheterodyne receiver tuned to 𝟔𝟎𝟎 kHz. If the local oscillator feeds a 𝟏𝟎𝟎𝟎 kHz signal to the mixer, the image frequency (in integer) is_____________ kHz.
   
Q.51 In a high school having equal number of boy students and girl students, 𝟕𝟓% of the students study Science and the remaining 𝟐𝟓% students study Commerce. Commerce students are two times more likely to be a boy than are Science students. The amount of information gained in knowing that a randomly selected girl student studies Commerce (rounded off to three decimal places) is ___________bits.
Q.52 A message signal having peak-to-peak value of 2 V, root mean square value of 0.1 V and bandwidth of 5 kHz is sampled and fed to a pulse code modulation (PCM) system that uses a uniform quantizer. The PCM output is transmitted over a channel that can support a maximum transmission rate of 50 kbps. Assuming that the quantization error is uniformly distributed, the maximum signal to quantization noise ratio that can be obtained by the PCM system (rounded off to two decimal places) is________
Q.53 Consider a polar non-return to zero (NRZ) waveform, using +𝟐 V and −𝟐 V for representing binary ‘1’ and ‘0’ respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance 𝟎. 𝟒 V2. If the a priori probability of transmission of a binary ‘1’ is 𝟎. 𝟒, the optimum threshold voltage for a maximum a posteriori (MAP) receiver (rounded off to two decimal places) is ______ V.
   
Q.54 A standard air-filled rectangular waveguide with dimensions 𝒂 = 𝟖 cm,𝒃 = 𝟒 cm, operates at 𝟑. 𝟒 GHz. For the dominant mode of wave propagation, the phase velocity of the signal is 𝒗𝒑. The value (rounded off to two decimal places) of 𝒗𝒑⁄𝒄, where 𝒄 denotes the velocity of light, is___________
   
   
Q.55 An antenna with a directive gain of 𝟔 dB is radiating a total power of 𝟏𝟔 kW. The amplitude of the electric field in free space at a distance of 𝟖 km from the antenna in the direction of 𝟔 dB gain (rounded off to three decimal places) is___________V/m.

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 A  11 B  21 2.0 to 2.0  31 C  41 7.9 to 8.1  51 3.320 to 3.325 
2 B  2 B  12 C  22 94.2 to 94.6  32 A  42 8.1 to 8.4  52 30.00 to 34.00 
3 C  3 B  13 C  23 9.24 to 9.28  33 D  43 10 to 10  53 0.03 to 0.05 
4 C  4 B  14 D  24 2.80 to 3.20  34 C  44 0.5 to 0.5  54 1.15 to 1.25 
5 B  5 C  15 A  25 9.30 to 9.44  35 A  45 -12 to -12  55 0.224 to 0.264 
6 C  6 D  16 8.0 to 8.0  26 MTA  36 10.0 to 10.0  46 5 to 5     
7 D  7 A  17 0 to 0  27 B  37 56.50 to 56.60  47 1.40 to 1.50     
8 A  8 D  18 0.5 to 0.5  28 C  38 0.132 to 0.146  48 3.125 to 3.125     
9 C  9 MTA  19 1.0 to 1.0  29 C  39 31.9 to 32.1  49 1011310.0 to  1011320.0     
10 A  10 A  20 4.5 to 4.5  30 A  40 0.0 to 0.0  50 1400 to 1400     

GATE 2021 Chemistry Previous Year Paper

GATE 2021 Chemistry 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.2


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

(D)

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.4
(A) y2
(B) y
(C) 3y2
(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
  1. 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.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 θ, in degrees, is_________  
(A) 36
(B) 45
(C) 72
(D) 108
Q.9 A function, λ, is defined by        
(A) −1
(B) 0
(C) 163
(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.

Chemistry (CY)

  1. – Q.14 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
Q.1 The rates of alkaline hydrolysis of the compounds shown below      follow the order:
(A) I > II > III
(B) II > I > III
(C) II > III > I
(D) III > I > II
Q.7 An organic compound exhibits the [M]+, [M+2]+ and [M+4]+ peaks in the intensity ratio 1:2:1 in the mass spectrum, and shows a singlet at  7.49 in the 1H NMR spectrum in CDCl3. The compound is:
(A) 1,4-dichlorobenzene
(B) 1,4-dibromobenzene
(C) 1,2-dibromobenzene
(D) 1,2-dichlorobenzene
 
Q.8 Reaction of LiAlH4 with one equivalent of Me3N∙HCl gives a tetrahedral compound, which reacts with another equivalent of Me3N∙HCl to give compound N. The compound N and its geometry, respectively, are:
(A) LiAlH4NMe3 and trigonal bipyramidal
(B) Li2AlH4Cl and square pyramidal
(C) AlH3(NMe3)2 and trigonal bipyramidal
(D) AlH3(NMe3)2 and pentagonal
 
Q.9 Which one of the following is a non-heme protein?
(A) hemoglobin
(B) hemocyanin
(C) myoglobin
(D) cytochrome P-450
Q.10 A correct example of a nucleotide is:
(A) adenosine monophosphate (AMP)
(B) RNA
(C) uridine
(D) DNA
 

Q.11		 The equilibrium constant for the reaction   3 NO (g) ⇌ N2O (g) + NO2 (g)  at 25 °C is closest to:[ΔG° = -104.18 kJ; R = 8.314 J mol-1 K-1]
(A) 1.043
(B) 1.8 × 1018
(C) 1.651
(D) 5.7 × 10-19
 
Q.12 The reaction of NiBr2 with two equivalents of PPh3 in CS2 at –78 °C gives a red-colored diamagnetic complex, [NiBr2(PPh3)2]. This transforms to a green-colored paramagnetic complex with the same molecular formula at 25°C. The geometry and the number of unpaired electrons in thegreen-colored complex, respectively, are:
(A) tetrahedral and 1
(B) tetrahedral and 2
(C) square planar and 2
(D) square planar and 4

Q.13		 The rate of the substitution reaction of [Co(CN)5Cl]3– with OH– to give [Co(CN)5(OH)]3–
(A) depends on the concentrations of both [Co(CN)5Cl]3– and OH–
(B) depends on the concentration of [Co(CN)5Cl]3– only
(C) is directly proportional to the concentration of OH– only
(D) is inversely proportional to the concentration of OH–
 
Q.14 The Δo of[Cr(H2O)6]3+, [CrF6]3– and [Cr(CN)6]3–follows the order:
(A) [Cr(H2O)6]3+ > [CrF6]3– > [Cr(CN)6]3–
(B) [CrF6]3– > [Cr(H2O)6]3+ > [Cr(CN)6]3–
(C) [Cr(CN)6]3– > [Cr(H2O)6]3+ > [CrF6]3–
(D) [CrF6]3– > [Cr(CN)6]3– > [Cr(H2O)6]3+

Q.15 – Q.18 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

Q.15 The phase diagram of CO2 is shown below:
The correct statement(s) about CO2 is/are:
(A) Below Tc, it does not exist in liquid state.
(B) Above Tc, it does not exist in liquid state.
(C) At Tc, it can exist in all three phases.
(D) Above T1, it does not exist in solid state.

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

 

Q. 19		 A reversible heat engine absorbs 20 kJ of heat from a source at 500 K and dissipates it to the reservoir at 400 K. The efficiency of the heat engine is_____%.

Q. 20		 Among the following eight compounds,                   the number of compound (s)which can exhibit stereoisomerism is___________.
   

Q. 21		 The Mo-Mo bond order in [(η5-C5H5)Mo(CO)2]2 which obeys the 18- electron rule is___________.
   
Q. 22 The change in enthalpy (ΔH) for the reaction  2 P (s) + 3 Br2 (l) → 2 PBr3 (l)is -243 kJ. In this reaction, if the amount of phosphorusconsumed is 3.1 g, the change in enthalpy(rounded off to two decimal places) is________kJ.[Atomic Wt. of P = 31]
Q. 23 The number of signal(s) in the 1H NMR spectrum of the following compound  recorded at 25 °C in CDCl3 is___.
   

Q. 24		 A 5 V battery delivers a steady current of 1.5 A for a period of 2 h. The total charge that has passed through the circuit is________________Coulombs.
   

Q. 25		 The spin-only magnetic moment of [Co(H2O)6]2+ (rounded off to one decimal place) is________BM.

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

Q.26 The geometry and the number of unpaired electrons in tetrakis(1- norbornyl)Co
respectively, are:
(A) tetrahedral and one
(B) tetrahedral and five
(C) square planar and one
(D) square planar and three
Q.27 The yellow color of an aqueous solution of K2CrO4 changes to red-orange upon the addition of a few drops of HCl. The red-orange complex, the oxidation state of its central element(s), and the origin of its color, respectively, are:
(A) chromium chloride, +3, d-d transition
(B) dichromate ion, +6 and +6, charge transfer
(C) perchlorate ion, +7, charge transfer
(D) chromic acid, +6, charge transfer
Q.28 The shapes of the compoundsClF3, XeOF2, N3– and XeO3F2 respectively, are:
(A) T-shape, T-shape, linear and trigonal bipyramidal
(B) trigonal planar, T-shape, V-shape and square pyramidal
(C) T-shape, trigonal planar, linear and square pyramidal
(D) trigonal planar, trigonal planar, V-shape and trigonal bipyramidal
Q.29 The metal borides that contain isolated boron atoms are:
(A) Tc7B3 and Re7B3
(B) Cr5B3 and V3B2
(C) Ti4B4 and V3B4
(D) TiB and HfB
 
Q.30 The major product formed in the following reaction is:
(A) non-6-yn-2-one
(B) non -3-yn-8 -one
(C) non-2-yn-6-one
(D) non-3-en-8-one
Q.34 In an electrochemical cell, Ag+ ions in AgNO3 are reduced to Ag metal at the cathode and Cu is oxidized to Cu2+ at the anode. A current of 0.7 A is passed through the cell for 10 min. The mass (in grams) of silver deposited and copper dissolved, respectively, are:[Faraday Constant = 96,485 C mol-1, Atomic Weight of Ag = 107.9, Atomic Weight of Cu = 63.55]
(A) 0.469 and 0.138
(B) 0.235 and 0.138
(C) 0.469 and 0.069
(D) 0.235 and 0.069
 
Q.35 Among the following              the compounds which can be prepared by nucleophilic substitution reaction are:
(A) III, IV, and V
(B) I, II, and VI
(C) II, IV, and VI
(D) I, III, and V
Q.38 The major product formed in the reaction of (2R,3R)-2-bromo-3-methylpentane with NaOMe is:
(A) (Z)-3-methylpent-2-ene
(B) (E)-3-methylpent-2-ene
(C) (2R,3R)-2-methoxy-3-methylpentane
(D) (2S,3R)-2-methoxy-3-methylpentane
Q.40 Hexane and heptane are completely miscible. At 25 °C, the vapor pressures of hexane and heptane are 0.198 atm and 0.06 atm, respectively. The mole fractions of hexane and heptane in the vapor phase for a solution containing 4 M hexane and 6 M heptane, respectively, are:
(A) 0.688 and 0.312
(B) 0.400 and 0.600
(C) 0.312 and 0.688
(D) 0.600 and 0.400
Q.41 The correct order of Lewis acid strengths of BF2Cl, BFClBr, BF2Br and BFBr2 is:
(A) BF2Cl > BFClBr > BF2Br > BFBr2
(B) BFBr2 > BFClBr > BF2Br > BF2Cl
(C) BF2Cl > BF2Br > BFClBr > BFBr2
(D) BFClBr > BFBr2> BF2Cl > BF2Br
 
Q.42 The correct order of increasing intensity (molar absorptivity) of the UV-visible absorption bands for the ions [Ti(H2O)6]3+, [Mn(H2O)6]2+, [CrO4]2–, and [NiCl4]2– is:
(A) [Ti(H2O)6]3+ < [Mn(H2O)6]2+ < [CrO4]2– < [NiCl4]2–
(B) [Mn(H2O)6]2+ < [Ti(H2O)6]3+ < [NiCl4]2– < [CrO4]2–
(C) [NiCl4]2– < [Ti(H2O)6]3+ < [Mn(H2O)6]2+ < [CrO4]2–
(D) [Ti(H2O)6]3+ < [NiCl4]2– < [CrO4]2– < [Mn(H2O)6]2+

Q.43 – Q.44 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

Q.43 The correct statement(s) about the concentration of Na+ and K+ ions in animal cells is/are:
(A) [K+] inside the cell > [K+] outside the cell
(B) [Na+] inside the cell > [Na+] outside the cell
(C) [Na+] inside the cell < [Na+] outside the cell
(D) [K+] inside the cell < [K+] outside the cell
Q.44 The correct statement(s) about actinides is/are:
(A) The 5f electrons of actinides are bound less tightly than the 4f electrons.
(B) The trans uranium elements are prepared artificially.
(C) All the actinides are radioactive.
(D) Actinides do not exhibit actinide contraction.

Q.45 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

 
Q.45 The number of photons emitted per nanosecond by a deuterium lamp (400 nm) having a power of 1 microwatt (rounded off to the nearest integer) is .[h = 6.626 × 10-34 kg m2 s-1; c = 3.0 × 108 m s-1]
   
Q.46 Given the initial weight of 1 mg of radioactive 60/27𝐂𝐨 (half-life = 5.27 years), the amount disintegrated in 1 year (rounded off to two decimal places) is______mg.
   
Q.47 The de Broglie wavelength of an argon atom (mass = 40 amu) traveling at a speed of 250 m s1 (rounded off to one decimal place) is __________picometers.[N = 6.022 × 1023; h = 6.626 × 10-34 kg m2 s-1]
   
Q.48 The molar absorption coefficient of a substance dissolved in cyclohexane is 1710 L mol-1 cm-1 at 500 nm. The reduction in intensity of light of the same wavelength that passes through a cell of 1 mm path length containing a 2 mmol L-1 solution (rounded off to one decimal place) is          %.

Q.49		 The fundamental vibrational frequency of 1H127I is 2309 cm-1. The force constant for this molecule (rounded off to the nearest integer) is_______________N m-1.[N = 6.022 × 1023, c = 3.0 × 108 m s1]
   
Q.50 A laser Raman spectrometer operating at 532 nm is used to record the vibrational spectrum of Cl2 having its fundamental vibration at 560 cm-1. The Stokes line corresponding to this vibration will be observed at      cm-1. (Rounded off to the nearest integer)
Q.51 The vapor pressure of toluene (Mol. Wt. = 92) is 0.13 atm at 25 °C. If 6 g of a hydrocarbon is dissolved in 92 g of toluene, the vapor pressure drops to 0.12 atm. The molar mass of the hydrocarbon (rounded off to the nearest integer) is_____.
   
Q.52 The reactionCO (g) + Cl2 (g) ⇌ COCl2 (g)at 500 °C, with initial pressures of 0.7 bar of CO and 1.0 bar of Cl2, is allowed to reach equilibrium. The partial pressure of COCl2 (g) at equilibrium is 0.15 bar. The equilibrium constant for this reaction at 500 °C (rounded off to two decimal places) is         .
   
Q.53 The rate constants for the decomposition of a molecule in the presence of oxygen are 0.237 × 10-4 L mol-1 s-1 at 0 °C and 2.64 × 10-4 L mol-1 s-1 at 25 °C(R = 8.314 J mol-1 K-1).The activation energy for this reaction (rounded off to one decimal place) is__________kJ mol-1.
   
Q.54 2 L of a gas at 1 atm pressure is reversibly heated to reach a final volume of 3.5L. The absolute value of the work done on the gas (rounded off to the nearest integer) is             Joules.
   
Q.55 The quantity of the cobalt ore [Co3(AsO4)2∙H2O] required to obtain 1 kg of cobalt (rounded off to two decimal places)  is____________kg.[Atomic Wt. of Co = 59, As = 75, O = 16, H = 1]


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 C  11 B  21 3 to 3  31 B  41 B  51 71 to 73 
2 B  2 A  12 B  22 -12.16 to -12.14  32 D  42 B  52 0.30 to 0.34 
3 C  3 C  13 B  23 3 to 3  33 B  43 A; C  53 65.0 to 66.0 
4 B  4 A  14 C  24 10800 to 10800  34 A  44 A; B; C  54 151 to 153 
5 C  5 A  15 A; C  25 3.8 to 4.0  35 C  45 2000 to 2020  55 2.50 to 2.80 
6 B  6 C  16 C; D  26 A  36 C  46 0.11 to 0.13     
7 A  7 B  17 A; C  27 B  37 B  47 39.5 to 40.5     
8 A  8 C  18 A; B; C  28 A  38 B  48 54.0 to 55.0     
9 B  9 B  19 20 to 20  29 A  39 A  49 309 to 315     
10 C  10 A  20 6 to 6  30 A  40 A  50 18225 to 18245     

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

GATE 2021 Computer Science and Information Technology 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
Gauri said that she can play the keyboard_________her sister.

(A)
as well as

(B)
as better as

(C)
as nicest as

(D)
as worse as

Q.2		 A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like .

Q.4 If (x-1/2)2 – (x-3/2)2=x+2 then the  value of

(A) 2

(B) 4

(C) 6

(D) 8


Q.5


Pen : Write :: Knife :    

Which one of the following options maintains a similar logical relation in the above?

(A)
Vegetables

(B)
Sharp

(C)
Cut

(D)
Blunt

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


Q.6
Listening to music during exercise improves exercise performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while students who did not need any external stimulation benefited from music.
Which one of the following statements is the CORRECT inference of the above passage?

(A)
Listening to music has no effect on learning and a positive effect on physical exercise.

(B)
Listening to music has a clear positive effect both on physical exercise and on learning.

(C)
Listening to music has a clear positive effect on physical exercise. Music has a positive effect on learning only in some students.

(D)
Listening to music has a clear positive effect on learning in all students. Music has a positive effect only in some students who exercise.

Q.7

A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.

Q.8
The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21.The total number of students in all the three classes in the beginning was:

(A)
22

(B)
66

(C)
88

(D)
110


Q.9
The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ` 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.
The ratio of the selling price in Year 2 to the selling price in Year 3 is .

A)
4:3

(B)
1:1

(C)
3:4

(D)
1:2

Q.10

Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.
Observation I: S is taller than R.

Observation II: Q is the shortest of all.

Observation III: U is taller than only one student.

Observation IV: T is taller than S but is not the tallest.

The number of students that are taller than R is the same as the number of students shorter than_________.

(A)
T

(B)
R

(C)
S

(D)
P
Computer Science and Information Technology (CS, Set-2)

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





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



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



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





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


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




Answer Key 

Q.No. Ans Q.No. Ans Q.No. Ans Q.No. Ans Q.No. Ans Q.No. Ans Q.No. Ans
1 A  1 C  11 B; C 21 698 to 698  31 B  41 B; C; D  51 8 to 8 
2 B  2 C  12 B; C; D  22 15.00 to 16.00  32 B  42 A; D  52 6 to 6 
3 B  3 C  13 D  23 15 to 15  33 A  43 A; B; C  53 1.87 to 1.88 
4 B  4 C  14 A; C; D  24 4 to 4  34 C  44 A; D  54 130 to 140 
5 C  5 A  15 B; D  25 19 to 19  35 D  45 B; C  55 929 to 929 
6 C  6 D  16 1 to 1  26 B  36 C  46 A; B     
7 A  7 C  17 256 to 256  27 A  37 B  47 A; B; C     
8 C  8 B  18 3 to 3  28 B  38 A  48 4108 to 4108     
9 A  9 C  19 2 to 2  29 D  39 C  49 60 to 60     
10 C  10 C  20 80000 to  80000  30 D  40 A; C; D  50 59049 to  59049     
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