Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3, ... will be

- 164√3
- 188√3
- 248√3
- 192√3

In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?

- 27
- 28
- 26
- 25

If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be

- 93
- 26
- 23
- 96

In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

- √12
- √14
- √13
- √11

A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is

- 26
- 16
- 20
- 22

If log log_{2} (5 + log_{3} a) = 3 and log_{5} (4a + 12 + log_{2} b) = 3, then a + b is equal to

- 67
- 40
- 32
- 59

Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is

Given that x^{2018}y^{2017} = 1/2 and x^{2016}y^{2019} = 8, the value of x^{2} + y^{3} is

- 35/4
- 37/4
- 31/4
- 33/4

A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is:

- 3/6
- 3/2
- 5/2
- 1/6

1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O.

The four sentences (labelled 1, 2, 3, and 4) given in this question, when properly sequenced, form a coherent paragraph. Decide on the proper order for the sentences and key in this sequence of four numbers as your answer.

- The eventual diagnosis was skin cancer and after treatment all seemed well.
- The viola player didn’t know what it was; nor did her GP.
- Then a routine scan showed it had come back and spread to her lungs.
- It started with a lump on Cathy Perkins’ index finger.

Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out.

- Displacement in Bengal is thus not very significant in view of its magnitude.
- A factor of displacement in Bengal is the shifting course of the Ganges leading to erosion of river banks.
- The nature of displacement in Bengal makes it an interesting case study.
- Since displacement due to erosion is well spread over a long period of time, it remains invisible.
- Rapid displacement would have helped sanitize the public to its human costs.

Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out.

- In many cases time inconsistency is what prevents our going from intention to action.
- For people to continuously postpone getting their children immunized, they would need to be constantly fooled by themselves.
- In the specific case of immunization, however, it is hard to believe that time inconsistency by itself would be sufficient to make people permanently postpone the decision if they were fully cognizant of its benefits.
- In most cases, even a small cost of immunization was large enough to discourage most people.
- Not only do they have to think that they prefer to spend time going to the camp next month rather than today, they also have to believe that they will indeed go next month.

The four sentences (labelled 1,2,3,4) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the proper sequence of order of the sentences and key in this sequence of four numbers as your answer:

- But now we have another group: the unwitting enablers.
- Democracy and high levels of inequality of the kind that have come to characterize the United States are simply incompatible.
- Believing these people are working for a better world, they are, actually, at most, chipping away at the margins, making slight course corrections, ensuring the system goes on as it is, uninterrupted.
- Very rich people will always use money to maintain their political and economic power.

The passage given below is followed by four summaries. Choose the option that best captures the author’s position.

The conceptualization of landscape as a geometric object first occurred in Europe and is historically related to the European conceptualization of the organism, particularly the human body, as a geometric object with parts having a rational, three-dimensional organization and integration. The European idea of landscape appeared before the science of landscape emerged, and it is no coincidence that Renaissance artists such as Leonardo da Vinci, who studied the structure of the human body, also facilitated an understanding of the structure of landscape. Landscape which had been a subordinate background to religious or historical narratives, became an independent genre or subject of art by the end of sixteenth century or the beginning of the seventeenth century.

- Landscape became a major subject of art at the turn of the sixteenth century.
- The three-dimensional understanding of the organism in Europe led to a similar approach towards the understanding of landscape.
- The study of landscape as an independent genre was aided by the Renaissance artists.
- The Renaissance artists were responsible for the study of landscape as a subject of art.

The passage given below is followed by four summaries. Choose the option that best captures the author’s position.

Artificial embryo twinning is a relatively low-tech way to make clones. As the name suggests, this technique mimics the natural process that creates identical twins. In nature, twins form very early in development when the embryo splits in two. Twinning happens in the first days after egg and sperm join, while the embryo is made of just a small number of unspecialized cells. Each half of the embryo continues dividing on its own, ultimately developing into separate, complete individuals. Since they developed from the same fertilized egg, the resulting individuals are genetically identical.

- Artificial embryo twinning is low-tech and mimetic of the natural development of genetically identical twins from the embryo after fertilization.
- Artificial embryo twinning is low-tech unlike the natural development of identical twins from the embryo after fertilization.
- Artificial embryo twinning is just like the natural development of twins, where during fertilization twins are formed.
- Artificial embryo twinning is low-tech and is close to the natural development of twins where the embryo splits into two identical twins.

The passage given below is followed by four summaries. Choose the option that best captures the author’s position.

Production and legitimation of scientific knowledge can be approached from a number of perspectives. To study knowledge production from the sociology of professions perspective would mean a focus on the institutionalization of a body of knowledge. The professions approach informed earlier research on managerial occupation, business schools and management knowledge. It however tends to reify institutional power structures in its understanding of the links between knowledge and authority. Knowledge production is restricted in the perspective to the selected members of the professional community, most notably to the university faculties and professional colleges. Power is understood as a negative mechanism, which prevents the non-professional actors from offering their ideas and information as legitimate knowledge.

- Professions-approach aims at the institutionalization of knowledge but restricts knowledge production as a function of a select few.
- The study of knowledge production can be done through many perspectives.
- Professions-approach focuses on the creation of institutions of higher education and disciplines to promote knowledge production.
- The professions-approach has been one of the most relied upon perspective in the study of management knowledge production.

The four sentences (labelled 1, 2, 3, and 4) given in this question, when properly sequenced, form a coherent paragraph. Decide on the proper order for the sentences and key in this sequence of four numbers as your answer.

- The woodland’s canopy receives most of the sunlight that falls on the trees.
- Swifts do not confine themselves to woodlands, but hunt wherever there are insects in the air.
- With their streamlined bodies, swifts are agile flyers, ideally adapted to twisting and turning through the air as they chase flying insects - the creatures that form their staple diet.
- Hundreds of thousands of insects fly in the sunshine up above the canopy, some falling prey to swifts and swallows.

The four sentences (labelled 1,2,3,4) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the proper sequence of order of the sentences and key in this sequence of four numbers as your answer:

- Impartiality and objectivity are fiendishly difficult concepts that can cause all sorts of injustices even if transparently implemented.
- It encourages us into bubbles of people we know and like, while blinding us to different perspectives, but the deeper problem of ‘transparency’ lies in the words “…and much more”.
- Twitter’s website says that “tweets you are likely to care about most will show up first in your timeline…based on accounts you interact with most, tweets you engage with, and much more.”
- We are only told some of the basic principles, and we can’t see the algorithm itself, making it hard for citizens to analyze the system sensibly or fairly or be convinced of its impartiality and objectivity.

[The] Indian government [has] announced an international competition to design a National War Memorial in New Delhi, to honour all of the Indian soldiers who served in the various wars and counter-insurgency campaigns from 1947 onwards. The terms of the competition also specified that the new structure would be built adjacent to the India Gate – a memorial to the Indian soldiers who died in the First World War. Between the old imperialist memorial and the proposed nationalist one, India’s contribution to the Second World War is airbrushed out of existence.

Economists have spent most of the 20th century ignoring psychology, positive or otherwise. But today there is a great deal of emphasis on how happiness can shape global economies, or — on a smaller scale — successful business practice. This is driven, in part, by a trend in "measuring" positive emotions, mostly so they can be optimized. Neuroscientists, for example, claim to be able to locate specific emotions, such as happiness or disappointment, in particular areas of the brain. Wearable technologies, such as Spire, offer data-driven advice on how to reduce stress.

When researchers at Emory University in Atlanta trained mice to fear the smell of almonds (by pairing it with electric shocks), they found, to their consternation, that both the children and grandchildren of these mice were spontaneously afraid of the same smell. That is not supposed to happen. Generations of schoolchildren have been taught that the inheritance of acquired characteristics is impossible. A mouse should not be born with something its parents have learned during their lifetimes, any more than a mouse that loses its tail in an accident should give birth to tailless mice. . . .

The only thing worse than being lied to is not knowing you’re being lied to. It’s true that plastic pollution is a huge problem, of planetary proportions. And it’s true we could all do more to reduce our plastic footprint. The lie is that blame for the plastic problem is wasteful consumers and that changing our individual habits will fix it.

Recycling plastic is to saving the Earth what hammering a nail is to halting a falling skyscraper. You struggle to find a place to do it and feel pleased when you succeed. But your effort is wholly inadequate and distracts from the real problem of why the building is collapsing in the first place. The real problem is that single-use plastic - the very idea of producing plastic items like grocery bags, which we use for an average of 12 minutes but can persist in the environment for half a millennium - is an incredibly reckless abuse of technology. Encouraging individuals to recycle more will never solve the problem of a massive production of single-use plastic that should have been avoided in the first place.

"Everybody pretty much agrees that the relationship between elephants and people has dramatically changed,” [says psychologist Gay] Bradshaw. . . . "Where for centuries humans and elephants lived in relatively peaceful coexistence, there is now hostility and violence. Now, I use the term ‘violence’ because of the intentionality associated with it, both in the aggression of humans and, at times, the recently observed behavior of elephants.” . . .

Typically, elephant researchers have cited, as a cause of aggression, the high levels of testosterone in newly matured male elephants or the competition for land and resources between elephants and humans. But. . . Bradshaw and several colleagues argue. . . that today’s elephant populations are suffering from a form of chronic stress, a kind of specieswide trauma. Decades of poaching and culling and habitat loss, they claim, have so disrupted the intricate web of familial and societal relations by which young elephants have traditionally been raised in the wild, and by which established elephant herds are governed, that what we are now witnessing is nothing less than a precipitous collapse of elephant culture. . . .

If n is any odd number greater than 1, then n(n^{2} - 1) is

- divisible by 24 always
- divisible by 96 always
- divisible by 48 always
- None of these

Let N = 55^{3} + 17^{3} - 72^{3}. N is divisible by

- both 3 and 17
- both 7 and 13
- both 3 and 13
- both 17 and 7

After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number?

- 53
- 75
- 41
- 80

When 2^{256} is divided by 17, the remainder would be

- 1
- 14
- 16
- None of these

What will be remainder when (67^{67} + 67) is divided by 68?

- 67
- 63
- 66
- 1

Find the minimum integral value of n such that the division 55n/124 leaves no remainder

- 124
- 123
- 31
- 62

Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals

- 7
- 5
- 9
- 3

Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?

- 0
- 9
- 6
- 3

On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5?

- 0
- 1
- 2
- 4

What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?

- 676
- 777
- 683
- 666

The remainder obtained when a prime number greater than 6 is divided by 6 is

- 1 or 3
- 1 or 5
- 3 or 5
- 4 or 5

The remainder when 7^{84} is divided by 342 is

- 0
- 1
- 49
- 341

The smallest number which when divided by 4, 6 or 7 leaves a remainder of 2, is

- 86
- 80
- 62
- 44

What is the remainder when 4^{96} is divided by 6?

- 0
- 2
- 3
- 4

If x = (16^{3} + 17^{3} + 18^{3} + 19^{3}), then x divided by 70 leaves a remainder of

- 0
- 1
- 35
- 69

Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12, and 16 is 4.

- 137
- 140
- 172
- 1361

What is the greatest number which exactly divides 110, 154 and 242?

What is the highest 3 digit number which is exactly divisible by 3, 5, 6 and 7?

A man earns x% on the first Rs. 2,000 and y% on the rest of his income. If he earns Rs. 700 from income of Rs. 4,000 and Rs. 900 from if his income is Rs. 5,000, find x%.

- 10%
- 15%
- 20%
- 25%

How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

- 4 years
- 4.5 years
- 5 years
- 5.5 years

A certain sum of money invested at some rate of simple interest triple itself in 4 years. In how many years the principal will become 9 times of itself at the same rate?

In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having either cable TV or VCR?

- 23/30
- 2/3
- 17/30
- 19/30

In a certain village, 22% of the families own agricultural land, 18% own a mobile phone and 1600 families own both agricultural land and a mobile phone. If 68% of the families neither own agricultural land nor a mobile phone, then the total number of families living in the village is

- 20000
- 10000
- 8000
- 5000

A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?

- 6666666
- 6666600
- 6666660
- 6666000