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The number of positive integers which divide (1890)*(130)*(170) and are not divisible by 45 is ____________.
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The sum up to 10 terms of the series 1.3 + 5.7 + 9.11 + ... is ____________
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It is given that the sequence $${x_{n}}$$ satisfies $$x_{1} = 0, x_{n+1} = x_{n} + 1 + 2\sqrt{1+ x_{n}}$$ for 𝑛 = 1, 2, ..... Then $$x_{31}$$ is ______________.
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There are 5 parallel lines on the plane. On the same plane, there are n other lines which are perpendicular to the 5 parallel lines. If the number of distinct rectangles formed by these lines is 360, what is the value of n?
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There are two taps, T1 and T2, at the bottom of a water tank, either or both of which may be opened to empty the water tank, each at a constant rate. If T1 is opened keeping T2 closed, the water tank (initially full) becomes empty in half an hour. If both T1 and T2 are kept open, the water tank (initially full) becomes empty in 20 minutes. Then, the time (in minutes) it takes for the water tank (initially full) to become empty if T2 is opened while T1 is closed is ____________.
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A class consists of 30 students. Each of them has registered for 5 courses. Each course instructor conducts an exam of 200 marks. The average percentage marks of all 30 students across all courses they have registered for is 80%. Two of them apply for revaluation in a course. If none of their marks reduce, and the average of all 30 students across all courses becomes 80.02%, the maximum possible increase in marks for either of the 2 students is
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What is the minimum number of weights which enable us to weigh any integer number of grams of gold from 1 to 100 on a standard balance with two pans? (Weights can be placed only on the left pan.)
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If one of the lines given by the equation $$2x^{2} + axy + 3y^{2} = 0$$ coincides with one of those given by $$2x^{2} + bxy — 3𝑦^{2} = 0$$, and the other lines represented by them are perpendicular then $$a^{2} + b^{2}$$ is .
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If a function f(a) = max (a, 0) then the smallest integer value of x for which the equation f(x — 3) + 2𝑓(x + 1) = 8 holds true is _______________.
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In a class, 60% and 68% of students passed their Physics and Mathematics examinations respectively. Then at least ___________percentage of students passed both their Physics and Mathematics examinations.
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Suppose that a real-valued function f(x) of real numbers satisfies f(x + xy) = f(x) + f(xy) for all real x, y, and that f(2020) = 1. Compute f(2021)
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Suppose that $$\log_{2} [\log_{3}(\log_{4}a)] = \log_{3} [\log_{4} (\log_{2}b)] = \log_{4} [\log_{2} (\log_{3}c)] = 0$$. Then the value of a + b + c is
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Let $$S_{n}$$ be sum of the first n terms of an A.P. If $$S_{5} = S_{9}$$, what is the ratio of $$a_3:a_5$$
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If A, B and A + B are non-singular matrices and AB = BA, then $$2A — B — A(A + B)^{−1}A + B(A + B)^{−1}B$$ equals
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If the angles A, B,C of a triangle are in arithmetic progression such that $$\sin(2A + B) = 1/2$$ then $$\sin(B + 2C)$$ is equal to
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The unit digit in $$(743)^{85} −(525)^{37} + (987)^{96}$$ IS ________
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The set of all real values of p for which the equation $$3 \sin^{2}x + 12 \cos x - 3 = p$$ has at least one solution is
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ABCD is a quadrilateral whose diagonals AC and BD intersect at O. If triangles AOB and COD have areas 4 and 9 respectively, then the minimum area that ABCD can have is
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The highest possible value of the ratio of a four digit number and the sum of its four digits is:
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Consider the polynomials $$f(x) = ax^{2} + bx + c$$, where a > 0, b, c are real, and g(x) = -2x. If f(x) cuts the x-axis at (-2,0) and g(x) passes through (a, b), then the minimum value of f(x) + 9a + 1 is
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In a city, 50% of the population can speak in exactly one language among Hindi, English and Tamil, while 40% of the population can speak in at least two of these three languages. Moreover, the number of people who cannot speak in any of these three languages is twice the number of people who can speak in all these three languages. If 52% of the population can speak in Hindi and 25% of the population can speak exactly in one language among English and Tamil, then the percentage of the population who can speak in Hindi and in exactly one more language among English and Tamil is _______________.
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A train left point A at 12 noon. Two hours later, another train started from point A in the same direction. It overtook the first train at 8 PM. It is known that the sum of the speeds of the two trains is 140 km/hr. Then, at what time would the second train overtake the first train, if instead the second train had started from point A in the same direction 5 hours after the first train? Assume that both the trains travel at constant speeds.
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The number of 5-digit numbers consisting of distinct digits that can be formed such that only odd digits occur at odd places is
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There are 10 points in the plane, of which 5 points are collinear and no three among the remaining are collinear. Then the number of distinct straight lines that can be formed out of these 10 points is
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The x-intercept of the line that passes through the intersection of the lines x + 2y = 4 and 2x + 3y = 6, and is perpendicular to the line 3x — y = 2 is
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In a football tournament six teams A, B, C, D, E and F participated. Every pair of teams had exactly one match among them. For any team, a win fetches 2 points, a draw fetches 1 point, and a loss fetches no points. Both the teams E and F ended with less than 5 points. At the end of the tournament points table is as follows (some of the entries are not shown):
It is known that: (1) Team B defeated Team C, and (2) Team C defeated Team D.
Total number of matches ending in draw is
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Which team had highest number of draws?
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Total points Team F got was
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Which team was not defeated by Team A?
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Team E was defeated by
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Read the following passage and choose the answer that is closest to each of the questions that are based on the passage.
From ancient Rome up to the Victorian era, a training in logic and rhetoric was meant to help privileged young men recognise spurious arguments and facts. Times have changed, but contemporary Italy is determined that its youth are prepared, as their ancient counterparts were, to engage meaningfully with the present-day version of the Forum — social media. At the end of October, 8,000 Italian schools will teach their students how to spot fake news through a programme developed with the help of journalists as well as tech giants Google and Facebook. In Israel, the University of Haifa is launching a course titled “Fake News”.
The purpose of these courses is to ensure that public debate, particularly during election campaigns, is not hijacked by vested interests. Since the US presidential election in 2016, the spectre of Russia and its use of online propaganda has loomed large over public discourse in the West. In other parts of the world too, doctored images and blatant lies have been published by “news” websites. Given the speed with which information is shared online, the damage is already done by the time a fake story is exposed. The voters of tomorrow certainly need to be armed with the ability to sift bare facts from motivated fiction. The effects of social media on the formation of opinion, however, go far beyond fake news.
Traditional or legacy media is ordered by a need for balance. A newspaper, for example, has sections that deal with politics, crime, sports, the arts et al. There is, at least in principle, an attempt to tell both sides of a story in each report. On social media, the only editor is the user herself. Algorithms ensure that people see more of what they “like”, that biases are reinforced rather than countered. Fake news is certainly a crucial aspect of online propaganda. But for young citizens to form opinions based on multiple viewpoints, they need to consciously seek out more than they are comfortable with.
The writer of the passage suggests that
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The passage points out that an important difference between traditional media and social media is that
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Social media is dangerous in its ability to influence opinion in readers through
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‘Vested interests’ (Para 2) means
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The antonym for ‘spurious’ (Para 1) is
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The writer of the passage calls social media ‘the present-day version of the Roman Forum’ because it is a space for
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Complete the following sentences by choosing the appropriate word/phrase from the options given below
The impatient and intolerant mother made every effort to_______
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To avoid the ecological issues, scientists and government agencies consider how sustainable development_________
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I now have more productive time during the day because I keep the office gossips_____.
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We need to cut down on our expenses, so that we are able to _________.
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A portion of the house collapsed because the contractor __________ and built it with very poor quality materials.
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Our team has won every single match that they have played since January. They seem to be __________.
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Choose the alternative so that the underlined part of the sentence is rendered correct.
Other politicians may have claims to seniority over their peers, based upon their accomplishments and their ability to lead campaigns, but Alexandria Ocasio-Cortez, who is often described as merely being a junior member of the House of Representatives, has an unparalleled seniority over all of them by virtue of her prowess in social media management.
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Although the coastal city of Kundapur was once home to a flourishing maritime trade, their economy has been dependent in more recent years on the cotton textile and sugar industries.
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Due to the progress in the field of modern medicine and advances in nutrition and hygiene, less people die every year from infectious diseases then ever before.
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Each of the paragraphs given below has a sentence missing which is indicated by a blank. From the choices given below each paragraph, choose the sentence that seems most logically appropriate to complete the paragraph.
Captive breeding has helped revive wildlife such as the Eurasian beaver, the cheetah and the Arabian Onyx. Several species have been reintroduced into locations in order that the ecological balance is restored. When herbivorous bandicoots were set free in the wild, they dug the ground and redistributed dry leaves and branches, reducing the chance of bush fires. But some predators may overhunt or threaten other vulnerable species. _____________
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Postponed from last year, the Tokyo Olympics are set to begin this year. The locals are wary, the athletes are anxious, training sessions are truncated, and restrictions are extensive._____________
Yet Japan, in many ways is seen as a safe choice, because of its past experience of hosting big events. It has an impeccable reputation for discipline and the ability to deliver the goods.
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The sentences below have words that are missing. Choose the best option from those given below to complete the sentence.
When we think about listening, we tend to assume that it is basically the same as hearing; this is a ___________ because it leads us to believe that effective listening is ______. As a result, we make little effort to learn, or develop listening skills and thereby ______ a vital communication function.
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As vaccination rates rise and governments relax their pandemic ___________. The recovery of the event ecosystem is happening faster than expected. Event management __________ see the number of events and event attendance reaching and potentially ________ pre-pandemic levels in 2019.
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This __________, ________man was actually the ___________ manager the company ever had.
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The best strategy to give an ___________ is to deliver it orally as well as in ___________ . It is also important to the ___________ employee's achievements in the same manner.
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The Aravalli range is the oldest ___________ geological feature anywhere in the world. These were once tall mountains, possibly as high as the Himalayas. Over hundreds of millions of years these tall mountains have been___________ to low hills and ridges. Yet, these diminutive hills have been ___________ to many important events in Indian history.
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One of the statements below contains a word used incorrectly. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly. Choose the option which has the incorrect or inappropriate usage of the word.
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The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided, for e.g., 1234.
(1) In the past, companies with international aspirations simply familiarised themselves with any differences in the legal system or in the procedures used in the day-to-day business of import and export.
(2) Modern trade, however, demands more from companies.
(3) Today, the company seeking international success must also understand the people who live and work in countries they deal with, how they think, behave and do business.
(4) To succeed in today’s global market place, it is essential to learn as much as possible about the conditions in overseas markets.
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The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided, for e.g., 1234.
(1) It mentions a video on TikTok that questioned an influencer’s possible views on the Israel-Palestine crisis.
(2) Social media has given us the expectation that every video, every tweet needs to be irreproachable and encompass the lived experiences of the audience.
(3) Should celebs always have a take, asks an article in a magazine.
(4) “Do you guys even care about the issue or do you care about influencers caring about the issue?”
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The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided, for e.g., 1234.
(1) In a recent incident, villagers in a tea estate were shocked to find a leopard cub in a trench.
(2) The cub was then taken to the area where she was discovered and reunited with her mother.
(3) The 12,500 leopards in India stray into villages due to their shrinking habitat.
(4) The wildlife vet examined and declared it to be uninjured but dehydrated.
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