List of top Questions asked in NPAT

A shopkeeper has two varieties of rice A and B. By selling A at ₹75 per kg, he loses 20%; and by selling B at ₹90 per kg, he gains 25%. If he mixes A and B in the ratio 4 : 5 and sells the mixture at ₹110.25 per kg, then his profit percentage is:
If \( \sec \theta = a + \frac{1}{4a^2} \), \( 0^\circ<\theta<90^\circ \), then \( \csc \theta + \cot \theta = \):
Evaluate: \[ \frac{\sin \theta (1 + \tan \theta) + \cos \theta (1 + \cot \theta)}{(\cos \theta - \sin \theta)(\sec \theta - \cos \theta)(\tan \theta + \cot \theta)} \]
The income of A is \( \frac{3}{5} \) of B's income, and the expenditure of A is \( \frac{4}{5} \) of B's expenditure. If A's income is \( \frac{9}{10} \) of B's expenditure, then the ratio of savings of A and B is:
If \( 3\sin^2 x + 10\cos x - 6 = 0 \), \( 0^\circ<x<90^\circ \), then the value of \( \sec x + \cosec x + \cot x \) is:
The value of \( \left( \frac{5}{13} \cdot \frac{1}{14} + \frac{2}{25} \cdot \frac{3}{10} - \frac{7}{18} \cdot \frac{1}{35} \right) \div \left( \frac{3}{5} \cdot \frac{4}{21} \cdot \frac{2}{5} \right) \) lies between:
If \( \frac{46}{159} = \frac{1}{x} + \frac{1}{y + \frac{1}{z}} \), where \( x, y, z \) are positive integers, then the value of \( (2x + 3y - 4z) \) is:
In a class of 100 students, 55 students passed in Mathematics and 65 passed in English. Five students failed in both the subjects. Let \( m \) be the number of students who passed in exactly one of the two subjects and \( n \) be the number of students who failed in at least one subject, then what is the value of \( (m - n) \)?
Let \( f(x) = \frac{3x - 5}{2x + 1} \). If \( f^{-1}(x) = \frac{-x + a}{bx + c} \), then what is the value of \( (a - b + c) \)?
Given \( f(x) = \frac{-4x + 1}{4} \) and \( g(x) = \sqrt[3]{x} \), then \( (g \circ f^{-1})\left(\frac{3}{8}\right) = \)
X and Y are two points that are 135 m apart on the ground on either side of a pole and in the same line. The angles of elevation of a bird sitting on the top of the pole from X and Y are \( 30^\circ \) and \( 60^\circ \) respectively. The distance of Y from the foot of the pole (in m) is:
The value of \( \frac{(1 + \cot \theta - \csc \theta)(1 + \tan \theta + \sec \theta)}{\tan^2 \theta + \cot^2 \theta - \sec^2 \theta \csc^2 \theta} \) is:
Let \( A = \{1,2,5,6\}, B = \{1,2,3\} \) and \( C = (A \times B) \cap (B \times A) \). Which of the following is INCORRECT?
If \( f(2x) = \frac{2}{2 + x} \) for all \( x>0 \), and \( 5f(x) = 8 \), then what is the value of \( x \)?
Let \( U \) be the universal set, and \( A, B, C \) are the sets such that \( C \subset A \) and \( B \cap C = \emptyset \). If \( n(U) = 105 \), \( n(A) = 58 \), \( n(B) = 50 \), \( n(A \cap B) = 20 \) and \( n(A \cup C) = 32 \), then \( n(A \cup B) - n(B \cap C) \) is:
Let \( U = \{1,2,3,4,5,6,7,8,9\}, A = \{1,2,3,4\}, B = \{2,4,6,8\}, C = \{3,4,5,6\} \). The number of elements in \( A \cap C - (B - C) \), where \( A \cap C \) and \( B - C \) are the complements of \( A \cap C \) and \( B - C \), respectively is:
Given below are five sentences, labelled A, B, C, D and E. They are NOT in a meaningful order. Select the option that arranges the sentences in the correct order to form a meaningful paragraph.
A: Cells called fibroblasts from an animal are used to make sheets of skin.
B: According to a study, yarn grown from human skin cells could be woven or knitted into ‘human textiles’ for tissue grafts or organ repair.
C: Since it is made from animal cells and is not synthetic, scientists believe that it will not be rejected by the immune system of the recipient.
D: These sheets are cut into ribbons and twisted to form various forms of yarn.
E: The threads can then be used in surgery to help treat animals and humans.
Under capitalism, the argument goes, it’s every man for himself. Through the relentless pursuit of self-interest, everyone benefits, as if an invisible hand were guiding each of us toward the common good. Everyone should accordingly try to get as much as they can, not only for their goods but also for their labour. Whatever the market price is, in turn, what the buyer should pay. Just like the idea that there should be a minimum wage, the idea that there should be a maximum wage seems to undermine the very freedom that the free market is supposed to guarantee.
This view, however, has some dramatic consequences. One is the explosion in economic inequality that almost all liberal capitalist democracies have experienced over the past 30-40 years. The difference between the top and the bottom of the income distribution now lies about where it did in the Gilded Age and the roaring 1920s, up until the Great Depression. Unlike these earlier periods, however, this rise in economic inequality has not been driven by returns on capital assets. This time, one of the most important contributors to the rise has been the payment of extraordinarily high levels of compensation to corporate executives... More troubling still, while the compensation for corporate executives has been almost continually rising during this period, real (inflation-adjusted) wages for almost everybody else have been stagnating.
Many people find this upsetting but, even so, they tend to treat it as something capitalism requires us to tolerate. Others think it is something that capitalism requires us to applaud. But nothing in capitalism actually says that such sky-high levels of compensation are permissible. What capitalism says instead is that people need incentives to be maximally productive. But will someone who makes \(\$\)100 million a year really work harder than someone who makes \(\$\)10 million? Compensation, like everything else, has what economists call ‘diminishing marginal utility’. More of it has less and less of an incentivising effect, until eventually it has no incentivising effect at all – people are already working as hard as they can. At which point capitalism suggests that we should not pay someone even more money, for we are going to get nothing in return.
But wait – aren’t CEOs just getting paid the market rate for their labour? Their compensation is calculated according to a formula set when they were hired and, as long as this formula represents the going wage, then this is what they should receive. The market rate for CEO labour, however, is not set in a competitive manner. The formula is set by a special group of the company’s directors, called the ‘compensation committee’…
Next time someone hires a CEO and another compensation committee conducts a survey, the average will be higher. The market is not bidding up the price; the price is going up simply because everyone always wants to beat the current average. We have what economists call a market failure. Setting a maximum wage would therefore not interfere with market freedom because, in this instance, the market is not working.
Read the below passage and answer the questions that follow.
In a world still churning out trendy throw-away fashion pieces at breakneck speed, the idea of upcycled or refashioned apparel can be an anomaly. But it is a continuously growing trend and is one of the most sustainable things people can do in fashion. As upcycling makes use of already existing pieces, it often uses few resources in its creation and actually keeps 'unwanted' items out of the waste stream.
There are more textiles produced in the world today than can be used. And once these clothes have fulfilled their 'useful' lives they are sent to the landfill or are donated to thrift stores. This is not as beneficial as people think as only about 20 to 30 percent of donated clothing is actually re-sold. Massive amounts of donated clothing that are not deemed as 're-sellable' in the U.S. are shipped to developing countries, inundating them with unnecessary goods that stifle any emerging economic development in textiles. While many people may have the idea that they are helping clothe the poor in these countries, access to the Internet and cell phones has made many of these countries more fashion-forward recently, and they may have no interest in our American cast-offs. Since this model relies on a waste economy, what happens when exportation is no longer an option?
This is where upcycling offers an answer. Upcycling is a way of processing an item to make it better than the original. It can be done using either pre-consumer or post-consumer waste or a combination of the two. Pre-consumer waste is produced while items are being manufactured and post-consumer waste results from the finished product reaching the end of its useful life for the consumer. Upcycling stops adding stuff to a world that is already overwhelmed with material things and reuses materials in creative and innovative ways - producing original often one-of-a-kind items from what many consider to be waste. It is a way for companies and designers to be more efficient with leftover materials such as upholstery scraps or vintage textiles and to give new life to worn-out jeans and tattered T-shirts. Whether as everyday apparel or runway exhibition pieces, upcycling can challenge cultural codes - questioning what we consider to be trash versus fashion or beautiful versus ugly. For some it can also be a connection to our heritage - incorporating vintage clothing or using a family heirloom to create an original piece preserving a bit of history.

Read the passage below and answer the questions that follow.
Social media, magazines and shop windows bombard people daily with things to buy, and British consumers are buying more clothes and shoes than ever before. Online shopping means it is easy for customers to buy without thinking. Major brands offer such cheap clothes that they can be treated like disposable items. 
In Britain, the average person spends more than £1,000 on new clothes a year, which is around four per cent of their income. That might not sound like much, but that figure hides two far more worrying trends for society and for the environment: a lot of the consumer spending is via credit cards. British people currently owe approximately £670 per adult to credit card companies. Not only are people spending money they don't have, they're using it to buy things they don't need. Approximately 300,000 tons of clothing a year goes into landfill sites. Clothes donated to charities often don't sell and so are either thrown away or are sent abroad, causing economic and environmental problems.
Lately, a different trend is springing up in opposition to consumerism - the 'buy nothing' trend. It originated in Canada in the early 1990s and then moved to the US, where it became a rejection of the overspending and overconsumption of Black Friday and Cyber Monday during Thanksgiving weekend. On Buy Nothing Day people organise various types of protests and cut up their credit cards. Throughout the year, Buy Nothing groups organise the exchange and repair of items they already own.
The trend has now reached influencers on social media who usually share posts of clothing and make-up that they recommend for people to buy. Some YouTube stars now encourage their viewers not to buy anything at all for periods as long as a year. Two friends in Canada spent a year working towards buying only food. For the first three months they learned how to live without buying electrical goods, clothes or things for the house. For the next stage, they gave up services, for example haircuts, eating out at restaurants or buying petrol for their cars. In one year, they'd saved $55,000.
The changes they made meant two fewer cars on the roads, a reduction in plastic and paper packaging and a positive impact on the environment from all the energy saved. If everyone followed a similar plan, the results would be impressive. But even if you can't manage a full year without going shopping, you can participate in the anti-consumerist movement by refusing to buy things you don' t need. Buy Nothing groups send a clear message to companies that people are no longer willing to accept the environmental and human cost of overconsumption.

The following are the criteria for admitting students to an engineering college:
The student candidate must:
  1. have passed 12th standard science examination having secured more than 65% in Mathematics and at least 60% in the aggregate.
  2. be of 20 years age or more as on January 01, 2020
  3. have obtained at least 65% in the interview and more than 60% in the entrance test.
However, if a student fulfills all the above criteria, EXCEPT:
  1. at (1) and/or (2) above but has obtained at least 75% in the interview and more than 65% in the entrance test, the case should be referred to the Principal.
  2. at (2) and/or (3) above but is an SC candidate securing more than 70% in the aggregate as well as in Mathematics in 12th standard science examination, the case should be referred to the Director.
Based on the criteria given above and without assuming any additional information, you have to take a decision for the candidates whose profiles have given in the five questions. Mark your answer by choosing the appropriate option in each case.
In the figure, the triangle stands for 'hardworking'; the circle stands for 'graduate'; the rectangle stands for 'rich' and the square stands for 'employed'. The numbers in different segments show the number of persons.
'hardworking'; the circle stands for 'graduate';
Select the option that is related to the third figure in the same way as the second figure is related to the first figure.
option that is related to the third figure
Find the figure that will come next in the following figure series.
figure that will come next

If the signs ‘×’ and ‘+’ are interchanged in each of the given equations, then which one equation would be correct?