Question:
The number of rectangles that you can find on a chessboard is
The number of rectangles that you can find on a chessboard is
Updated On: Oct 1, 2024
- 1764
- 1600
- 1825
- 1296
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct option is (D): 1296
Explanation: Total number of squares in a chessboard= \(∑_1^n\)\((n)^2\)
and total number of rectangles in chessboard=\(C_2^{n+1} \times C_2^{n+1}\)
So, number of rectangles = \(C_2^{9} \times C_2^{9}\)\(=36\times36=1296\)
\(\therefore \) Total no. of rectangles in the chess board= 1296
Was this answer helpful?
0
0
Top Questions on Geometry
- ABCD is a rectangle where points C and D have coordinates (−2, 0) and (2, 0), respectively. If the area of the rectangle is 24, what is the best way to describe the equation of the line AB?
- The points A(4, -2, 1), B(7, -4, 7), C(2, -5, 10), and D(-1, -3, 4) are the vertices of a:
- The coordinates of the foot of perpendicular from the point \( (2, 3) \) on the line \( y = 3x + 4 \) is given by:
- If A, B, C, D are the angles of a quadrilateral, then \[ \frac{\tan A + \tan B + \tan C + \tan D}{\cot A + \cot B + \cot C + \cot D} = \]
- In a square, the lengths of the diagonals are $(4k + 6)$ cm and $(7k - 3)$ cm. What is the area of the square (in cm²)?
View More Questions
Questions Asked in MAT exam
- Read the following passage carefully and answer the questions that follow.
Amid the sharp rise in NPA, talks of setting up a ‘bad’ bank have been gaining momentum. The government and the RBI are drawing up strategies on how to operationalise such a scheme. The economic survey of 2016-17 pointed out the twin balance sheet problem — stressed companies on one hand and NPA-laden banks on the other — and advocated a centralised Public Sector Asset Rehabilitation Agency (PARA) be established to deal with the bad loans problem.
“Private Asset Reconstruction Companies (ARCs) haven’t proved any more successful than banks in resolving bad debts,” the economic survey had said while proposing the ‘bad’ bank. “But international experience shows that a professionally-run central agency with government backing — while not without its own difficulties — can overcome the difficulties that have impeded progress,” it added.
One challenge private sector ARCs face is that of capital. None of the entities till now has been allowed to tap the capital market for raising funds. Kotak Mahindra Bank, which recently took its board’s approval to raise Rs. 5,300 crore equity said the bank also wanted to capitalise on opportunities in acquisition and resolution of stressed assets in the banking sector including participation in a ‘bad’ bank. Kotak Mahindra Prime and Kotak Mahindra Investments, companies in the Kotak Mahindra Group are sponsors of the asset reconstruction company Phoenix and together own 49% stake in it. “The ARCs are badly capitalised. We see significant opportunity for Kotak in this,” Mr. Kotak said adding the country would need 2-3 well-capitalised ‘bad’ banks. Some central bank as well as government officials also admitted capital was the biggest challenge in setting up a ‘bad’ bank. “At least Rs. 25,000 to Rs. 30,000 crore of capital will be required to set up a bad bank in the initial stages. Where will the money come from?” asked a senior central bank official.- MAT - 2022
- Reading Comprehension
- Read the following passage carefully and answer the questions that follow.
E-pharmacies, which operate through websites or smartphone apps on the Internet, offer medicines for sale at a discount of at least 20% when compared to traditional pharmacists, with the added convenience of home delivery of medicines to one’s doorstep. For scheduled drugs, patients can submit photographs of prescriptions while placing orders. Despite operating in India for at least four years now, the legal status of these e-pharmacies is not clear because the government is yet to notify into law draft rules that it published in 2018. The fiercest opponents of e-pharmacies are trade associations of existing pharmacists and chemists. They argue that their livelihoods are threatened by venture capital backed e-pharmacies and that jobs of thousands are on the line. Apart from these obvious arguments, these trade associations also spin imaginary tales of how e-pharmacies will open the door to drug abuse and also the sale of sub-standard or counterfeit drugs, thereby threatening public health. There is enough evidence on record to demonstrate how existing pharmacies contribute generously to drug abuse and sale of sub-standard medicine. There is no reason to suspect that e-pharmacies are going to worsen the situation in anyway. The more prudent way of looking at the entry of e-pharmacies is competition and the resultant effect it will have on lowering the price of medicine for Indian patients. Viewed from this perspective, there is virtually no doubt that e-pharmacies should be allowed to operate because the history of India’s trade associations of pharmacists is one of rampant, unabashed cartelisation that has resulted in an artificial inflation of medicine prices. This practice of two competitors colluding to fix the sale price and area of operation is called cartelisation, and is illegal under India’s Competition Act. The premise of this law is that a free market is efficient only if all sellers are competing with each other to offer the lowest price to the customer.- MAT - 2022
- Reading Comprehension
- Read the following passage carefully and answer the questions that follow:
The rapid industrial development in Malaysia has created significant industrial waste pollution problems that need immediate attention. Domestic waste and industrial waste are discharged unto surface water through the sewage systems. In some cases, industrial waste is released directly unto surface water.
On land, the release of industrial waste is closely controlled. However, offshore oil and manganese extraction lead to direct discharge of pollutants into the seas. Radioactive waste is dumped at sea in large concrete barrels to decay. Often, the barrels will start to have defects after a while. Representatives of factories often ship waste onto sea to dump it illegally because it is very expensive to have their water purified. Oil is released into the sea through oil tankers and shipwrecks and pesticides are applied to water to control aquatic pests. Paints on boats will decay during long trips on the ocean and will eventually end up in the water. The effects of pollutants are noticed mostly in small inland seas and lakes. This is because the oceans have a natural dilution system for incoming pollutants whereas lakes have no effective outlet. The pollutants can exist in water in different states. They can be dissolved or they can be in suspension, which means that they exist in the form of droplets or particles. These pollutants can travel farthest when they are in solution in a river that is fast flowing. High-rate microbial processes have been studied in recent years in the attempt to develop cost-effective and yet, full-scale waste treatment technologies. Management of industrial waste is a growing concern in Malaysia. The waste if improperly segregated or disposed off can lead to dangerous results. Therefore, the proper management of such toxic and hazardous waste requires discipline, vigilance and at times, just common sense.- MAT - 2022
- Reading Comprehension
- Read the following passage carefully and answer the questions that follow.
In a recent discussion paper, NITI Aayog has chalked out an ambitious strategy for India to become an artificial intelligence (AI) powerhouse. AI is the use of computers to make decisions that are normally made by humans. Many forms of AI surround Indians already, including chatbots on retail websites and programs that flag fraudulent bank activity. But NITI Aayog envisions AI solutions for India on a scale not seen anywhere in the world today, especially in five key sectors — agriculture, healthcare, education, smart cities and infrastructure, and transport. In agriculture, for example, machines will provide information to farmers on the quality of soil, when to sow, where to spray herbicide, and when to expect pest infestations. It’s an idea with great potential: India has 30 million farmers with smartphones, but poor extension services. If computers help agricultural universities advise farmers on best practices, India could see a farming revolution.
However, there are formidable obstacles. AI start-ups already offer some solutions, but the challenge lies in scaling these to cover the entire value chain, as NITI Aayog envisions. The first problem is data. Machine learning, the set of technologies used to create AI, is a data-guzzling monster. It takes reams of historical data as input, identifies the relationships among data elements, and makes predictions. More sophisticated forms of machine learning, like “deep learning,” attempt to mimic the human brain. And even though they promise greater accuracy, they also need more data than what is required by traditional machine learning. Unfortunately, India has sparse data in sectors like agriculture, and this is already hampering AI-based businesses today.
In fact, the lack of data means that deep learning doesn’t work for all companies in India. One example is Climate-Connect, a Delhi-based firm, which uses AI to predict the amount of power a solar plant will generate every 15 minutes. This is critical because solar electricity generation can change dramatically every hour depending on weather conditions and the position of the sun.
When this happens, the plant must communicate expected changes to power distributors, which will then switch to alternative sources.
With India planning to install 100 GW of solar power by 2022, such AI will play a central role in power planning.
But to generate such data, Climate-Connect needs historical inputs like the time of sunrise and sunset, and cloud cover where the plant is located. Unfortunately, since most Indian solar plants are recent, data are available only for a couple of years, whereas deep learning needs data over many years to predict generation. Today, the firm uses traditional machine learning technologies such as regression analysis that work with less data. These methods have an accuracy of around 95%. While deep learning can boost accuracy for operations such as Climate-Connect, it hasn’t worked very well in the Indian scenario, says Nitin Tanwar, cofounder of the firm.
Another problem for AI firms today is finding the right people. NITI Aayog’s report has bleak news: only about 50 Indian scientists carry out ”serious research” and they are concentrated in elite institutions such as the Indian Institutes of Technology and the Indian Institutes of Science. Meanwhile,only about 4% of AI professionals have worked in emerging technologies like deep learning. A survey of LinkedIn found 386 out ofthe 22,000 people with PhDs in AI across the world to be Indians. How does this skill gap impact companies? To some extent, open libraries of machine learning code, which can be customised to solve Indian problems, help. This means that companies need not write code from scratch, and even computer science graduates can carry out the customisation.- MAT - 2022
- Reading Comprehension
- Read the following passage carefully and answer the questions that follow.
The Reserve Bank of India’s annual report for 2017-18 reveals that 99.3% of currency notes that were demonetised at midnight on November 8, 2016 have returned to the banking system. This is only marginally higher than its provisional estimate last year that over 99% — or Rs.15.28 lakh crore worth of the old Rs.500 and Rs.1,000 notes — out of the Rs.15.44 lakh crore that were in circulation at the time had been deposited by June 30, 2017. This makes a couple of things crystal clear. First, the hope that a large chunk of unaccounted money would not return to the system — arguably, the principal reason for the exercise — was almost wholly belied. As a result, the plan to transfer the arising surplus from the RBI to the Centre, which was not formally declared but strongly rumoured, was a non-starter. Second, given the sheer logistical difficulty in penalising all those who converted unaccounted money into legal tender, demonetisation worked as an unintended amnesty scheme. Despite the significant cost to the economy, demonetisation, to the disappointment of the Prime Minister’s critics, had no political fallout. Narendra Modi succeeded in portraying the move as one that would knock out the corrupt rich — a harsh but necessary shock therapy. This was perhaps why the massive disruption caused by the overnight removal of 86% of the currency in value terms did not cause agitations.
Nevertheless, the RBI report, which points to a spurt in counterfeiting of the new Rs.500 and Rs.2,000 notes, raises the old question all over again. Was it worth the slowdown in growth, the damage to informal sector supply chains, and job losses in sectors such as construction that were the bulwark of employment creation for the unskilled? True, there have been some benefits. For instance, the number of income tax returns filed has surged a little over the trend growth rate. But surely this could have been achieved by other policy measures. Cashless modes of payment have become more common, but financial savings in the form of currency have also risen, suggesting that people still value cash. Not all policy choices work out and accepting mistakes or planning flaws helps strengthen governance processes. For example, learning from the UPA’s mistakes, a cleaner auction process for natural resources has been worked out. The government must not disown its biggest reform attempt or try to sidestep parliamentary scrutiny of the outcomes of demonetisation. Instead, it could focus on fixing the problems that people still face — transactions with Rs.2,000 notes in the absence of Rs.1,000 notes are difficult as it is a departure from the currency denomination principle every note should be twice or two and a half times its preceding denomination). Even as these issues are sorted out, the larger lesson must be heeded: sudden shocks to the economy don’t always yield intended policy objectives.- MAT - 2022
- Reading Comprehension
View More Questions