List of practice Questions

The figure shows a circle of diameter AB and radius 6.5 cm. If chord CA is 5 cm long, find the area of triangle ∆ABC.

A, S, M, and D are functions of \( x \) and \( y \), and they are defined as follows: \[ A(x, y) = x + y, \quad S(x, y) = x - y \] \[ M(x, y) = x \cdot y, \quad D(x, y) = \frac{x}{y}, \quad y \neq 0 \] What is the value of \( M(M(A(M(x, y), S(x, y)), D(x, y)), A(x, y)) \) for \( x = 2 \), \( y = 3 \)?

A wooden box (open at the top) of thickness 0.5 cm, length 21 cm, width 11 cm, and height 6 cm is painted on the inside. The expenses of painting are Rs. 70. What is the rate of painting per square centimetre?

From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.

A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?

If ABCD is a square and BCE is an equilateral triangle, what is the measure of \( \angle DEC \)?

In a locality, there are five small cities: A, B, C, D, and E. The distances of these cities from each other are as follows. AB = 2 km; AC = 2 km; AD>2 km; AE>3 km; BC = 2 km; BD = 4 km; BE = 3 km; CD = 2 km; CE = 3 km; DE>3 km. If a ration shop is to be set up within 3 km of each city, how many ration shops will be required?

Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?

Evidence has been presented that the unconscious mind, still viewed by many psychological scientists as the shadow of a ‘‘real’’ conscious mind, is identifiably more deliberate, action oriented and complex than its conscious counterpart. Furthermore researchers have proven that the mind is incredibly efficient at extracting meaning from stimuli of which one is not consciously aware. The claims above are made on conclusive experimentations in which test subjects who were allowed to sleep during a decision making process made more optimal decisions when compared to the subjects who were given the exact same amount of information but were not allowed to sleep, leading researchers to believe that rationality comes on the way of making a rational decision. Researchers explain that while the conscious mind can only follow strict rules, unconscious mind can handle and integrate a larger amount of information, explaining why it can make better decisions. Even more surprising than this unconscious mind’s ability is that the mental processes that drive such decision making are necessarily minimal and unsophisticated and do not require humongous amount of calories to make us arrive at the best decision whereas using conscious mind for complex decisions burns up a lot of energy, setting in fatigue, forcing the conscious mind to give up and leading to subconscious decisions. Overall, researchers agree that there is no need to have sleepless night pondering over a complex issue to resolve it when it can actually be solved more efficiently by snoring the night away.
(A) highlight the differences among psychologists regarding the importance of the unconscious mind in making complex decisions.
(B) contrast and compare the workings of the rationality with that of deliberate, action-oriented, and complex decision-making processes.
(C) prove that the unconscious mind is more effective than the conscious mind in complex decision-making.
(D) show that conscious mind is not that undependable as previously thought.
(E) ascertain that using conscious and unconscious minds together yield second-to-none judgements.

French cuisine is highly regarded all over the world. Yet in Paris there are more American restaurants selling burgers and fries (which many people now class as junk food) than there are in any other European capital city. Obviously the French are very fond of junk food, and are not too proud to eat it. Which of the following, if true, would most weaken the author’s contention? (A) There are also a larger number of Lebanese restaurants in Paris than there are in other European capital cities.
(B) French Cordon Bleu cuisine is very expensive.
(C) The number of French tourists eating in New York burger restaurants is very low.
(D) Junk food actually has high nutritional value when eaten in moderation.
(E) There are an unusually large number of American tourists in Paris who eat at burger joints.

In research designed to investigate the possibility of animals developing friendship with other, unrelated, members of their species, a group of 29 chimpanzees were reared together for 15 years. At the end of that time the chimps were presented with two options for obtaining food: press a lever and feed themselves, or press another identical lever and feed themselves, and at the same time deliver food to the chimp next door. (The chimps were able to see each other). The researchers found that the chimps were no more likely to choose the lever that fed a neighbour. The researchers concluded that the chimps had no concept of friendship. However, one critic has suggested that the animals were in an artificial environment from which little can be concluded, and that, at the least, the test ought to have involved the animals being able to touch.
What role do the parts in boldface play in the argument above?
(A) The first is a position that the critic opposes. The second is a position that the critic supports.
(B) The first is an observation that supports the researcher’s position. The second is an observation that opposes the researcher’s position.
(C) The first is a finding on which the researchers base their conclusion. The second is a suggestion that might cast doubt on that finding.
(D) The first is an observation that supports the critic’s conclusion. The second is the critic’s conclusion.
(E) The first is part of the evidence that the critic disputes. The second is a suggestion that the researchers do not accept.

A number of sentences are given below which, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. However, one of the statements is illogically placed. Choose the illogically placed sentence from among the five given choices so that the remaining four can construct a coherent paragraph.
A. It is turning off the tap.
B. And with no consensus of the exit policy, the government is damned if it supports loss-making units and damned if it doesn’t.
C. The private sector did the same in the past because securing legal sanction for closure was virtually impossible.
D. After sûrement years of funding the losses of public sector companies, the government is doing the unthinkable.
E. Private sector and public sector companies act in a similar fashion when in crisis.

A number of sentences are given below which, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. However, one of the statements is illogically placed. Choose the illogically placed sentence from among the five given choices so that the remaining four can construct a coherent paragraph.
A. Trade protocols were signed, the dollar as the medium of exchange was ignored, trade was denominated in rupees and the exchange rate between the two countries was to be fixed outside the ambit of free markets.
B. A young India, some years after independence fashioning her foreign policy of nonalignment, found it prudent to stay close to the former Soviet Union.
C. Therefore it led to the escalation of cold war between Soviet Union and the U.S.A.
D. Once upon a time there was a superpower named Soviet Union that attracted nations apprehensive of the global aspirations of the other superpower, the U.S.A.
E. One way of doing this was to evolve a bilateral relations in trade that could be called upon provide a buffer against the arm-twisting by the U.S.A

A number of sentences are given below which, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. However, one of the statements is illogically placed. Choose the illogically placed sentence from among the five given choices so that the remaining four can construct a coherent paragraph.
A. There are also a larger number of Lebanese restaurants in Paris than there are in other European capital cities
B. French Cordon Bleu cuisine is very expensive
C. The number of French tourists eating in New York burger restaurants is very low
D. Junk food is actually has high nutritional value when eaten in moderation
E. There are an unusually large number of American tourists in Paris who eat at burger joints

Arrange the sentences A, B, C, and D to form a logical sequence between sentences 1 and 6.
1. Amount of published information available varies widely by industry.
A. Unfortunately for the researcher, many industries do not meet these criteria, and there may be little published information available.
B. Generally, the problem the researcher will face in using published data for analysing an economically meaningful industry is that they are too broad or too arranged to fit the industry.
C. However, it is always possible to gain some important information about an industry from published sources and these sources should be aggressively pursued.
D. Larger the industry, the older it is, and the slower the rate of technological change, better is the available published information.
6. If a researcher starts a searching for data with this reality in mind, the uselessness of broad data will be better recognized and the tendency to give up will be avoided.

Arrange the sentences A, B, C, and D to form a logical sequence between sentences 1 and 6.
1. The main source of power in industrial undertaking is electricity.
A. Electricity from water also requires enormous river valley projects involving huge expenditure.
B. In contrast, electricity from atomic power stations will result in a tremendous saving in expenditure.
C. Besides, the mineral resources of the world required for generation of electricity are being rapidly depleted.
D. But the production of electricity needs huge quantities of coal.
6. The installation of atomic plants will help in meeting the shortage of these resources.

Arrange the sentences A, B, C, and D to form a logical sequence between sentences 1 and 6.
1. Intensity of competition in an industry is neither a matter of coincidence nor bad luck.
A. The collective strength of these forces determines the ultimate profit potential in the industry where profit potential is measured in terms of long run returns on invested capital.
B. Rather, competition in an industry is rooted in its underlying economic structure and goes well beyond the behavior of current competitors.
C. Not all industries have the same potential.
D. Beyond the behavior of current competitors, there are five basic competitive forces which determine the intensity of competition in an industry.
6. Different industries can sustain different levels of profitability depending upon these forces.

A shopkeeper allows a discount of 10% on the marked price of an article and still makes a profit of 20%. If the marked price is Rs. 200, what is the cost price?

If \( \sin \theta + \cos \theta = \sqrt{2} \), then what is the value of \( \theta \) (in degrees)?

A man invests Rs. 10,000 at 5% per annum compound interest for 3 years. What is the amount he receives at the end of 3 years?