IPMAT Indore · Paper 15

Arjun and Bina start a business with ₹45,000 and ₹30,000 respectively. After 4 months, Arjun withdraws ₹15,000 of his capital. At the end of the year, the profit is ₹26,000. What is Bina's share of the profit?

Walking at $\frac{4}{5}$ of his usual speed, Kunal reaches his office 12 minutes late. How long does his usual walk to the office take?

How many of the positive factors of 720 are even?

A kite is flying at a height of 60 m above level ground. Its string is pulled tight and makes an angle of $60^\circ$ with the ground. Assuming the string is straight, what is its length?

What is the maximum value of $Z = 3x + 2y$ subject to the constraints $x + y \le 4$, $x \le 3$, $x \ge 0$ and $y \ge 0$?

What is the sum of all the real roots of the equation $|x - 2|^2 + |x - 2| - 6 = 0$?

A farmer has 120 m of fencing to enclose a rectangular plot beside a long straight wall. The wall forms one side of the plot, and the fencing is used for the other three sides. What is the largest area he can enclose?

In how many ways can 10 identical chocolates be distributed among 4 children so that every child gets at least 1 chocolate and no child gets more than 4?

Choose the word closest in meaning to the underlined word as used in the sentence.

The benevolent landlord let the struggling family stay rent-free through the winter.

Choose the word most nearly opposite in meaning to the underlined word as used in the sentence.

The prize went to an obscure poet whose books had sold only a few hundred copies.

Choose the one word that means: a place where bees are kept.

Choose the option that best explains the meaning of the underlined phrasal verb.

Talks between the union and the management broke down after the two sides could not agree on wages, and the strike continued.

Identify the part of the sentence that contains a grammatical error.

The prize money / will be shared equally / between the two winners, / Anil and I.

In the sentence below, choose the meaning of the underlined word as used in context.

She wrote in a spare style, using no word that was not needed and no image that did not earn its place.

Choose the word that best completes the sentence.

The case against him was only ________: no one had actually seen him at the scene, though his car had been parked nearby that night.

The sentences given below, when properly sequenced, form a coherent paragraph. Choose the most logical order.

1. Over the next twenty years he learnt how to insulate his cargo and how to create demand, giving away cold drinks until customers were hooked.

2. By the 1830s, packed in sawdust and stored in specially built ice houses, his ice was surviving voyages of four months, all the way to Calcutta.

3. In the early 1800s, a Boston businessman named Frederic Tudor had what most people thought a foolish idea: cutting ice from frozen ponds and shipping it to hot countries.

4. In 1806 he sent his first cargo to the Caribbean island of Martinique, where much of it melted and the islanders had little idea what to do with the rest.

Choose the option that best replaces the part in square brackets.

After the long drive, the doctor advised him to [lay down for an hour] before eating anything.

Choose the sentence that best completes the paragraph.

Violins made by Antonio Stradivari three centuries ago sell for millions, and many players insist that no modern instrument can match their tone. Researchers decided to test the claim. They asked experienced violinists to play a mix of old Italian violins and good modern ones while wearing goggles that hid which was which. Most players could not reliably tell the old instruments from the new, and when asked which violin they would most like to take home, a majority chose a modern one. ________

Read the passage and answer the question that follows.

Across large parts of Mizoram, the hills are covered with a single species of bamboo that flowers only about once every fifty years. When it does, almost every plant across the region flowers at the same time, produces a heavy crop of fruit, and then dies. The sudden feast is a windfall for black rats. Well fed, they breed far faster than usual, and their numbers explode. Once the bamboo fruit is gone, the hungry rats move into the fields and granaries of nearby villages and devour the rice and other crops. The flowering of the late 1950s was followed by a famine, and anger at the slow official response fed a long insurgency in the region. When the bamboo flowered again in 2006 and 2007, the state prepared in advance, offering rewards for rats killed and encouraging farmers to grow crops that rats are less fond of.

Which of the following can be inferred from the passage?

Read the passage and answer the question that follows.

Analysing the finishing times of nearly ten million marathon runners, a team of economists found something odd. Finishing times are not spread smoothly. Instead, they bunch up just before round numbers: far more runners finish in 3 hours 59 minutes than in 4 hours 1 minute, and similar bunching appears just before 3 hours, 3 hours 30 minutes and 4 hours 30 minutes. Nothing about the human body makes four hours special. What makes it special is that runners treat it as a target. Those who see the round number slipping away in the final kilometres speed up to beat it, while those who will clearly miss it have less reason to push. Researchers have reported the same pattern in other settings where people chase round figures. An arbitrary number, once it is chosen as a goal, can change how hard people try.

Which of the following best expresses the main idea of the passage?