IPMAT Indore · Paper 13

$x$ varies inversely as the square of $y$. If $x = 8$ when $y = 3$, what is the value of $x$ when $y = 6$?

A man can row at 6 km/h in still water, and the river flows at 2 km/h. It takes him 3 hours in all to row downstream to a village and back to his starting point. How far away is the village?

A college recorded the applications it received and the seats it offered in three courses:

Taking the three courses together, how many applications were received per seat?

The sides of a triangle are 13 cm, 14 cm and 15 cm. What is the length of the altitude drawn to the 14 cm side?

If $2^x = 3^y = 6^{-z}$, where $x$, $y$ and $z$ are non-zero real numbers, what is the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$?

What is the domain of the real function $f(x) = \sqrt{\dfrac{x - 2}{5 - x}}$?

A number is chosen at random from the integers 1 to 100. What is the probability that it is a perfect square or a perfect cube?

What is the remainder when $17^{23} + 23^{23}$ is divided by 40?

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

Despite his wealth, he avoided ostentatious displays, driving an old car and wearing plain clothes.

Choose the option that best explains the meaning of the underlined idiom.

The huge stadium built for the games has become a white elephant: it costs crores a year to maintain but is used only twice a year.

Choose the one word that means: an extreme or irrational fear of heights.

In which of the following sentences is the underlined word used incorrectly?

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

He drove / very careful / through the crowded market / because it was raining.

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

Having worked with her for ten years, the committee entertained no doubts about her honesty.

Choose the phrasal verb that best completes the sentence.

Rather than ________ the error in the accounts, the manager admitted it openly at the meeting and explained how it would be corrected.

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

1. Rowland Hill proposed a single low charge for any letter sent within the country, paid in advance by the sender.

2. Before 1840, letters in Britain were usually paid for by the person who received them, at a price that depended on the distance travelled.

3. Proof of payment would be a small printed label stuck on the envelope, and in 1840 the Penny Black, the world's first adhesive postage stamp, went on sale.

4. Many people simply refused to accept their letters, leaving the post office with the cost of carrying them for nothing.

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

The job requires [not only patience but also being able to work] calmly under pressure.

Choose the sentence that best completes the paragraph.

Open-plan offices were sold as a way to make colleagues talk more. Walls came down, and managers expected chance conversations to spark new ideas. When researchers fitted employees at two large companies with sensors that recorded who spoke to whom, they found the opposite: after the move to open plans, face-to-face conversation fell by about two-thirds, while email and messaging rose. Surrounded by colleagues, people seemed to protect what privacy they could by putting on headphones and keeping their heads down. ________

Read the passage and answer the question that follows.

For most of its life, the desert locust is a shy, solitary grasshopper, green or sandy brown, that avoids others of its kind. After good rains, however, plants flourish and locusts breed rapidly; when the vegetation later dries out, the insects are forced together on the patches that remain. Crowding sets off a remarkable change. Experiments have shown that when the hind legs of a solitary locust are repeatedly touched, as happens when it is jostled by its neighbours, its nervous system releases a surge of serotonin. Within hours the animal begins to seek out other locusts instead of avoiding them, and over the following generations the insects turn black and yellow and grow stronger flight muscles. The result is a swarm that can stretch across hundreds of square kilometres and strip crops in whole countries.

Which of the following can be inferred from the passage?

Read the passage and answer the question that follows.

In a well-known experiment, people watched a wheel of fortune that had been rigged to stop at either 10 or 65, and were then asked what percentage of African countries belonged to the United Nations. Those who had seen 65 gave much higher estimates than those who had seen 10, though the number on the wheel plainly had nothing to do with the question. Psychologists call this anchoring: a number we meet first, even an irrelevant one, pulls our later judgements towards it. The effect is not confined to laboratories. Experienced estate agents shown the same house have valued it differently depending on the asking price they were given, and the first offer in a negotiation tends to shape where the final price ends up. For this reason, negotiators are often advised to make the first offer themselves, and to make it boldly.

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