IPMAT Indore · Paper 11

In a class, 40% of the students are girls. If 25% of the girls and 50% of the boys are members of the chess club, what percentage of the whole class is in the chess club?

Ravi can type a project report in 10 hours and Sneha can type it in 15 hours. They start typing it together, but Ravi leaves after 3 hours and Sneha finishes the rest alone. For how many hours in all does Sneha type?

What is the units digit of $7^{86} + 3^{87}$?

Given $\log_{10} 2 = 0.3010$, how many digits does $2^{50}$ have when written out in full?

What is the distance between the parallel lines $3x + 4y = 7$ and $6x + 8y + 11 = 0$?

Three students, Asha, Bilal and Chitra, try a puzzle independently. Their chances of solving it are $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{4}$ respectively. What is the probability that exactly one of them solves it?

$A$ is a $3 \times 3$ matrix with $\det A = 3$. What is the value of $\det(2\,\text{adj}\,A)$?

The sum of the first $n$ terms of a sequence is $S_n = 3n^2 + 5n$ for every $n$. What is its 12th term?

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

The auditor was meticulous, checking every receipt against the ledger twice before signing the report.

Choose the one word that means: a person appointed to carry out the instructions in someone's will.

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

After months of not speaking to each other over the boundary wall, the two neighbours finally decided to bury the hatchet.

Choose the word that correctly completes the sentence.

The doctor warned that skipping meals for weeks could seriously ________ his concentration during the examinations.

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

The list of items / that the committee approved / for the new laboratory / were sent to the supplier on Monday.

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

The witness gave a sober account of the accident, sticking to what she had seen and adding no drama of her own.

Choose the option that best fills both blanks.

Critics had expected the sequel to be a ________ copy of the first film, but the director surprised them with a story so ________ that it barely resembled the original.

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

1. Each tin is marked with a short code of colours and numbers that tells the carriers where it starts, which station it goes to and which building it must reach.

2. Every working day, Mumbai's dabbawalas carry around two lakh home-cooked lunches from homes to offices across the city.

3. Remarkably, most of the carriers have little formal schooling, yet the system is famous for how rarely a lunch goes astray.

4. With nothing more than this code, the tins are sorted and re-sorted several times at railway stations along the way.

Read the passage and answer the question that follows.

Mapmaking is slow and expensive, while copying a finished map is quick and cheap. To protect their work, some mapmakers have quietly added features that do not exist: a short dead-end lane, a bend in a river, even a whole village. These 'trap streets' do little harm to most users, who are unlikely ever to look for them, but if one turns up on a rival's map, it is strong evidence that the rival copied rather than surveyed. The best-known case is Agloe, a hamlet invented for a road map of New York State in the 1930s. Years later it appeared on a competitor's map, and a copying dispute followed. The rival's defence was unexpected: by then someone had built a general store at the spot and named it after the town on the map, so Agloe could now be said to exist.

Which of the following can be inferred from the passage?

Choose the sentence that best completes the paragraph.

Most of us assume that offering more choices makes customers happier. A well-known experiment in a supermarket suggests otherwise. On one day, shoppers passing a tasting stall were offered 24 flavours of jam; on another day, only 6. The larger display drew more people to the stall, but far fewer of them went on to buy a jar. Faced with two dozen similar options, many shoppers seem to have found the decision so tiring that they put it off altogether. ________

Read the passage and answer the question that follows.

During British rule in Delhi, the story goes, officials worried about the number of cobras in the city offered a reward for every dead snake brought to them. At first the scheme seemed to work, as dead cobras arrived in large numbers. Then some residents began breeding cobras simply to kill them and collect the reward. When the officials discovered this and cancelled the scheme, the breeders released their now worthless snakes, and the city ended up with more cobras than before. Whether or not every detail is true, economists use the tale to name a common trap, the 'cobra effect'. A reward attached to a measurable result invites people to produce that result in the cheapest way available, which may have little to do with the goal the reward was meant to serve. A target for the number of cases a police station closes, for instance, can push officers to close cases rather than solve them.

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

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

[Having finished the assignment late at night, the laptop was switched off by Neha before she went to bed.]