IPMAT Indore · Paper 8

The data set for the number of mock tests attempted by 7 students is: 14, 22, $x$, 18, 22, 26, 16. If the mean of the data set is 20, what is the sum of its median and mode?

In a startup finance model, the determinant of the matrix $\begin{vmatrix} 2 & -1 & 3 \\ 0 & 4 & x \\ 1 & 2 & 1 \end{vmatrix}$ is 21. What is the value of $x$?

In a survey of 200 students about three study apps P, Q and R, 100 students said they use P, 90 use Q and 70 use R, while 20 students use none of the three. If 40 students use exactly two of the apps, how many students use all three?

Seven student founders are to be seated in a row for a pitch-day photograph. If Riya and Kabir must sit next to each other, in how many different ways can the seven founders be arranged?

On a coordinate map of a business park, three kiosks are located at $P(2,-1)$, $Q(6,3)$ and $R(-1,5)$. What is the area of triangle $PQR$?

The line passing through the points $(2, 5)$ and $(8, 17)$ is perpendicular to another line that passes through $(4, -3)$. What is the y-intercept of this second line?

A delivery executive covers a fixed route of 96 km every morning. If he increases his usual speed by 4 km/h, he reaches 2 hours earlier than usual. What is his usual speed?

A student-run snack stall estimates its weekly profit, in thousand rupees, as $P=-2x^2+120x-400$, where $x$ is the number of combo packs sold in hundreds. What is the maximum possible weekly profit?

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

1. The peaks were too remote for the surveyors to learn their local names, so they simply numbered them, and one was entered in the records as Peak XV.

2. The survey announced its height in 1856, and the peak was later named after a former head of the survey, George Everest.

3. Radhanath Sikdar, a mathematician in the survey's office, is credited with working through the readings for this peak and finding that it was higher than any other then known.

4. In the mid-nineteenth century, the Great Trigonometrical Survey of India was measuring Himalayan peaks from stations on the plains far below.

Read the passage and answer the question that follows.

For generations, economics textbooks used the lighthouse as the perfect example of a service that markets cannot provide. A lighthouse guides every passing ship, the argument ran, but its keeper has no way of charging the ships that benefit, so no private owner would ever build one, and the state must step in. In 1974 the economist Ronald Coase decided to check how British lighthouses had actually been paid for. He found that for long stretches of history many had been built and run by private individuals, who were allowed to collect fees, called light dues, from ships when they docked at nearby ports. The keeper could not charge a ship at sea, but the port could charge it on arrival. Coase did not claim that private provision was always better; the system depended on government permission to collect the dues. His point was narrower and more uncomfortable for his colleagues: an example repeated so often that no one thought to test it had turned out to describe a world that never quite existed.

The author refers to Coase's investigation primarily in order to

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

The nurse applied ice packs to arrest the swelling before the doctor arrived.

Choose the option that best fills both blanks.

The scientist's early papers were dismissed as ________, but later experiments ________ her claims so thoroughly that they now appear in school textbooks.

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

Neither the coach nor the players / was willing / to admit that the defeat / had been caused by poor planning.

Read the passage and answer the question that follows.

No ant in a colony has a map of where the food lies or which route to it is shortest. Yet within an hour of a crumb being found, a colony often settles on an efficient path. The trick lies in a chemical trail. An ant returning with food lays down a scent that others tend to follow, and every ant that follows it adds scent of its own. Ants on a shorter route complete more round trips in the same time, so that route gathers scent faster, while the scent on longer routes fades because it evaporates before it is renewed. Over time the shorter path wins, not because any ant compared the routes but because the arithmetic of reinforcement and decay compared them for the colony. Computer scientists have borrowed this idea to plan delivery routes and to direct data through networks, letting many simple agents find good solutions that none of them could work out alone.

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

Choose the sentence that best completes the paragraph.

Many people assume that the best way to learn a skill is to practise it in long, uninterrupted blocks: an hour of serves, then an hour of volleys. Studies of athletes and musicians suggest otherwise. When practice is mixed, with different shots or pieces taken in an unpredictable order, performance during the session is usually worse, and learners say they feel less confident. Yet when they are tested days later, the mixed group typically outperforms the group that practised in blocks. ________

Choose the word that best completes the sentence.

Years of drought had left the once-busy river town ________: its markets empty, its boats beached and most of its young people gone to the cities.

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

When the club's treasurer resigned a week before the annual audit, several members began to smell a rat.

Read the passage and answer the question that follows.

A placebo is supposed to work only if the patient is fooled. That, at least, was the assumption until researchers began running an odd kind of trial. Patients with certain long-term conditions, such as irritable bowel syndrome, were handed pills and told plainly that the pills contained no medicine at all. Some were also told that placebos can trigger the body's own responses through expectation and habit. In several such studies, those who took the honest placebos reported noticeably more relief than those who received nothing. The findings are intriguing, but they deserve care. The trials have been small, the improvements are mostly in symptoms that patients report themselves, such as pain and discomfort, and no one expects a sugar pill to shrink a tumour or cure an infection. Still, if the effect holds up in larger studies, it would suggest that the ritual of treatment, and not only its chemistry, plays a part in how people feel.

The author's attitude towards the findings on honest placebos is best described as

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

The annual rainfall in Cherrapunji is far heavier [than Jaisalmer].

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

1. He also found that reviewing a list at spaced intervals fixed it far better than the same number of repetitions crammed together.

2. In the 1880s the German psychologist Hermann Ebbinghaus set out to measure memory, using himself as the only subject.

3. Language apps that schedule a review just as a word is about to be forgotten are built on that second finding.

4. To keep meaning from helping him, he memorised long lists of nonsense syllables such as 'wid' and 'zof'.

5. He found that much of what he learnt slipped away within a day, after which forgetting slowed down sharply.