IPMAT Indore · Paper 7

A startup founder numbers the pages of her pitch deck from 1 to 375. How many times does the digit ‘7’ appear in all the page numbers?

A 180 m long metro train is moving at 54 km/h. Another 220 m long train is moving towards it on a parallel track at 36 km/h. How long will the two trains take to completely cross each other?

A circular logo on a startup’s stall has diameter 14 cm. From a point P outside the logo, the distance to the centre of the circle is 25 cm. What is the length of the tangent drawn from P to the circle?

A conical flask with base radius 10 cm and height 24 cm is completely full of water. All of this water is poured into an empty cylindrical jar of base radius 8 cm, which is tall enough not to overflow. A solid metal ball of radius 6 cm is then lowered into the jar and rests on the bottom, fully under water. What is the height of the water in the jar now?

A college consulting club must select a 4-member team from 6 analytics students and 5 strategy students. The team must have at least 2 analytics students. Also, two specific strategy students, Meera and Tara, cannot both be selected together. How many teams are possible?

Find the remainder left when the number $3^{100} + 4^{100}$ is divided by 13.

A campus merchandise seller buys hoodies at cost price and marks them up by 60%. During a fest sale, he gives a 20% discount on the marked price and then an additional 10% discount on the reduced price. If he still makes a profit of ₹2,280, what was his cost price?

From a balcony 15 m above level ground, the angle of elevation of the top of a mobile tower across the road is $60^\circ$, and the angle of depression of the foot of the tower is $30^\circ$. What is the height of the tower?

Read the passage and answer the question that follows.

In 1912 Alfred Wegener argued that the continents had once been joined and had slowly drifted apart. His evidence was varied and, in hindsight, persuasive: the coastlines of South America and Africa fit together like the torn halves of a page, fossils of the same reptiles turn up on both sides of the Atlantic, and rocks of the same age and type line up across oceans. Yet most geologists rejected the idea for almost half a century. Their main objection was not to his evidence but to his mechanism. Wegener could not say what force was strong enough to push whole continents across the solid ocean floor, and the forces he did propose were shown to be far too weak. Only in the 1960s, when maps of the sea floor revealed new crust forming along ocean ridges, did a mechanism emerge, and drift was absorbed into the theory of plate tectonics. Wegener's story is often told as the tale of a genius ignored, but it may say more about how science works: a pattern without a cause tends to be treated as a coincidence until the cause is found.

The author's main purpose in the passage is to

Choose the word that best completes the sentence.

The committee's report was so ________ that even supporters of the project could not say what, exactly, it recommended.

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

1. Instead, he rolled a sheet of paper into a tight tube, placed one end on her chest and listened at the other.

2. He soon replaced the paper with a wooden cylinder, and the stethoscope was born.

3. In 1816 a French doctor, René Laennec, was asked to examine a young woman with symptoms of heart disease.

4. To his surprise, her heartbeat came through more clearly than it ever had through his bare ear.

5. Pressing an ear directly to a patient's chest was the usual method, but he felt it would be improper here.

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

The new manager wanted the team to arrive on time, to keep their desks tidy and [that they should reply to every email within a day].

Read the passage and answer the question that follows.

Managers who want to shorten queues usually reach for the obvious tools: more counters, faster staff, better software. Researchers who study waiting point out that customers do not experience a queue in minutes alone. Several findings keep recurring. Time spent with nothing to do feels longer than the same time spent occupied, which is why lift lobbies often have mirrors and why some restaurants hand menus to people still waiting for a table. A wait of unknown length feels longer than one whose length has been announced. And a wait that seems unfair, as when a later arrival is served first, can anger people far more than a long but orderly one. None of this means that real delays do not matter. It means that two queues of identical length can leave customers feeling very differently about the place where they have just waited.

Which of the following can be inferred from the passage?

Choose the phrasal verb that best completes the sentence.

The company decided to ________ its paper invoices over two years rather than abolish them overnight, so that older customers would have time to switch to email.

Choose the sentence that best completes the paragraph.

When a new campus is planned, architects usually draw the footpaths first and expect people to keep to them. People rarely do. Within months, narrow brown trails appear across the lawns, cutting corners and joining doorways the designers never thought to connect. Planners call these trails desire lines, and for years they treated them as damage to be fenced off. Some campuses now do the opposite: they leave a new lawn unpaved for a year, watch where the trails form, and only then lay the paths. ________

Choose the option that best fills both blanks.

Although the drug performed well in early trials, regulators remained ________, insisting that a larger study was needed before the results could be called ________.

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

My grandfather is living / in the same small town / since he retired / from the railways in 1998.

Read the passage and answer the question that follows.

Travellers to western India often mistake a stepwell for a ruined palace. Long flights of stone steps descend, storey by storey, to a pool far below the ground, and the walls are lined with carved pillars, galleries and niches for deities. The design was not decorative excess. In a region where most rain falls in a few months and the water table drops steadily through the dry season, a well had to reach water that kept sinking. The steps let people follow it down, and the deep, shaded shaft kept the water cool and slowed evaporation. Because women in particular came daily to draw water, many stepwells also became places to rest and meet, which helps explain why their builders lavished so much ornament on them. Their decline in the colonial period is sometimes blamed on changing taste, but a more prosaic cause was the arrival of piped water and pumps, which made the long climb unnecessary and left many stepwells to silt up.

As used in the passage, the word 'prosaic' most nearly means

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

The professor's laconic reply, a single 'Possibly' where the student had hoped for a page of comments, was typical of a man who never used two words when one would do.

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

1. Its real effect, though, was less on ships than on geography, as cheap transport let factories move far from the customers they served.

2. A ship could spend as long tied up in port as it did at sea, and theft and breakage were routine.

3. Until the 1950s, cargo was loaded onto ships piece by piece: sacks, barrels and crates carried aboard by teams of dock workers.

4. The steel shipping container changed this by turning thousands of odd-shaped items into a single box that a crane could lift in minutes.