IPMAT Indore · Paper 6

In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make a fruit punch. Madhu drinks 50 ml of this fruit punch and comments that the proportion of orange juice needs to be higher for better taste. How much orange juice should be poured into the fruit punch that remained, in order to bring up the level of orange juice to 50 percentage?

If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4?

A student travels from Campus A to Campus B and back through two different routes of equal length. He rides to Campus B at 45 km/h and returns at 75 km/h. What is his average speed for the entire journey?

Three friends, Aarav, Bhavna, and Chirag, start a small online stationery venture. Aarav invests ₹80,000 for 12 months, Bhavna invests ₹60,000 for 8 months, and Chirag invests some amount for 6 months. At the end of the year, the total profit is ₹1,74,000, and Chirag’s share is ₹54,000. How much did Chirag invest?

A $2 \times 2$ matrix is filled with four distinct integers randomly chosen from the set $\{1, 2, 3, 4, 5, 6\}$. Then the probability that the matrix generated in such a way is singular is

A startup models its daily net engagement score as $E=-2x^2+56x-180$, where $x$ is the number of influencer posts promoted in a day. What is the maximum possible value of $E$?

A startup founder invests ₹80,000 at 10% per annum, compounded half-yearly, for 1.5 years. What is the difference between the compound interest earned and the simple interest that would have been earned at the same annual rate for the same time?

The terms of a geometric progression are all positive. The sum of its first 3 terms is 13 and the sum of its first 6 terms is 364. What is the sum of its first 5 terms?

Read the passage and answer the question that follows.

Fruit sellers have long known that one ripe fruit can hurry along a whole basket of unripe ones, but the reason was understood only in the twentieth century. Ripening fruit gives off ethylene, a simple gas, and ethylene in turn signals nearby fruit to begin ripening. The effect feeds on itself: as more fruit ripens, more gas is released, and the whole batch speeds up. Bananas, mangoes and tomatoes respond strongly to the gas. This is why they can be picked hard and green, carried long distances, and then ripened close to the market in sealed rooms given a measured dose of ethylene. Grapes, cherries and strawberries behave differently. They do not ripen in response to the gas, and once cut from the plant they gain no further sweetness, so growers must leave them on the plant until they are ready to eat. In a storeroom, ethylene does these fruits no good and can even hasten their decay.

Which of the following can be inferred from the passage?

Choose the option that best fills both blanks.

The museum's claim that the sword had once belonged to a king rested on ________ evidence alone, a story handed down in the family of the man who sold it, and visiting historians pointed out that a cherished story, however often it is repeated, cannot ________ proof.

Read the passage and choose the word that best fills the blank.

Pilots and air traffic controllers around the world talk to one another in a deliberately narrow kind of English. Words are chosen not for elegance but because they are hard to mishear over a crackling radio: 'affirm' instead of 'yes', 'niner' instead of 'nine'. The vocabulary is small and the order of each message is fixed, so that a tired pilot whose first language is not English can still follow it. Where one misheard word can cost lives, this ________ is not a weakness of the system but its whole purpose.

The following sentences form a coherent paragraph when arranged logically. Choose the correct order.

P. This is why several student-run startups now test their ideas in weekend pop-up stalls before building full apps.

Q. However, early enthusiasm can hide whether customers will actually pay for the product.

R. Campus founders often begin with a strong personal frustration, such as long cafeteria queues or unreliable event updates.

S. The feedback from these small trials helps them revise pricing, features and delivery before spending heavily.

T. Such experiments also reduce the risk of confusing appreciation from friends with real market demand.

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

The reviewer qualified her praise of the debut novel, noting that its final chapters felt rushed and its ending unearned.

Choose the option that best fills both blanks.

Far from ________ the old reading room, the new digital archive was designed to ________ it, nudging readers who found a rare book online to come in and see the original.

Read the passage and answer the question that follows.

In some years an oak tree drops almost no acorns; in others it carpets the ground with them. What long puzzled foresters was that the oaks across a whole region tend to do this together, with bumper crops in the same autumn and lean years in between. The leading explanation is that this timing is a defence against the animals that eat seeds. In lean years, populations of mice, squirrels and jays shrink because food is scarce. When a bumper year then arrives, the reduced population of seed-eaters cannot possibly eat everything, and many acorns survive long enough to sprout. A tree that fruited heavily every year would simply feed a permanently large population of animals, and a tree that fruited on its own schedule would see its whole crop eaten. Weather seems to act as the shared signal that keeps the trees in step, although exactly how they stay in step is still debated.

Which of the following can be inferred from the passage?

Choose the option that best completes the sentence.

After eleven failed trials, the research team was ready to ________ and close the project, but a last experiment finally produced the result they had been chasing.

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

No sooner [had the referee blown the final whistle when the fans] rushed onto the field to celebrate.

Choose the sentence that best completes the paragraph.

For decades, cities measured their green cover by counting the trees they planted. The number was easy to announce and easy to grow: a single weekend drive could add ten thousand saplings. Foresters point out, however, that a sapling planted in hard roadside soil, with no one assigned to water it through its first two summers, has a poor chance of living long enough to give shade. Some cities have therefore begun to publish a different figure: the number of trees still alive three years after planting. ________

Read the passage and answer the question that follows.

Adam Smith noticed something odd. Water, without which no one can live, can usually be had for almost nothing, while diamonds, which no one needs, fetch enormous prices. For about a century the puzzle seemed to show that price has little to do with usefulness. The answer economists eventually settled on, in the 1870s, turned on a single idea: the margin. People do not choose between all the water in the world and all the diamonds in the world; they choose whether to buy one more glass or one more stone. Because water is plentiful, the next glass adds very little to anyone's well-being, so no one will pay much for it. Diamonds are scarce, so the next one is still prized. Usefulness matters, in other words, but it is the usefulness of the last unit, not of the whole supply, that sets the price. A traveller lost in a desert, with no water at all, would gladly trade a diamond for a single glass.

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

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

1. How long the bee waggles during that run adds the second piece of information: how far away the flowers are.

2. A honeybee that finds a rich patch of flowers flies home and performs a short dance on the comb; the dance includes a straight run during which the bee waggles its body.

3. Karl von Frisch, who decoded this language of movement, shared a Nobel Prize for the work in 1973.

4. The angle of that straight run, measured from the vertical, tells the other bees the direction of the flowers relative to the sun.