IPMAT Indore · Paper 10

A college canteen recorded its sales of three items, in ₹ thousand, for two months:

Tea: April 40, May 50

Sandwiches: April 60, May 66

Juice: April 50, May 44

By what percentage did the canteen's total sales of these three items change from April to May?

The point $P$ divides the line segment joining $A(2, -3)$ and $B(8, 9)$ internally in the ratio $1 : 2$. What is the distance of $P$ from the origin?

The present ages of Naina and Kabir are in the ratio $5 : 7$. After 12 years, their ages will be in the ratio $7 : 9$. What is the sum of their present ages?

Two chords $AB$ and $CD$ of a circle cut each other at a point $P$ inside the circle. If $AP = 6$ cm, $PB = 8$ cm and $CD = 16$ cm, what is the length of the shorter of the two parts $CP$ and $PD$?

The roots of the quadratic equation $2x^2 - 7x + 3 = 0$ are $\alpha$ and $\beta$. What is the value of $\alpha^2 + \beta^2$?

Two inlet pipes can fill a hostel's empty water tank in 12 hours and 15 hours respectively, and an outlet pipe can empty the full tank in 20 hours. With the tank empty, all three pipes are opened together, and after 4 hours the outlet pipe is closed. How many hours in all does it take for the tank to be filled?

Solve for $x$: $\log_2(x - 3) + \log_2(x + 1) = 5$.

A radio show will play 6 different songs and 3 different advertisements, one at a time. The show must begin with a song, and no two advertisements may be played one right after the other. In how many different orders can the show be arranged?

Read the passage and answer the question that follows.

English spelling is notorious for words like 'knight', in which the 'k' and the 'gh' are silent and the vowel is not the one the letter suggests. The oddity is a fossil. When English spelling began to settle, after printing arrived in England in the late fifteenth century, the 'k' in 'knight' was still pronounced, and the 'gh' stood for a throaty sound like the one at the end of the Scottish 'loch'. Over the next two centuries, however, English vowels kept shifting, and several consonants fell silent. Spelling did not follow. Printers, and later the makers of dictionaries, had every reason to keep spellings stable, since fixed spellings made books easier to set, read and sell. The result is a written language that records, in many words, how English sounded some five hundred years ago. Reformers have proposed spelling words as they are spoken today, but they face an awkward problem: speech keeps changing, so a spelling fitted to today's sounds would drift out of date as well.

Which of the following can be inferred from the passage?

Choose the option that best fills both blanks.

The new bridge was meant to ________ the old ferry route, but so many commuters still prefer the boat that the ferry service has, if anything, ________.

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

1. Some ancient civilisations, such as the Babylonians and the Maya, used a mark to show an empty place in a number, much as we write the 0 in 205.

2. Brahmagupta, writing in 628 CE, set down rules for adding, subtracting and multiplying with it, so that zero could take part in calculations like any other number.

3. Those rules travelled through scholars writing in Arabic to Europe, where, along with the Indian numerals, they eventually transformed bookkeeping and science.

4. What Indian mathematicians did, by the seventh century, was go further and treat zero as a number in its own right.

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

The committee found the explanation specious: it sounded convincing at first but fell apart under closer scrutiny.

Read the conversation and choose the option that best fills the blank.

Meera: The printer on our floor has jammed again, and I need forty copies of the agenda before the eleven o'clock meeting.

Arun: The one near the lift was working an hour ago.

Meera: ________

Arun: In that case, let's email the agenda to everyone and print copies only for the visitors.

Read the passage and answer the question that follows.

Imagine being offered a bet on a coin toss: lose ₹100 if it lands tails, win ₹150 if it lands heads. On average you would come out ahead, yet most people turn it down. Psychologists who have run versions of this test find that a loss typically weighs on people about twice as heavily as a gain of the same size. This loss aversion shapes behaviour well beyond betting. Consider a shop that charges card users ₹102 and cash users ₹100. It can describe the gap as a ₹2 surcharge for paying by card or as a ₹2 discount for paying cash. The money is identical, but the surcharge feels like a loss, and customers tend to resent it far more than a missing discount. For the same reason, investors often hold on to falling shares much longer than they should, because selling would turn a loss on paper into a real one.

Which of the following situations best illustrates loss aversion as the passage describes it?

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

Ravi [is knowing the answer] but is too shy to raise his hand.

Choose the option that best completes the sentence.

The two late payments turned out to be only the ________; an audit later uncovered debts of over ₹4 crore that had been hidden for years.

Choose the word that best completes the sentence.

Unlike her ________ predecessor, who announced every minor decision at a press conference, the new director preferred to work quietly and let the results speak.

Choose the sentence that best completes the paragraph.

When a bakery chain began printing calorie counts on its menu boards, customers' orders changed less than its managers had feared. The bigger change happened in the kitchen. Faced with having to display that a muffin contained 600 calories, the chain quietly made its muffins smaller and cut some of the butter. Researchers studying menu labels have found a similar pattern elsewhere: the effect on what customers choose is often modest, while the effect on what companies sell can be considerable. ________

Read the passage and answer the question that follows.

City birds do not sing quite like their country cousins. Researchers recording great tits in European cities found that urban males tend to sing with a higher lowest note than males in forests. The likely reason is traffic. The low rumble of engines overlaps with the lower notes of birdsong, so a bird that shifts its song upwards is more likely to be heard by rivals and potential mates. Some birds also sing louder in noisy places, and a few species in busy areas have been found singing more at night, when the streets are quieter. These adjustments come at a price. Higher notes carry less well through dense vegetation, and studies of some species suggest that females prefer lower songs, which may signal a larger, healthier male. A bird that changes its tune to be heard may, in other words, be heard as a less attractive singer. Noise, it seems, does not merely annoy wildlife; it reshapes how animals communicate, sometimes at a real cost.

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. As the water retreated, fishing towns found themselves stranded far from the shore, and winds lifted salt and dust from the exposed lakebed.

2. The Aral Sea, on the border of Kazakhstan and Uzbekistan, was once the fourth-largest lake in the world.

3. A dam built later across its northern part has let that section recover somewhat, but most of the old lake is gone for good.

4. Deprived of most of its inflow, the lake began to shrink, and within a few decades it had split into separate, much smaller bodies of water.

5. From the 1960s, engineers diverted the two rivers that fed it to irrigate vast cotton fields in the surrounding desert.