IPMAT Indore · Paper 9

For a market research project, Kabir and Tara were paid a total of ₹15,500. Kabir worked for 5 days and Tara worked for 8 days. Kabir’s efficiency is 1.5 times Tara’s efficiency. If wages are shared in proportion to the actual work done, what is Tara’s share?

Let $f(x) = \frac{4x + 7}{3x - 4}$ for every real number $x \neq \frac{4}{3}$. What is the value of $f(f(f(2)))$?

How many integers $x$ satisfy the inequality $|x - 3| + |x + 2| < 11$?

For a campus analytics dashboard, two matrices are defined as $A=\begin{bmatrix}2&-1\\3&4\end{bmatrix}$ and $B=\begin{bmatrix}1&5\\2&-3\end{bmatrix}$. If $C=AB$, what is the sum of all the elements of matrix $C$?

Dev and Ria initially have funds in the ratio $5 : 4$ for a campus pop-up event. Their total fund is ₹1,80,000. Dev transfers some money to Ria, after which their funds are in the ratio $7 : 8$. How much money does Ria have after the transfer?

In a 240 m race, Ishan beats Kabir by 24 m. Kabir beats Manav by 6 seconds in the same race. If Kabir runs at a speed of 8 m/s, by how many seconds does Ishan beat Manav?

A café blends two kinds of coffee beans that cost ₹400 per kg and ₹700 per kg. It sells the blend at ₹600 per kg and makes a profit of 20% on its cost. How many kg of the cheaper beans go into the blend for every 18 kg of the costlier beans?

A sells a bicycle to B at a profit of 20%. B sells it to C at a loss of 10%. If C paid ₹4,752 for the bicycle, how much did A pay for it?

Choose the option that best fills both blanks.

The documentary was praised for its ________ portrayal of village life, which neither romanticised poverty nor ________ the people it filmed.

Read the passage and answer the question that follows.

Ask people how a video call reaches another continent and many will point upwards, to satellites. In fact, almost all the data that crosses oceans travels along the sea floor, through cables often no thicker than a garden hose. Inside them, pulses of light race down hair-thin strands of glass, and a single modern cable can carry far more data than any satellite. Satellites still matter for ships, aircraft and remote places that no cable reaches, but they carry much less traffic and cost more for each unit of data they deliver. The cables have weaknesses of their own. Most damage comes not from sabotage but from the ordinary business of the sea: trawlers dragging fishing nets and ships dropping anchors break cables many times every year. Repair ships are kept on standby for this reason, and countries that depend on one or two cable routes are considered far more exposed than those served by many.

Which of the following can be inferred from the passage?

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

1. When a student sat alone, the smoke was usually reported within a few minutes.

2. The researchers concluded that people in a group look to one another to judge whether something is an emergency, and a calm face is easily mistaken for proof that all is well.

3. In a well-known experiment, students filling in a questionnaire saw smoke begin to seep into the room through a wall vent.

4. Put the same kind of student in a room with two strangers who had been told to ignore the smoke, and the reports mostly stopped.

Choose the option that best explains the meaning of the underlined phrasal verb.

The new evidence did not bear out the detective's theory, so the investigation had to start afresh.

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

[Walking through the old market, the smell of spices] reminded her of her grandmother's kitchen.

Read the passage and answer the question that follows.

Before the railways, every town kept its own time. Noon was simply the moment the sun stood highest over the town, so a clock in a western town ran several minutes behind one in a town to its east. No one minded, because no one travelled fast enough to notice. The railways changed that. A timetable listing departures in a dozen different local times was a recipe for missed connections and, worse, for collisions on single-track lines. Railway companies began to run their trains on a single standard time, and towns along the lines gradually set their public clocks to match. Some resisted. A few public clocks were given two minute hands, one for local time and one for 'railway time', as if unwilling to concede that the sun no longer had the final say. Within a few decades, however, the standard had won, and the idea that a clock should follow the sky above it came to seem quaint.

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

Choose the sentence that best fills the blank in the paragraph.

Cities often respond to traffic jams by building more lanes. ________ Within a few years, however, the new road is as crowded as the old one, because the extra space has drawn in trips that people previously chose not to make, or made at other times. Transport planners call this induced demand, and it is why some cities now manage roads by pricing them or by giving buses priority rather than by widening them alone.

Choose the word that best completes the sentence.

During the water shortage, residents were asked to ________ from using garden hoses until the reservoir levels recovered.

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

1. Their patent, granted in 1952, was decades ahead of its time, because the lasers and cheap computers needed to read such a code did not yet exist.

2. Today barcodes are scanned billions of times a day, though the two inventors earned little from the system that made their idea famous.

3. Silver and his friend Joseph Woodland took up the problem, and Woodland, tracing lines in the sand on a beach, hit upon the idea of a code made of bars.

4. In 1948 a graduate student named Bernard Silver overheard a supermarket executive asking a college dean to find a way of reading product details automatically at the checkout.

5. Only in 1974 did a cashier in Ohio scan the first product carrying a Universal Product Code, a packet of chewing gum.

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

The mediator's conciliatory tone eased the tension in the room, and both sides agreed to meet again the next morning.

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

Many critics believe / that the director's first film / is superior than / everything he has made since.

Read the passage and answer the question that follows.

When wolves were returned to Yellowstone National Park in 1995, after an absence of about seventy years, the results seemed to tell a perfect story. Wolves hunted elk, the story went, and frightened elk stopped lingering by rivers, so willows and aspens grew back along the banks, beavers returned, and even the shape of the rivers changed. Ecologists call this kind of chain a trophic cascade, and a short video retelling it has been watched many millions of times. The researchers who actually measure willows and count elk are more hesitant. Elk numbers also fell because of hunting by people outside the park, drought and a growing population of bears. Willow recovery has been patchy, strong in some places and absent in others, and where beavers had long disappeared, streams had cut so deep that new willows could not reach the water. None of this means the wolves made no difference. It means that a tidy story about one animal saving an ecosystem is easier to tell than the messier one the evidence supports.

The author's attitude towards the popular account of the wolves' return is best described as