IPMAT Indore · Paper 5

Fifty litres of a mixture of milk and water contains 30 percent of water. This mixture is added to eighty litres of another mixture of milk and water that contains 20 percent of water. Then, how many litres of water should be added to the resulting mixture to obtain a final mixture that contains 25 percent of water?

The value of $\cos^2\frac{\pi}{8} + \cos^2\frac{3\pi}{8} + \cos^2\frac{5\pi}{8} + \cos^2\frac{7\pi}{8}$ is

The angle of elevation of the top of a pole from a point A on the ground is $30^\circ$. The angle of elevation changes to $45^\circ$ after moving 20 meters towards the base of the pole. Then the height of the pole, in meters is

A natural number $n$ lies between 100 and 400, and the sum of its digits is 10. The probability that $n$ is divisible by 4, is

Let $S_n$ be the sum of the first $n$ terms of an A.P. $\{a_n\}$. If $S_5 = S_9$, what is the ratio of $a_3 : a_5$?

In a triangle $ABC$, let $D$ be the mid-point of $BC$, and $AM$ be the altitude on $BC$. If the lengths of $AB$, $BC$ and $CA$ are in the ratio of $2:4:3$, then the ratio of the lengths of $BM$ and $AD$ would be

Choose the single word that best means: “a person who strongly believes that human actions are guided by selfish motives rather than by sincerity or goodness.”

Reading comprehension: Read the passage and choose the option that best captures its central idea. Many young brands now prefer campus pop-ups to expensive mall launches. A pop-up inside a college festival gives them a concentrated audience, instant feedback, and content for social media. However, the best outcomes come when brands treat students as collaborators rather than as a crowd to be sold to. Workshops, founder talks, and student-led product trials often create more trust than a stall that simply hands out discount coupons.

A startup incubator in Jaipur argues that it should stop funding weekend pitch competitions and instead fund three-month founder residencies. Its director says, “Pitch competitions create excitement, but most teams disappear after winning certificates. Residencies force teams to test customers, revise pricing, and build discipline. Therefore, residencies will produce more investment-ready startups than pitch competitions.” Which of the following is an assumption on which the argument depends?

A coaching centre claims that it should replace all printed handouts with a mobile app because students who used the app last term scored higher on weekly vocabulary quizzes than students who collected printed sheets. Therefore, the app itself must be the reason for the better scores. Which assumption does the argument depend on?

A coaching centre argues: “We should replace our printed weekly worksheets with a mobile practice app. Students always carry their phones, so switching to the app will make them attempt more practice questions each week.” Which assumption does the argument depend on?

Choose the sentence that best completes the paragraph. The first few months of a family-run café are often judged by daily sales, but that number can be misleading. A rainy week, a nearby road repair, or a college exam season can temporarily depress footfall. More useful indicators are repeat visits, average order value, and whether customers recommend the place without being prompted. ________