IPMAT Indore · Paper 4

How many different numbers can be formed by using only the digits 1 and 3 which are smaller than $3000000$?

If $\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \dots$ up to $\infty = \frac{\pi^2}{6}$, then the value of $\frac{1}{1^2} + \frac{1}{3^2} + \frac{1}{5^2} + \dots$ up to $\infty$ is

In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by 150 metres, by how many metres does Bipin beat Chandan in the race?

A person standing at the center of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such walks in this pattern?

Choose the option that correctly completes both blanks. The investor’s comments did not immediately ________ the startup’s valuation, but their long-term ________ on employee morale was noticeable.

Synonyms & antonyms: Choose the word closest in meaning to “prudent” as used in this sentence: Before spending half the club budget on a celebrity speaker, the committee took a prudent decision to first estimate ticket sales.

In the sentence, “The investor passed on the proposal because the revenue forecast was built on very thin evidence,” what does “passed on” most nearly mean?

Read the passage and answer the question that follows. Many schools now run entrepreneurship clubs, but their value is often misunderstood. The point is not to turn every teenager into a company founder. Rather, these clubs create a safe space to test ideas, speak to users, handle rejection, and revise plans based on evidence. A student who learns why a stationery subscription failed may gain as much as one whose food stall makes a profit. In that sense, the club is less a mini-market and more a laboratory for judgement. What is the central idea of the passage?

Choose the option that correctly fills both blanks. The finance club’s ________ objective is to teach budgeting, but it also follows the ________ that investment advice must be transparent and responsible.

A coaching institute argues that it should replace its weekly printed handouts with a mobile practice app. The director claims this will reduce costs without hurting student performance, because most students already use smartphones and the app can deliver the same questions instantly. Which assumption is the argument most dependent on?

Idioms & phrases: Choose the meaning of the idiom in the sentence. When the sponsorship proposal was rejected twice, Aarav decided to go back to the drawing board before approaching another company.

Choose the sentence that best completes the paragraph. Many school-leavers now evaluate undergraduate business programmes not only by the brand name of the institution but also by the kind of projects they will handle in the first year. A brochure may promise “industry exposure,” but students increasingly ask whether that means shadowing a manager for a day or actually building a market-entry plan with a live client. This shift has forced colleges to describe learning outcomes more concretely. ________