IPMAT Indore · Paper 3

A circle touches the $y$-axis at $(0, 4)$ and passes through the point $(-2, 0)$. Then the radius of the circle is

If $\log_4 x = a$ and $\log_{25} x = b$, then $\log_x 10$ is

Ashok started a business with a certain investment. After a few months, Bharat joined him investing half amount of Ashok's initial investment. At the end of the first year, the total profit was divided between them in ratio $3:1$. Bharat joined Ashok after

Let $A(1, 3)$ and $B(5, 1)$ be two points. If a line with slope $m$ intersects $AB$ at an angle of $45^\circ$, then the possible values of $m$ are

Consider the following statements:

(i) When $0 < x < 1$, then $\frac{1}{1+x} < 1 - x + x^2$

(ii) When $0 < x < 1$, then $\frac{1}{1+x} > 1 - x + x^2$

(iii) When $-1 < x < 0$, then $\frac{1}{1+x} < 1 - x + x^2$

(iv) When $-1 < x < 0$, then $\frac{1}{1+x} > 1 - x + x^2$

Then the correct statements are

In a given village there are only three sizes of families: families with 2 members, families with 4 members and families with 6 members. The proportion of families with 2, 4 and 6 members are roughly equal. A poll is conducted in this village wherein a person is chosen at random and asked about his/her family size. The average family size computed by sampling 1000 such persons from the village would be closest to

Choose the option that is closest in meaning to the word “prudent” as used in the sentence: “A prudent entrepreneur keeps enough cash aside before launching a second outlet.”

In the sentence below, choose the meaning of the underlined word in context. “The admissions team found Rhea’s portfolio impressive, but they asked her to substantiate the revenue numbers claimed in her pitch deck.”

The founder’s apology sounded sincere, but the board asked for a more ________ plan that could be implemented within thirty days, not just a ________ promise to “do better.”

Read the passage and choose its main idea. Many student-run startups begin with enthusiasm but struggle when roles remain informal. At first, friendship makes decisions quick and meetings comfortable. But as orders, customers, and money increase, the absence of clear responsibility creates confusion: two people may contact the same vendor, while no one follows up with a delayed client. This does not mean startups should become rigid from day one. Rather, even small teams need simple systems - who owns sales, who handles payments, and how decisions are recorded - so that creativity is supported instead of slowed down.

A new co-working café near a business school plans to replace its printed loyalty cards with an app-based rewards system. The owner argues, “Most of our customers are students who always carry smartphones. Therefore, shifting to an app will increase repeat visits because students will find it easier to track their rewards.” Which of the following is an assumption on which the argument depends?

Read the passage and answer the question that follows. A campus café stopped offering plastic straws and introduced steel tumblers for dine-in orders. In the first month, takeaway sales fell slightly, but dine-in orders increased enough to raise total revenue by 8%. The manager said the change had “unexpectedly improved the café’s image among regular students.” Which of the following can be inferred from the passage?

A café near a college plans to stop offering heavy discounts during exam week because, last year, even with a 30% discount, its sales rose only slightly while profit per order fell sharply. The owner concludes that removing the discount this year will increase total profit during exam week. Which assumption is most necessary for the owner’s conclusion?