IPMAT Indore · Paper 2

In a chess tournament there are 5 contestants. Each player plays against all the others exactly once. No game results in a draw. The winner in a game gets one point and the loser gets zero points. Which of the following sequences cannot represent the scores of the five players?

A and B take part in a rifle shooting match. The probability of A hitting the target is 0.4, while the probability of B hitting the target is 0.6. If A has the first shot, post which both strike alternately, then the probability that A hits the target before B hits it is

$ABCD$ is a quadrilateral whose diagonals $AC$ and $BD$ intersect at $O$. If triangles $AOB$ and $COD$ have areas 4 and 9 respectively, then the minimum area that $ABCD$ can have is

If $(1 + x - 2x^2)^6 = A_0 + \sum_{r=1}^{12} A_r x^r$, then the value of $A_2 + A_4 + A_6 + \dots + A_{12}$ is

Let $ABC$ be an equilateral triangle, with each side of length $k$. If a circle is drawn with diameter $AB$, then the area of the portion of the triangle lying inside the circle is

Many colleges now advertise “AI-enabled learning” as if the phrase itself guarantees academic depth. A chatbot can certainly summarise a chapter, generate practice questions, and offer instant feedback. But unless students are taught how to question outputs, compare sources, and defend their own reasoning, the tool may only make shallow work look polished. The real challenge is not whether colleges buy AI software, but whether they redesign learning around judgment. What is the author’s tone in the passage?

In the sentence below, choose the meaning of the word “temper” as used in context. “The festival team wanted a bold marketing campaign, but the faculty mentor asked them to temper their promises so that students would not expect facilities the budget could not support.”

In the sentence below, choose the option that best explains the meaning of the highlighted phrase: “When the investor asked for proof of traction, the founder tried to brush off the concern by talking about the office redesign.”

Read the passage and answer the question that follows: Many small cafés now use loyalty apps to collect customer data, but the smartest ones do not treat data as a substitute for hospitality. They use purchase patterns to remember preferences, reduce waiting time, and offer relevant recommendations. However, when every interaction becomes automated, customers may feel tracked rather than valued. The real advantage, therefore, lies not in collecting more data, but in using limited data thoughtfully to make service feel more personal. What is the central idea of the passage?

In the sentence below, choose the meaning of the underlined word in context. The founder gave a candid account of the app’s failed launch, admitting that the team had ignored early user feedback.