Practice IPMAT Indore 2025 Quantitative Ability (MCQ) PYQs

Given that \(1 + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + ...\) \({}= \frac{\pi^2}{6}\), the value of \(1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + ...\) is

If \(y=a+b \log _{e} x\) then which of the following is true?

If \(a_1, a_2, ..., a_8\) are the roots of the equation \(x^8 + x^7 + ... + x + 1\) \({}= 0\), then the value of \(a_1^{2025} + a_2^{2025} + ...\) \({}+ a_8^{2025}\) is

Suppose \(a, b\) and \(c\) are three real numbers such that Max\((a, b, c) \ +\) Min\((a, b, c) = 15\), and Median\((a, b, c) \ -\) Mean\((a, b, c) = 2.\) Then the median of \(a, b\) and \(c\) is

If \(\log_{25} [5 \log_3 (1+\log_3(1+2\log_2x))]\) \({}= \frac12\) then \(x\) 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

In triangle \(ABC, AB = AC = x, ∠ABC = \theta\) and the circumradius is equal to \(y\). Then \(\frac{x}{y}\) equals

If \(8x^2 - 2kx + k = 0\) is a quadratic equation in \(x\), such that one of its roots is \(p\) times the other, and \(p, k\) are positive real numbers, then \(k\) equals

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

Let \(P(x)\) be a quadratic polynomial such that

\(\left|\begin{array}{ll} P(0) & P(1) \\ P(0) & P(2) \end{array}\right|=0\)

Let \(P(0)=2\) and \(P(1)+P(2)+P(3)\) \({}= 14\). Then \(P(4)\) equals