Practice IPMAT Indore 2022 Quantitative Ability (MCQ) PYQs

For \(0\lt\theta\lt\frac{\pi}{4}\), let \(a\) \({}= \left((\sin \theta)^{\sin \theta}\right)\left(\log _{2} \cos \theta\right),\) \(b\) \({}= \left((\cos \theta)^{\sin \theta}\right)\left(\log _{2} \sin \theta\right),\) \(c\) \({}= \left((\sin \theta)^{\cos \theta}\right)\left(\log _{2} \cos \theta\right)\) and \(d\) \({}= \left((\sin \theta)^{\sin \theta}\right)\left(\log _{2} \sin \theta\right)\). Then, the median value in the sequence \(a, b, c, d\) is

The set of real values of \(x\) for which the inequality \(\log _{27} 8\) \({}\leq \log _{3} x \lt 9^{\frac{1}{\log _{2} 3}}\) holds is

The set of all possible values of \(f(x)\) for which \((81)^{x}+(81)^{f(x)}=3\) is

Ayesha is standing atop a vertical tower \(200 m\) high and observes a car moving away from the tower on a straight, horizontal road from the foot of the tower. At 11:00 AM, she observes the angle of depression of the car to be \(45^{\circ}\). At 11:02 AM, she observes the angle of depression of the car to be \(30^{\circ}\). The speed at which the car is moving is approximately

The value of \(k\) for which the following lines are concurrent is

\(x-y-1\) \({}= 0 2x+3y-12\) \({}= 0 2x-3y+k = 0\)

The sum of the squares of all the roots of the equation \(x^{2} +|x +4| +|x -4|\) \({}-35 = 0\) is

The lengths of the sides of a triangle are \(x, 21\) and \(40\), where \(x\) is the shortest side. A possible value of \(x\) is:

If the five-digit number abcde is divisible by 6, then which of the following numbers is not necessarily divisible by 6?

In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?

In a room, there are \(n\) persons whose average height is \(160 \ \text{cm}\). If \(m\) more persons, whose average height is \(172 \ \text{cm}\), enter the room, then the average height of all persons in the room becomes \(164 \ \text{cm}\). Then \(m: n\) is