Practice IPMAT Indore 2020 Quantitative Ability (MCQ) PYQs

The probability that a randomly chosen factor of \(10^{19}\) is a multiple of \(10^{15}\) is

The number of acute angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is

The equation of the straight line passing through the point \(M (-5,4)\), such that the portion of it between the axes is divided by the point \(M\) into two equal halves, is

The value of \(\cos^2\left(\frac{\pi}{8}\right) + \cos^2\left(\frac{3\pi}{8}\right)\) \({}+ \cos^2\left(\frac{5\pi}{8}\right)\) \({}+ \cos^2\left(\frac{7\pi}{8}\right)\) is

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

If \(\log_5(\log_8(x^2 - 1)) = 0\), then a possible value of \(x\) is

Consider the following statements:

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

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

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

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

Fifty litres of a mixture of milk and water contains 30 percent of water. This mixture is added to eighty litres of another mixture of milk and water that contains 20 percent of water. Then, how many litres of water should be added to the resulting mixture to obtain a final mixture that contains 25 percent of water?

Three workers working together need 1 hour to construct a wall. The first worker, working alone, can construct the wall twice as fast as the third worker, and can complete the task an hour sooner than the second worker. Then, the average of time taken in hours by three workers, when working alone, to construct the wall is

In a class, students are assigned roll numbers from 1 to 140. All students with even roll numbers opted for cricket, all those whose roll numbers are divisible by 5 opted for football, and all those whose roll numbers are divisible by 3 opted for basketball. The number of students who did not opt for any of the three sports is