IPMAT Indore (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

A man is known to speak the truth on an average 4 out of 5 times. He throws a die and reports that it is a five. The probability that it is actually a five is

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

Consider the following statements: <br>(i) When $(0 < x < 1)$, then $(\frac{1}{1+x} < 1 - x + x^2)$ <br>(ii) When $(0 < x < 1)$, then $(\frac{1}{1+x} > 1 - x + x^2)$ <br>(iii) When $(-1 < x < 0)$, then $(\frac{1}{1+x} < 1 - x + x^2)$ <br>(iv) When $(-1 < x < 0)$, then $(\frac{1}{1+x} > 1 - x + x^2)$ <br>Then the correct statements are:

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

Given $f(x) = x^2 + \log_3 x$ and $g(y) = 2y + f(y)$, then the value of $g(3)$ equals

A $2 \times 2$ matrix is filled with four distinct integers randomly chosen from the set $\{1,2,3,4,5,6\}$. Then the probability that the matrix generated in such a way is singular is

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

The average marks of $6$ students in a test is $64$. All the students got different marks, one of the students obtained $70$ marks and all other students scored $40$ or above. The maximum possible difference between the second highest and the second lowest marks is