IPMAT Indore 2020

In a division problem, the product of the quotient and the remainder is 24 while their sum is 10. If the divisor is 5 then the dividend is __________.

The shortest distance from the point $(-4,3)$ to the circle $(x^2 + y^2 = 1)$ is __________.

The value of $(0.04^{log_{\sqrt{5}}(\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + ...)})$ is __________.

Suppose $\left|\begin{array}{lll}a & a^{2} & a^{3}-1 \\ b & b^{2} & b^{3}-1 \\ c & c^{2} & c^{3}-1\end{array}\right|=0$, where $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ are distinct real numbers. If ${a}=3$, then the value of $abc$ is:

The minimum value of $f(x)=|3-x|+|2+x|+|5-x|$ is equal to __________.

Ashok purchased pens and pencils in the ratio $2:3$ during his first visit and paid Rs. 86 to the shopkeeper. During his second visit, he purchased pens and pencils in the ratio $4:1$ and paid Rs. 112. The cost of a pen as well as a pencil in rupees is a positive integer. If Ashok purchased four pens during his second visit, then the amount he paid in rupees for the pens during the second visit is __________.

In a four-digit number, the product of the thousands digit and units digit is zero while their difference is 7. Product of the middle digits is 18. The thousands digit is as much more than the units digit as the hundreds digit is more than the tens digit. The four-digit number is __________.

Out of 80 students who appeared for the school exams in Mathematics (M), Physics (P) and Chemistry (C), 50 passed M, 30 passed P and 40 passed C. At most 20 students passed M and P, at most 20 students passed P and C, and at most 20 students passed C and M. The maximum number of students who could have passed all three exams is __________.

Two friends run a 3-kilometer race along a circular course of length 300 meters. If their speeds are in the ratio 3:2, the number of times the winner passes the other is __________.

Out of 13 objects, 4 are indistinguishable and the rest are distinct. The number of ways we can choose 4 objects out of 13 objects is __________.