# IPMAT (I) 2020 QASA

**1. IPMAT (I) 2020 QASA | Algebra - Number Theory**

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

Answer: 34

**Explanation** :

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**2. IPMAT (I) 2020 QASA | Geo - Coordinate Geometry**

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

Answer: 4

**Explanation** :

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**3. IPMAT (I) 2020 QASA | Algebra - Logarithms**

The value of $0.{04}^{{\mathrm{log}}_{\sqrt{5}}\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)}$ is _________.

[Round off your answer upto 1 decimal place]

Answer: 2.3

**Explanation** :

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**4. IPMAT (I) 2020 QASA | Modern Math - Determinants & Metrices**

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

Answer: 1

**Explanation** :

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**5. IPMAT (I) 2020 QASA | Algebra - Inequalities & Modulus**

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

Answer: 7

**Explanation** :

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**6. IPMAT (I) 2020 QASA | Algebra - Simple Equations**

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 __________.

Answer: 100

**Explanation** :

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**7. IPMAT (I) 2020 QASA | Algebra - Simple Equations**

In a four-digit number, the product of 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 __________.

Answer: 7920

**Explanation** :

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**8. IPMAT (I) 2020 QASA | Miscellaneous**

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 __________.

Answer: 20

**Explanation** :

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**9. IPMAT (I) 2020 QASA | Time, Speed & Distance**

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 __________.

Answer: 3

**Explanation** :

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**10. IPMAT (I) 2020 QASA | Modern Math - Permutation & Combination**

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

Answer: 256

**Explanation** :

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