IPMAT 2020 Quant - Makhija Academy

IPMAT 2020

Actual Question Paper

01. 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 __________.

02. The shortest distance from the point (-4,3) to the circle x² + y² = 1 is __________.

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

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

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

06. 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. I 12 . 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 __________.

07. 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 __________.

08. 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 __________.

09. 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 __________.

10. 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 __________.

11. The probability that a randomly chosen factor of 1019 is a multiple of 1015 is

$\frac{1}{25}$
$\frac{1}{12}$
$\frac{1}{20}$
$\frac{1}{16}$

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

13. The equation of the straight line passing through the point M (-5,1), such that the portion of it between the axes is divided by the point M in to two equal halves, is

14. The value of cos² $\frac{π}{8}$ + cos² $\frac{3π}{8}$ + cos² $\frac{5π}{8}$ + cos² $\frac{7π}{8}$ is

1
$\frac{3}{2}$
2
$\frac{9}{4}$

15. If $\frac{1}{1^{2}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{3^{2}}$ + .... upto ∞ = $\frac{π^{2}}{6}$ , then the value of $\frac{1}{1^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{5^{2}}$ + .... upto ∞ is

$\frac{π^{2}}{8}$
$\frac{π^{2}}{16}$
$\frac{π^{2}}{12}$
$\frac{π^{2}}{36}$

16. 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

$\frac{4}{9}$
$\frac{5}{9}$
$\frac{4}{15}$
$\frac{2}{15}$

17. If log₅log₈(x² - 1) = 0, then a possible value of x is

2√2
√2
2
3

18. Consider the following statements:
(i) When 0 < x < 1, then $\frac{1}{1+x}$ < 1 - x + x²
(ii) When 0 < x < 1, then $\frac{1}{1+x}$ > 1 - x + x²
(iii) When -1 < x < 0, then $\frac{1}{1+x}$ < 1 - x + x²
(iv) When -1 < x < 0, then $\frac{1}{1+x}$ > 1 - x + x²
Then the correct statements are

19. 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?

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

$\frac{√33 + 4}{3}$
$\frac{√33 + 5}{3}$
$\frac{√33 + 6}{3}$
$\frac{√33 + 7}{3}$

21. 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

22. Given f(x) = x² + log₃x and g(y) = 2y + f(y), then the value of g(3) equals

23. A 2 × 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

$\frac{2}{45}$
$\frac{1}{45}$
$\frac{4}{15}$
$\frac{1}{15}$

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

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

Q26 – 30:
The table below represents the buy and sell prices of five stocks during the five trading days of a given week. The quoted sell price is the price at which an investor can sell a stock in the market. The quoted buy price is the price at which an investor can buy a stock from the market. All the quoted numbers are in Indian Rupees.

Day	Monday		Tuesday		Wednesday		Thursday		Friday
Quote	Sell	Buy	Sell	Buy	Sell	Buy	Sell	Buy	Sell	Buy
Dabur	460	462	455	458	432	433	444	447	461	462
Marico	345	346	335	336	365	368	372	375	372	374
HUL	1931	1933	1952	1955	1979	1981	2044	2048	1966	1969
ITC	237	238	238	239	246	251	221	225	253	256
Britannia	3044	3046	3100	3101	3110	3115	3025	3027	3140	3144

26. If an investor had Rs 36,00,000 to invest in any particular single stock, and she could buy the stock only on Monday and sell it off only on Fridav. then the stock she should buy on Monday to earn the maximum possible profit during the week is

27. If an investor planned to invest Rs 36,00,000 in purchasing the stocks of HUL on Monday, sell them off on Wednesday and use the entire proceeds to purchase the stocks of Britannia on the same day and sell them off again on Friday, then the total investment return during the week would be

28. The difference between the quoted buy and sell price of a stock is referred to as the spread of the stock. The average spread of the stocks is lowest on

29. A brokerage firm charges 0.1 percent trading commission on the value of shares bought or sold through its trading platform. If an investor bought 1000 shares of Britannia on Tuesday, and sold all of them on Thursday, then the total brokerage fee that will be charged from the investor is

30. If you had decided to invest Rs.36,00,000 worth of ITC stocks on Monday, then the day of the week you should choose to sell the stocks to earn the maximum possible profit would be