IPMAT Indore 2020 Question Paper with Answers

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

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 more. The maximum possible difference between the second highest and the second lowest marks is

The following table presents the quoted 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

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 Friday, then the stock she should buy on Monday to earn the maximum possible profit during the week is

The following table presents the quoted 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

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

The following table presents the quoted 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

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

The following table presents the quoted 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

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

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

The following table presents the quoted 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

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

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. (Assume that when the outcome is not a five and he lies, he reports 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:
(i) When $(0 < x < 1)$, then $(\frac{1}{1+x} < 1 - x + x^2)$
(ii) When $(0 < x < 1)$, then $(\frac{1}{1+x} > 1 - x + x^2)$
(iii) When $(-1 < x < 0)$, then $(\frac{1}{1+x} < 1 - x + x^2)$
(iv) When $(-1 < x < 0)$, then $(\frac{1}{1+x} > 1 - x + x^2)$
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?