IPMAT (I) 2020 QA MCQ

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

• A.

  1/25

• B.

  1/12

• C.

  1/20

• D.

  1/16

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

• A.

  28

• B.

  29

• C.

  31

• D.

  33

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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

• A.

  10y - 8x = 80

• B.

  8y + 10x = 80

• C.

  10y + 8x = 80

• D.

  8y + 10x + 80 = 0

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The value of ${\cos }^2\frac{\mathrm{\pi }}{8}$ + ${\cos }^2\frac{3\mathrm{\pi }}{8}$ + ${\cos }^2\frac{5\mathrm{\pi }}{8}$ + ${\cos }^2\frac{7\mathrm{\pi }}{8}$

• A.

  1

• B.

  3/2

• C.

  2

• D.

  9/4

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

• A.

  $\frac{{\mathrm{\pi }}^2}{8}$

• B.

  $\frac{{\mathrm{\pi }}^2}{16}$

• C.

  $\frac{{\mathrm{\pi }}^2}{12}$

• D.

  $\frac{{\mathrm{\pi }}^2}{36}$

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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

• A.

  4/9

• B.

  5/9

• C.

  4/15

• D.

  2/15

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

• A.

  2√2

• B.

  √2

• C.

  2

• D.

  3

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Consider the following statements:

(i) When 0 < x < 1, then $\frac{1}{1+\mathrm{x}}$ < 1 - x + x²

(ii) When 0 < x < 1, then $\frac{1}{1+\mathrm{x}}$ > 1 - x + x²

(iii) When -1 < x < 0, then $\frac{1}{1+\mathrm{x}}$ < 1 - x + x²

(iv) When -1 < x < 0, then $\frac{1}{1+\mathrm{x}}$ > 1 - x + x²

^{​​​​​​​}Then the correct statements are

• A.

  (i) and (ii)

• B.

  (ii) and (iv)

• C.

  (i) and (iv)

• D.

  (ii) and (iii)

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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?

• A.

  1

• B.

  2

• C.

  3

• D.

  4

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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

• A.

  (√33 + 4)/3

• B.

  (√33 + 3)/3

• C.

  (√33 + 6)/5

• D.

  (√33 + 7)/3

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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

• A.

  102

• B.

  38

• C.

  98

• D.

  42

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

• A.

  16

• B.

  15

• C.

  25

• D.

  26

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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

• A.

  2/45

• B.

  1/45

• C.

  4/15

• D.

  1/15

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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

• A.

  2 months

• B.

  3 months

• C.

  4 months

• D.

  6 months

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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

• A.

  50

• B.

  54

• C.

  57

• D.

  58

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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

• A.

  Marico

• B.

  HUL

• C.

  ITC

• D.

  Britannia

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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

• A.

  2.8%

• B.

  3%

• C.

  3.2%

• D.

  3.4%

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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

• A.

  Monday

• B.

  Tuesday

• C.

  Thursday

• D.

  Friday

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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

• A.

  6,125

• B.

  6,126

• C.

  6,127

• D.

  6,128

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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

• A.

  Tuesday

• B.

  Wednesday

• C.

  Thursday

• D.

  Friday

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