# IPMAT (I) 2020 QA MCQ

**1. IPMAT (I) 2020 QA MCQ | Modern Math - Probability**

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

- A.
1/25

- B.
1/12

- C.
1/20

- D.
1/16

Answer: Option D

**Explanation** :

Workspace:

**2. IPMAT (I) 2020 QA MCQ | Geo - Triangles**

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

Answer: Option B

**Explanation** :

Workspace:

**3. IPMAT (I) 2020 QA MCQ | Geo - Coordinate Geometry**

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

Answer: Option A

**Explanation** :

Workspace:

**4. IPMAT (I) 2020 QA MCQ | Geo - Trigonometry**

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

- A.
1

- B.
3/2

- C.
2

- D.
9/4

Answer: Option C

**Explanation** :

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**5. IPMAT (I) 2020 QA MCQ | Algebra - Progressions**

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

Answer: Option A

**Explanation** :

Workspace:

**6. IPMAT (I) 2020 QA MCQ | Modern Math - Probability**

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

Answer: Option E

**Explanation** :

The answer should be 4/5.

Workspace:

**7. IPMAT (I) 2020 QA MCQ | Algebra - Logarithms**

If log_{5}log_{8}(x^{2} - 1) = 0, then a possible value of x is

- A.
2√2

- B.
√2

- C.
2

- D.
3

Answer: Option D

**Explanation** :

Workspace:

**8. IPMAT (I) 2020 QA MCQ | Algebra - Inequalities & Modulus**

Consider the following statements:

(i) When 0 < x < 1, then $\frac{1}{1+\mathrm{x}}$ < 1 - x + x^{2}

(ii) When 0 < x < 1, then $\frac{1}{1+\mathrm{x}}$ > 1 - x + x^{2}

(iii) When -1 < x < 0, then $\frac{1}{1+\mathrm{x}}$ < 1 - x + x^{2}

(iv) When -1 < x < 0, then $\frac{1}{1+\mathrm{x}}$ > 1 - x + x^{2}

^{}Then the correct statements are

- A.
(i) and (ii)

- B.
(ii) and (iv)

- C.
(i) and (iv)

- D.
(ii) and (iii)

Answer: Option C

**Explanation** :

Workspace:

**9. IPMAT (I) 2020 QA MCQ | Average, Mixture & Alligation**

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

Answer: Option B

**Explanation** :

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**10. IPMAT (I) 2020 QA MCQ | Time & Work**

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

Answer: Option A

**Explanation** :

Workspace:

**11. IPMAT (I) 2020 QA MCQ | Algebra - Number Theory**

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

Answer: Option B

**Explanation** :

Workspace:

**12. IPMAT (I) 2020 QA MCQ | Algebra - Logarithms**

Given f(x) = x^{2} + log_{3}x and g(y) = 2y + f(y), then the value of g(3) equals

- A.
16

- B.
15

- C.
25

- D.
26

Answer: Option A

**Explanation** :

Workspace:

**13. IPMAT (I) 2020 QA MCQ | Modern Math - Determinants & Metrices**

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

Answer: Option A

**Explanation** :

Workspace:

**14. IPMAT (I) 2020 QA MCQ | Ratio, Proportion & Variation**

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

Answer: Option C

**Explanation** :

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**15. IPMAT (I) 2020 QA MCQ | Average, Mixture & Alligation**

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

Answer: Option B

**Explanation** :

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**Answer the following questions based on the information given below:**

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.

**16. IPMAT (I) 2020 QA MCQ | Tables & Graphs**

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

Answer: Option A

**Explanation** :

Workspace:

**17. IPMAT (I) 2020 QA MCQ | Tables & Graphs**

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%

Answer: Option C

**Explanation** :

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**18. IPMAT (I) 2020 QA MCQ | Tables & Graphs**

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

Answer: Option A

**Explanation** :

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**19. IPMAT (I) 2020 QA MCQ | Tables & Graphs**

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

Answer: Option B

**Explanation** :

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**20. IPMAT (I) 2020 QA MCQ | Tables & Graphs**

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

Answer: Option D

**Explanation** :

Workspace: