SSC CHSL (Tier – 1) Online Exam Paper – 2018 “held on 11 JULY 2019”

## Evening-Shift (Quantitative Aptitude)

Q1. If a + b + c = 5 and ab + bc + ca = 4, then a^{3} + b^{3} + c^{3} – 3abc is equal to:

Options:

1. 65

2. 62

3. 68

4. 72

**Correct Answer: 65**

Q2. If a = √8 – √7 and a = 1/b, then a^{2} + b^{2} – 3ab/a^{2} + ab + b^{2} is equal to:

Options:

1. 27/31

2. 27/32

3. 21/27

4. 32/27

**Correct Answer: 27/31**

Q3. Given that x, y, z are position real numbers, if (x + y)^{2} – z^{2} = 8, (y + z)^{2} – x^{2} = 10 & (x + z)^{2} – y^{2} = 7, then ( x + y + z) is equal to:

Options:

1. 8

2. 7

3. 3

4. 5

**Correct Answer: 5**

Q4. The simplified value of 20 – [2.8 x 5 ÷ 0.7 – 3 ÷ 0.9 x 1.5 + 2] is equal to:

Options:

1. 3

2. 3.5

3. 3.8

4. 2.5

**Correct Answer: 3**

Q5. The cost price of an article is Rs. 425. A shopkeeper gives a discount of 20% and still gains 16%. What is the marked price of the article?

Options:

1. 616.25

2. 616.75

3. 620.25

4. 620.75

**Correct Answer: 616.25**

Q6. The average of 24 numbers is 65. The average of first 11 numbers is 67 and the average of last 10 numbers is 70. If the 12^{th} number is 13 less than the 13^{th} number, and the 14^{th} number is one more than the 13^{th} number, then the average of 12^{th} and 14^{th} number is:

Options:

1. 42

2. 39

3. 36

4. 37

**Correct Answer: 39**

Q7. A, B & C alone can do a piece of work in 9, 12 & 18 days respectively. They all started the work together, but A left after 3 days. In how many days, was the remaining work completed?

Options:

1. 11/4

2. 9/5

3. 5/9

4. 4/11

**Correct Answer: 9/5**

Q8. If tanΘ = 3/5, (0° < Θ < 90°) then sinΘcosΘ is equal to:

Options:

1. 14/√34

2. 15/34

3. 14/√35

4. 34/15

**Correct Answer: 15/34**

Q9. In ▲ABC, ∠ABC = 90° and BD is perpendicular to AC. If AD = 4 cm and CD = 5 cm, then BD is equal to:

Options:

1. 2/√5 cm

2. 4/√5 cm

3. 3/√5 cm

4. 3/√6 cm

**Correct Answer: 2/√5**

Q10. What is the ratio of the mean proportional between 14.4 and 3.6 and the third proportional of 5 and 4?

Options:

1. 6 : 5

2. 9 : 4

3. 3 : 5

4. 4 : 9

**Correct Answer: 9 : 4**

Q11. The given Bar Graph presents the percentages of population in the age groups, X, Y & Z in five different villages, A, B, C, D & E with total population of 5000, 6000, 8000, 4500 & 6000 respectively.

**The difference between the number of persons of ages below 20 years in villages D and E, taken together, is what percentage of the number of persons of the same age group in Village D?**

Options:

1. 185/3

2. 200/3

3. 182/3

4. 190/3

**Correct Answer: 200/3**

Q12. The difference between compound interest and simple interest on Rs. x at 6.5% per annum for 2 years is Rs. 33.80. What is the value of x?

Options:

1. 7800

2. 7600

3. 8000

4. 8200

**Correct Answer: 8000**

Q13. The given Bar Graph presents the percentages of population in the age groups, X, Y & Z in five different villages, A, B, C, D & E with total population of 5000, 6000, 8000, 4500 & 6000 respectively.

**The number of person having ages below 20 years in villages, B and C taken together is what percentage of the total population of the said villages?**

Options:

1. 190/7

2. 186/5

3. 184/5

4. 200/7

**Correct Answer: 200/7**

Q14. The price of petrol is increased by 24%. A person wants to increase his expenditure by 14% only. By what percentage should he decrease his consumption in order to maintain the same level of expenditure?

Options:

1. 8.1

2. 8.3

3. 7.4

4. 7.6

**Correct Answer: 8.1**

Q15. The eight digit number 5x32465y is divisible by 88. What is the value of (2x + 3y)?

Options:

1. 24

2. 26

3. 28

4. 29

**Correct Answer: 24**

Q16. The selling price of 24 articles is to the cost price of 26 articles. What is the gain percentage in such a situation?

Options:

1. 25/3%

2. 26/5%

3. 105/13%

4. 100/3%

**Correct Answer: 25/3%**

Q17. (sin^{2}36° + tan^{2}60° + sec^{2}30° + sin^{2}54°) is equal to:

Options:

1. 16/3

2. 14/3

3. 5

4. 17/3

**Correct Answer: 16/3**

Q18. The given Bar Graph presents the percentages of population in the age groups, X, Y & Z in five different villages, A, B, C, D & E with total population of 5000, 6000, 8000, 4500 & 6000 respectively.

**What is the ratio of the total number of persons of ages above 50 years in the villages, B and C, taken together to the total number of persons having ages between 20 and 50 years in the said villages?**

Options:

1. 34 : 27

2. 49 : 57

3. 47 : 53

4. 51/ 59

**Correct Answer: 47 : 53**

Q19. In a circle, chords AD and BC meet at a point E outside the circle. If ∠BAE = 76° and ∠ADC = 102°, then ∠AEC is equal to:

Options:

1. 24°

2. 26°

3. 29°

4. 28°

**Correct Answer: 26°**

Q20. Four cubes, each of edge 5 cm are joined end to end. What is the total surface area of the resulting cuboid?

Options:

1. 450 cm^{2}

2. 600 cm^{2}

3. 500 cm^{2}

4. 475 cm^{2}

**Correct Answer: 450 cm ^{2}**

Q21. If 2sin^{2}Θ + 3sin – 2 = 0, (0° < Θ < 90°) then then the value of Θ is:

Options:

1. 45°

2. 30°

3. 60°

4. 90°

**Correct Answer: 30°**

Q22. The given Bar Graph presents the percentages of population in the age groups, X, Y & Z in five different villages, A, B, C, D & E with total population of 5000, 6000, 8000, 4500 & 6000 respectively.

**What is the total number of persons in the age group of 20 to 50 years in the villages A and B, taken together?**

Options:

1. 4100

2. 4200

3. 4300

4. 4400

**Correct Answer: 4100**

Q23. A person covers 40% of a distance with a speed of 60 km/hr and the remaining with a speed of 40 km/hr. What is average speed for the whole journey in km/hr?

Options:

1. 600/11

2. 500/13

3. 500/11

4. 600/13

**Correct Answer: 600/13**

Q24. A quadrilateral ABCD is inscribed in a circle with centre O. If ∠BOC = 92° and ∠ADC = 112°, then ∠ABO is equal to:

Options:

1. 24°

2. 26°

3. 22°

4. 28°

**Correct Answer: 24°**

Q25. If in ▲ABC, D is a point on BC, such that BD : BC = 2 : 5, what is the ration area ( ▲ABD) : area(▲ADC)?

Options:

1. 4 : 9

2. 2 : 3

3. 3 : 2

4. 9 : 4

**Correct Answer: 2 : 3**