SSC CHSL (Tier – 1) Online Exam Paper – 2018 “held on 10 JULY 2019”

## Afternoon Shift (Quantitative Aptitude)

Q1. ABCDEFGH is a regular octagon inscribed in a circle with centre at O. The ratio of ∠OAB to ∠AOB is equal to:

Options:

1. 8 : 3

2. 3 : 2

3. 4 : 3

4. 3 : 1

**Correct Answer: 3 : 2**

2. A borrows a sum of Rs. 2000 from his friend B on 31 December 2011 on the condition that he will return the same after one year with simple interest at 8% per annum. However, A get into a position of returning the money on 1 July 2012. How much amount he has to return to B?

Options:

1. 2088

2. 2200

3. 2070

4. 2080

**Correct Answer: 2080**

Q3. Θ being an acute angle, it is given that sec^{2}Θ + 4tan^{2}Θ = 6. What is the value of Θ ?

Options:

1. 0°

2. 45°

3. 60°

4. 30°

**Correct Answer: 45°**

Q4. If a + b – c = 12 and a^{2} + b^{2} + c^{2} = 110, then which among the following relations is true?

**(p) ab + bc + ca = 34,
(q) ab + bc – ca = 17,
(r) ab – bc + ca = 17,
(s) ab – bc – ca = 17**

Options:

1. (s)

2. (q)

3. (p)

4. (r)

**Correct Answer: (s)**

Q5. Fill in the Blank.

The average of first 101 _______ numbers is equal to 102.

Options:

1. even

2. odd

3. perfect square

4. natural

**Correct Answer: even**

Q6. By selling an article for Rs. 144, a shopkeeper loses 28%. What should be the selling price for bringing down the loss to 14%?

Options:

1. 172

2. 180

3. 176

4. 178

**Correct Answer: 172**

Q7. a^{1/3} + b^{1/3} + c^{1/3} = 0, then (a + b + c)^{6} is equal to:

Options:

1. 81 a^{2}b^{2}c^{2}

2. 729 abc

3. 729 a^{2}b^{2}c^{2}

4. 81 abc

**Correct Answer: 729 a ^{2}b^{2}c^{2}**

Q8. Which among the following number is exactly divisible by 11, 13 and 7?

**(a) 624613
(b) 624624
(c) 624635
(d) 624646**

Options:

1. (d)

2. (b)

3. (a)

4. (c)

**Correct Answer: (b)**

Q9. A shopkeeper normally allows a discount of 10% on the marked price of each article. During a sale season, he decides to give two more discounts, the first being at a rate of 50% of the original and the second at a rate of 40% of the first. What is the percentage rate of the equivalent single discount?

Options:

1. 13.27

2. 16.21

3. 11.25

4. 14.85

**Correct Answer: 16.21**

Q10. Rs. 10,000/- has to be distributed among 3 craftsmen, 5 helpers and 6 labourers such that each helper receives the amount twice as much as a labourer receives and each craftsman receives the amount thrice as much as a labourer receives. What is the amount received by the three craftsmen?

Options:

1. 4000

2. 2400

3. 2700

4. 3600

**Correct Answer: 3600**

Q11. The price of sugar got raised by 25%. To maintain the same level of expenses on sugar, a person reduced the consumption of sugar by 4% and also increased his expenditure on sugar by x%. The value of x is:

Options:

1. 21

2. 19.5

3. 20

4. 18

**Correct Answer: 20**

12. If a + 1/a, the the value of (a^{6} + 1/a^{6}) is equal to:

Options:

1. 319

2. 780

3. 730

4. 322

**Correct Answer: 322**

Q13. A book has been co-authored by X and Y. The prices of the book in India and abroad are Rs. 800 and Rs. 1000 respectively. The royalties earned on sale in India and abroad are 10% and 16% respectively. The royalty amount is distributed among X and Y in the ratio 5 : 3. The given Bar graph presents the number of copies of the book sold in India (A) and abroad (B) during 2012-2016).

**What is the difference between the royalties earned by X and Y during the years 2014 and 2015 taken together?**

Options:

1. 57000

2. 57550

3. 41250

4. 41340

**Correct Answer: 57000**

Q14. What is the simplified value of sin^{3}21°+ cos^{3}19°/sin21°+ cos19°+ sin6^{2}0°+ sin^{2}71°+ 1/sin69°cosec71°is:

Options:

1. 1

2. 2

3. 3

4. 4

**Correct Answer: 2**

Q15. The simplified value of 1/2 of 8/5 ÷{11/5 -(5/16 + 3/5 x 15/8 ÷ 2/3)} is:

Options:

1. 1/5

2. 2/5

3. 1

4. 4

**Correct Answer: 4**

Q16. Which among the following is an irrational quantity?

**(a) tan30°tan60°
(b) sin 30°
(c) tan 45°
(d) cos 30°**

Options:

1. (b)

2. (d)

3. (a)

4. (c)

**Correct Answer: (d)**

Q17. It is given that the area of a triangle is A. The values of its perimeter, in radius, circumradius and the average of the lengths of the medians are respectively, p, r, R and d. The ration A : p is equal to:

Options:

1. r : 1

2. (R : r)^{2} : d

3. r : 2

4. (R – r)^{2} : r

**Correct Answer: r : 2**

Q18. Equilateral triangles are drawn on the hypotenuse and one of the perpendicular sides of a right-angled isosceles triangles. Their areas are H and A respectively. A/H is equal to:

Options:

1. 1/4

2. 1/√2

3. 1/2

4. 1/2√2

**Correct Answer: 1/2**

Q19. Given that the lengths of the paths of a ball thrown with different speeds by two boys are the same, if they take 0.6 sec and 1 sec respectively to cover the said length, what is the average speed of travel for the first throw, if the same for the second is 96 km/hr?

Options:

1. 100 km/hr

2. 150 km/hr

3. 160 km/hr

4. 120 km/hr

**Correct Answer: 160 km/hr**

Q20. A book has been co-authored by X and Y. The prices of the book in India and abroad are Rs. 800 and Rs. 1000 respectively. The royalties earned on sale in India and abroad are 10% and 16% respectively. The royalty amount is distributed among X and Y in the ratio 5 : 3. The given Bar graph presents the number of copies of the book sold in India (A) and abroad (B) during 2012-2016).

**What is the total amount of royalty paid to the author during the years 2012, 2013 and 2016?**

Options:

1. 272000

2. 273400

3. 316000

4. 271600

**Correct Answer: 316000**

Q21. Twelve sticks, each of length 1 unit, are used to form a right – angled triangle. The area of the triangle is:

Options:

1. 6 sq units

2. 4 sq units

3. 10 sq units

4. 8 sq units

**Correct Answer: 6 sq units**

Q22. If 40 men working 12 hrs a day can complete a work in 8 days, then how many men working 4 hrs a day can complete the same work in 16 days?

Options:

1. 54

2. 60

3. 45

4. 50

**Correct Answer: 60**

Q23. A book has been co-authored by X and Y. The prices of the book in India and abroad are Rs. 800 and Rs. 1000 respectively. The royalties earned on sale in India and abroad are 10% and 16% respectively. The royalty amount is distributed among X and Y in the ratio 5 : 3. The given Bar graph presents the number of copies of the book sold in India (A) and abroad (B) during 2012-2016).

**What is the ratio of royalties earned in the following cases – By X for sale of book in India in 2013 and 2014 and by Y for sale of book in Abroad in 2015 and 2016 ?**

Options:

1. 62 : 117

2. 63 : 130

3. 64 :135

4. 65 : 138

**Correct Answer: 65 : 138**

Q24. Two circles of diameters 2 cm and 5.6 cm are such that the distance between their centre is 8.2 cm. What is the length of a common tangent to the circles that does not intersect the line joining the centre?

Options:

1. 8 cm

2. 7.2 cm

3. 6.4 cm

4. 8.4 cm

**Correct Answer: 8 cm**

Q25. A book has been co-authored by X and Y. The prices of the book in India and abroad are Rs. 800 and Rs. 1000 respectively. The royalties earned on sale in India and abroad are 10% and 16% respectively. The royalty amount is distributed among X and Y in the ratio 5 : 3. The given Bar graph presents the number of copies of the book sold in India (A) and abroad (B) during 2012-2016).

**What is the total numbers of the copies of the book sold in India during 2012-2015?**

Options:

1. 1600

2. 1400

3. 1800

4. 2000

**Correct Answer: 1400**