SSC CGL EXAMS 2018 | Quantitative Aptitude Practice Questions (Day-15)

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SSC CGL EXAMS 2018 | Quantitative Aptitude Questions (Day-15)

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1) Find the value of sin2 7 ½° + sin2 82 ½° + tan2 2° . tan2 88° is

a) 2

b) 1

c) 0

d) 4

2) The angle of elevation of the summit of a hill the top and bottom of a nearby pole are 300 and 600 respectively. If the height of the pole is h, find the height of the hill.

a) 2h

b) √3h

c) √3x

d) 3x

3) A larger cube of certain side is divided into smaller cubes of side 5 cm. If the ratio of the surface area of larger cube to the sum of the surface area of the smaller cubes 1: 2. Find the length of side of the larger cube.

a) 10 cm

b) 20 cm

c) 15 cm

d) 12 cm

4) Find the value of 1 – 2 sin2 θ + sin4 θ.

a) 1 – sin4 θ

b) sin2 θ. Cos2 θ

c) cos4 θ

d) sin4 θ

5) Amar is 3 times faster than suman. Suman can complete a work in 15 days. If they work together then how long the work will complete?

a) 4 days

b) 3 ½ days

c) 3 ¾ days

d) 4 ½ days

6) A certain amount of money triples itself in 5 years at simple interest per annum. Find the rate of interest of the amount?

a) 10%

b) 20 %

c) 40%

d) 60%

7) If x = 6 + 26, then what is the value of √(x-1)+ 1/√(x – 1)

a) 5√3

b) 2√3

c) 3√2

d) 5√2

Direction (8 – 10): Read the instruction carefully and answer the questions.

Given line graph indicates the employee details of two companies.  Total employees are working in various years of company A and company B is given below

8) If in Company A, 45% of employees are females in 2015 and 2016 respectively. Then find the ratio of total males of company A in the same years?

a) 2: 5

b) 5: 4

c) 3: 5

d) 5: 2

9) What is the average of total workers of Company B  between 2012 and 2015?

a) 1250

b) 1300

c) 1350

d) 1400

10) If in the year 2017, number of employees in company A and B were increased 30% and 40% respectively with respect to previous year. Then the total employees worked in the both the companies in 2017 are?

a) 4004

b) 4040

c) 4440

d) 4044

Answers :

1) Answer: a)

sin2 7 ½° + sin2 82 ½° + tan2 2° + tan2 88°

Sin 7 ½° = cos 82 ½ °

Similarly, tan2 88 = cos2

(cos 82 ½ °+ sin2 82 ½° )+ (tan2 2°. Cot22°) = 1 + 1 = 2 [∵ sin2 θ + cos2 θ = 1]

∵ [Cot22° = 1/ tan22°]

2) Answer: d)

Let AB is height of the pole = h

Let CD is the height of the hill = x + h

Let distance between the pole and hill = BD = y

CE = x

3) Answer: a)

Side of the larger cube =a

Volume of the larger cube = a3

Side of smaller cube = 5 cm

Volume of the smaller cube = 53 = 125 cm

Total surface area of larger cube = 6a2

Total surface area of smaller cubes = 6 (5)2 = 6 * 25 = 150 cm2

Sum of total surface area of smaller cubes = 150 * (a3/125)

[∵Total surface area of smaller cubes*(volume of the larger cube/ volume of the smaller cube)]

4) Answer: c)

1 – 2 sin2 θ + sin4 θ

= 12 – 2(1) (sin2θ) + sin4 θ = (1 – sin2θ)2 [∵ (a – b) = a2 + b2 – 2ab]

(1 – sin2θ)2 = (sin2 θ + cos2 θ – sin2θ) 2  [∵Sin2 θ + cos2 θ = 1  ]

= (cos2 θ)2 = cos4 θ

5) Answer: c)

Work ratio of Amar and Suman = 3 : 1

Time = 1 : 3

Amar = 1/ 15

Suman = 3 /1 5= 5 days=(3/15)*5

1/15 + 1/5 = (1+ 3) / 15

The work will complete = 15 / 4 = 3 ¾ days

6) Answer: c)

If the sum of money becomes n times in the n years at simple interest, then the rate of interest will be

R = 100 (multiply times – 1)/no of years

Rate = 100 (3 – 1)/5 = 100 *2/5 = 40%

7) Answer: b)

x-1 = 5 + 2√6.

Then,

x-1 = 3 + 2 + 2√((3)(2))

∴ x-1 = (√3)² + (√2)² + 2(√3)(√2) = (√3 + √2)²

∴ √x-1 = √3 + √2

∴ 1/(√x-1) = 1/(√3 + √2) = √3 – √2

∴ (√x-1) + (1/√x-1) = (√3 + √2) + (√3 – √2)

= 2√3

Direction (8-10) :

8) Answer: b)

Total Employees in 2015 in company A = 2000

Total Males in 2015 = 2000 * (55/100) = 20* 55

Total Employees in 2016 in company A = 1600

Total Males in 2016 = 1600 * (55/100) = 16* 55

Ratio of Males 2015 : male 2016

= 20* 55 : 16 : 55

= 5 : 4

9) Answer: c)

Sum of the workers 2012 to 2015 of company B = 1000 + 1500 + 1700 + 1200

= 5400/4 = 1350

10) Answer: b)

Number of employees in companies A in 2016 = 1600

Number of employees in companies A in 2017 = 1600(130/100) = 2080

Number of employees in companies B in 2016 = 1400

Number of employees in companies B in 2017 = 1400 (140/100) = 1960

Sum of employees in 2017 = 2080 + 1960 = 4040

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