SSC Quantitative Aptitude Questions (Day-38)

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1) If 4sin²θ – 3 = 0 and θ is acute, then what is the value of (cot²θ + tan²θ)?

(a) 2

(b) 0

(c) 10/3

(d) 6

2)   

(a) 30

(b) 45

(c) 60

(d) 90

3) 

(a) -1

(b) 0

(c) 1

(d) 2

4) 

(a) 1

(b) 2

(c) 3

(d) 4

5) If cosec θ + cosec²θ = 1, then what is the value of (cot¹² θ –3 cot¹⁰ θ + 3 cot⁸ θ – cot⁶ θ)?

(a) -2

(b) -1

(c) 0

(d) 1

Direction (6-10); The pie chart given below shows the percentage distribution of annual expenditure on various items of a company. The annual expenditure of the company is Rs. 72 crores.

6) How much is the expenditure (in Rs crores) on Operations annually?

(a) 1.52

(b) 7.14

(c) 11.52

(d) 1.152

7) What is the monthly expenditure (in Rs crores) on Miscellaneous by the company?

(a) 14.4

(b) 1.44

(c) 1.21

(d) 1.69

8) If 5% of Miscellaneous is spent on research of nanotubes, then how much is spent (in Rs crores) on research of nanotubes annually?

(a) 0.864

(b) 0.362

(c) 0.544

(d) 0.962

9) By what percentage is the total expenditure on Interest and Miscellaneous more that the total expenditure on Tax and Salary?

(a) 20

(b) 15

(c) 8

(d) 10

10) Total amount spent on Raw material is 50% of the total amount spent on Interest. If the ratio of amount of expenditure on Rent and Raw material is 1 : 2 respectively, then what will be the amount (in Rs) spent on Rent annually?

(a) 28000000

(b) 36000000

(c) 40000000

(d) 32000000

Answers :

1) Answer: C

2) Answer: C

3) Answer: D

Sinθ + cosecθ = 2

Here, sinθ = 1, cosecθ = 1

Sin¹⁰⁰θ + cosec¹⁰⁰θ = 1

= 1 + 1 = 2

4) Answer: C

5) Answer: D

Cosecθ + cosec²θ = 1

Cosecθ = 1- cosec²θ

Cosecθ = – cot²θ

cot²θ = – cosecθ                                ..(i)

(cot¹²θ – 3cot¹⁰θ + 3cot⁸θ – cot⁶θ )

= (– cot²θ)³

= ((cosecθ)² – cot²θ)             (from eq (i))

= (cosec²θ – cot²θ)³ = 1³ = 1

6) Answer: C

Expenditure on a operations annually

=16 / 100 × 72 crores

= 11.52

7) Answer: B

Annually expenditure on miscellaneous

= 24 / 100 × 72 = 17.28

Monthly expenditure = 17.28 / 12

= 1.44

8) Answer: A

Expenditure on miscellaneous annually = 17.28

Expenditure on research of Nano tubes

=17.28 ×5 / 100 = 0.864

9) Answer: D

Total expenditure on interest and miscellaneous = 44%

Total expenditure on tax and salary = 40%

Required % = 4 / 40 × 100 = 10%

10) Answer: B

Total amount spent on Raw material = 50% of interest

= 10%

Ratio of amount of expenditure on Rent and Raw material = 1 : 2 → 10 %

Rent = 5%

Rent = 5 / 100 × 720000000

= 36000000