SSC Quantitative Aptitude Questions (Day-27)

Dear Aspirants, you can find the Quantitative Aptitude questions with detailed explanations for the SSC exams. Nowadays the competitive level of the exam has been increasing consistently. Due to the great demand for the government job, the level of the toughness reached greater. Candidates have to enhance the preparation process in order to drive in the right path. It doesn’t need to clear the prescribed cutoff. You must have to score good marks more than the cut off marks to get into the final provisional list. Here we have updating the Quantitative Aptitude questions with detailed explanations on a daily basis. You can practice with us and measure your level of preparation. According to that you can sculpt yourself in a proper way. SSC aspirants kindly make use of it and grab your success in your career.

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1) If sec θ= 13/12 and  is acute, then what is the value of (√(cotθ+tanθ))?

(a) 13/(2√15)

(b) 12/(2√13)

(c) 13/(2√5)

(d) 2/13

 

2) If (1+tan2 θ) = 625/49  and θ is acute, then what is the value of (√(sinθ+cosθ))?

(a) 1

(b) 5/4 √(31/42)

(c)

(d) 5/7

 

3) If sin θ + sin2 θ = 1, then what is the value of (cos12 θ + 3 cos10 θ + 3 cos8 θ + cos6 θ – 1)?

(a) -1

(b) 0

(c) 1

(d) 2

 

4) If cot θ = √11 and θ is acute, then what is the value of (cosec2 θ + sec2 θ) /(cosec2 θ – sec2 θ)

(a) 2/3

(b) -6/5

(c) 3/4

(d) 7/6

 

5) If (cos θ/(1+sin  θ)) + (cos θ/(1- sin  θ))=2 and  is acute, then what is the value (in degrees) of θ?

(a) 30

(b) 45

(c) 60

(d) 90

 

Directions (6-10): The given pie chart shows the distribution (in degrees) of cars sold of different models by a company in 2015-16.

6) If the number of cars sold of model D is 40500, then how many more cars of model E are sold than that of A?

(a) 8100

(b) 16200

(c) 24300

(d) 13500

 

7) If the number of cars sold of model D is 40500, what is the ratio between the number of cars sold of model D and E?

(a) 9 : 5

(b) 6 : 5

(c) 11 : 9

(d) 9 : 7

 

8) If the number of cars sold of model D is 72900, then what is the total number of cars sold of all the models together by the company?

(a) 291600

(b) 208100

(c) 162000

(d) 214160

 

9) If number of cars sold of model C are 22000, then what will be the difference in the number of cars sold of model A and B?

(a) 800

(b) 1200

(c) 1000

(d) 1500

 

10) If 5% of the total number of cars sold of model E is 750, then what is the average number of cars sold of all the models?

(a) 15000

(b) 14400

(c) 16800

(d) 14000

 

Answers:

1) Answer: C

secθ=13/12 [Triplet, 5, 12, 13]

cotθ=(12/ 5) & tanθ= (5/12)

So, √(cotθ+tanθ)=√(12/5+5/12)=13/√60

=13/(2√15)

 

2) Answer: C

(1+tan θ) = secθ = 625/49

sec θ = 25/7

sin θ = 24/25

cos θ = 7/25

√sin θ  + cos θ

= √31/5

 

3) Answer: B

sin θ = (1 – sin2 θ)

sin2 θ = cos4 θ

1 – cos2 θ = cos4 θ

1 = cos4 θ + cos2 θ

1 = (cos4 θ + cos2 θ )3

1 = cos12 θ + 3 cos10 θ + 3 cos8 θ + cos6 θ

cos12 θ + 3 cos10 θ + 3 cos8 θ + cos6 θ – 1 = 0

 

4) Answer: B

cot θ = √11 ⇒ cot2 θ = 11

(cosec2 θ + sec2 θ) /(cosec2 θ – sec2 θ) = 1/(cos2 θ – sin2 θ) = 1/ (cos 2θ) = 1/(2 cos2θ – 1)

cos2 θ = 1/2 ⇒ (1/(2×(1/2)-1)) = -(6/5)

 

5) Answer: B

put θ = 45°(cos θ/(1+sin  θ)) + (cos θ/(1- sin  θ)) = 2 √2

 

6) Answer: D

No. of cars = (40600/90) 30=13500

 

7) Answer: B

Required ratio = 40500/33750 = 162/135 = 6/5

 

8) Answer: A

Required No. of models cars = 810 × 360 = 291600

 

9) Answer: C

Difference in the no. of ears = 200 × 5 = 1000

 

10) Answer: B

100% of E = 15000

E =  15000/75×360

⇒72000/5=14400

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