**Dear Aspirants,** **Our SSC Crackers team** is providing a new series of Quantitative Aptitude Questions for **Upcoming Exam **so the aspirants can practice it on a daily basis. These questions are framed by our skilled experts after understanding your needs thoroughly. Aspirants can practice these new series questions daily to familiarize with the exact exam pattern and make your preparation effective.

**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+tan ^{2} 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 + sin ^{2} θ = 1, then what is the value of (cos^{12} θ + 3 cos^{10} θ + 3 cos^{8} θ + cos^{6} 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 (cosec ^{2} θ + sec^{2} θ) /(cosec^{2} θ – sec^{2} 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 ^{2 }θ) = sec^{2 }θ = 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 – sin^{2} θ)

sin^{2} θ = cos^{4} θ

1 – cos^{2} θ = cos^{4} θ

1 = cos^{4} θ + cos^{2} θ

1 = (cos^{4} θ + cos^{2} θ )^{3}

1 = cos^{12} θ + 3 cos^{10} θ + 3 cos^{8} θ + cos^{6} θ

cos^{12} θ + 3 cos^{10} θ + 3 cos^{8} θ + cos^{6} θ – 1 = 0

**4) ****Answer: B**

cot θ = √11 ⇒ cot^{2} θ = 11

(cosec^{2} θ + sec^{2} θ) /(cosec^{2} θ – sec^{2} θ) = 1/(cos^{2} θ – sin^{2} θ) = 1/ (cos 2θ) = 1/(2 cos^{2}θ – 1)

cos^{2 }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