# SSC CGL 2019 EXAM PAPER : Held on 03-March-2020 Shift-2 (Quantative Aptitude)

Q.1 A can complete a certain piece of work in 40 days. B is 25% more efficient than A and C is 28% more efficient than B. They work together for 5 days. The remaining work will be complete by B alone, in:

1. 20 1/2 days
2. 16 1/5 days
3. 16 3/5 days
4.  20 3/4 days

#### Correct answer is option 3 i.e. 16 7/8

##### Correct answer is option 2 i.e. 604

2 sin θ + 15 cos2 θ = 7

⇒ 2 sin θ + 15 (1 – sin2 θ) = 7

⇒ 2 sin θ + 15 – 15 sin2 θ = 7

⇒ 15 sin2 θ – 2 sin θ – 8 = 0

⇒ 15 sin2 θ – 12 sin θ + 10 sin θ – 8 = 0

⇒ 3 sin θ (5 sin θ – 4) + 2 (5 sin θ – 4) = 0

⇒ (3 sin θ + 2) (5 sin θ – 4) = 0

Taking,

(5 sin θ – 4) = 0 (as in 0° < θ < 90° sinθ will be + ve)

⇒ sin θ = 4/5

Perpendicular = P, Hypotenuse = H and Base = B.

sin θ = P/H = 4/5

P = 4 and H = 5

As we know,

H2 = P2 + B2

⇒ 52 = 42 + B2

⇒ B2 = 25 – 16 = 9

⇒ B = √9 = 3

Now,

tan θ + cos θ + sec θ

⇒ 4/3 + 3/5 + 5/3

⇒ 9/3 + 3/5

⇒ 3 + 3/5

⇒ 3 3/5