Special Quant Quiz (triogonometry) SSC CGL Tier-II 2016

Q1. The angle of elevation from the bank of a river to the top of a tree standing on the opposite side of bank is 60°. The angle of elevation becomes 30° when observed from a point 40 m backwards in a direction perpendicular to the length of the river. What is the width of the river?
(a) 10 m
(b) 20 m
(c) 30 m
(d) 40 m



Q2. A round balloon of unit radius subtends an angle of 90° at the eye of an observer standing at the a point, say A. What is the distance between the centre of the balloon from the point A?
(a) 1/√2
(b) √2
(c) 2
(d) 1/2

Q3. The angle of elevation of the top of a tower from the bottom of a building is twice that from its, top. What is the height of the building, if the height of the tower is 75 m and the angle of elevation of the top of the tower from the bottom of the building is 60°?
(a) 25 m
(b) 37.5 m
(c) 50 m
(d) 60 m

Q5. The maximum and minimum value of (1 + cos 2x) are:

(a) -1 and 1

(b) 1 and 2

(c) -1/2 and 1/2

(d) 0 and 2

Q6. Cos 3 θ + sin3 θ is maximum when θ is:

(a) 15°

(b) 30°

(c) 45°

(d) 60°

Q7. If A + B + C = 3π/2, then cos2A + cos2B + cos2C = ?

(a) 1 – 4 sinA sinB sinC

(b) 1 – sinA sinB sinC

(c) 1 – 2 sinA sinB sinC

(d) 1 – 3 sinA sinB sinC

Q14. Which of the following statements is true in respect of the expression sin 31° + sin 32°?

(a) Its value is 0

(b) Its value is 1

(c) Its value is less than 1

(d) Its value is greater than 1

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