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Q:

What is the value of $\sin^{6} θ + \cos^{6} θ + 3 \sin^{2} θ \cos^{2} θ - 1$ ?

A) 0	B) 1
C) 2	D) 4

Answer & Explanation Answer: A) 0

Explanation:

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Filed Under: Simplification
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Q:

What is the value of $\sin^{2} 25 ° + \sin^{2} 65 °$ ?

A) 0	B) 1
C) 2	D) 4

Answer & Explanation Answer: B) 1

Explanation:

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Q:

If 3 tan θ = cot θ where $0 < θ < π / 2$ , then what is the value of θ ?

A) π/6	B) π/4
C) π/2	D) 1

Answer & Explanation Answer: A) π/6

Explanation:

3tan θ = cot θ

3tan θ = 1/tan θ

tan2θ = 1/3

tan θ = 1/√3

θ = π/6

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Q:

There are two parallel streets each directed north to south. A person in the first street travelling from south to north wishes to take the second street which is on his right side. At some place, he makes a 150 deg turn to the right and he travels for 15 minutes at the speed of 20 km/hr. After that he takes a left turn of 60 deg and travels for 20 minutes at the speed of 30 km/hr in order to meet the second street. What is the distance between the two streets?

A) 7.5 km	B) 10.5 km
C) 12.5 km	D) 15 km

Answer & Explanation Answer: C) 12.5 km

Explanation:

Initially the person is travelling from south to north i.e. D to A

He takes 150 deg right turn and moves AB distance and then he takes 60 deg left turn travels BC

AB = 20km/hr * 15/60 hr = 5km

BC = 30 * 20/60 = 10 km

We know that distance between both the streets is DC = DB + BC

DB = AB cos 60o= 5. ½ =2.5 km

So the distance between streets = 12.5 km

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Filed Under: Height and Distance
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Q:

What is the value of $\tan 1 ° \tan 2 ° \tan 3 ° . . . . . . . \tan 89 °$ ?

A) 0	B) 1
C) 2	D) infinity

Answer & Explanation Answer: B) 1

Explanation:

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Q:

Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30 deg, and the angle of elevation to the top of the tower at C is 45 deg. What is the ratio of the height of towers at B and C?

A) 1:√3	B) 1:3
C) 1:2	D) 1:2√3

Answer & Explanation Answer: B) 1:3

Explanation:

Let the side of regular hexagon be ‘a’

Let height of the tower 1 be h1 and tower 2 be h2

Height of tower 1 = h1 = (distance between A and B)* (tan 30o)= a.1/√3

Distance between A and C = 2*√3.a/2= √3a

Height of tower 2 = h2 = (distance between A and C)* (tan 45o) = √3a.1 = √3a

Ratio of height of towers at B and C respectively =a/√3/√3a = 1/3.

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Q:

Suppose 0 < θ < 90, then for every θ 4 sin2 θ + 1 is greater than or equal to ?

A) 2	B) 4 sin θ
C) 4 cos θ	D) 4 tan θ

Answer & Explanation Answer: B) 4 sin θ

Explanation:

We know that,

Arithmetic mean ≥ Geometric mean

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Q:

What is the value of sin 46 cos 44+ cos 46 sin 44?

A) 2	B) sin 2
C) 1	D) 0

Answer & Explanation Answer: C) 1

Explanation:

sin 46. cos 44+ cos 46. sin 44

sin 46. sin (90 -44)+ cos 46. cos (90 -44)

= sin^2 46 + cos^2 46

= 1

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