Trigonometry & Height and Distances

Question 1

What is the maximum value of 3 Sinθ + 4 cosθ?

• 12

• 5

• 6

• 1

Question 2

What is minimum value of Sinθ + cosθ ?

• -2

• √3/2

• -1

• -√2

Question 3

If tan (x+y) tan (x-y) = 1, then find tan (2x/3)?

• 1/√3

• 1/2

• 1/√2

• 2/√3

Question 4

Find the Value of tan30^o + tan120^o?

• √3

• -1/√3

• 0

• -2/√3

Question 5

The least value of 2sin²θ + 3cos²θ

• 1/3
• 4/3
• 2
• 3/4

Question 6

The angle of elevation of the sun, when the length of the shadow of a tree is 1/√3 times the height of the tree, is:

• 30 degrees

• 45 degrees

• 60 degrees

• 90 degrees

Question 7

From a point A on a level ground, the angle of elevation of the top of a tower is 30 degrees. If the tower is 100 m high, the distance of point A from the foot of the tower is:

• 148 m

• 156 m

• 173 m

• 200 m

Question 8

Amit is standing at a point P is watching the top of a tower, which makes an angle of elevation of 45° with Amit\'s eye. He walks some distance towards the tower to watch its top and the angle of elevation becomes 60°. What is the distance between the base of the tower and the point P?

• 4.2 units

• 8 units

• 10 units

• Data inadequate

Question 9

A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man\'s eye when at a distance of 60 meters from the tower. After 5 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?

• 32 kmph

• 36 kmph

• 40 kmph

• 44 kmph

Question 10

x = a cos(t), y = b sin(t) is the parametric form of

• Ellipse
• Hyperbola
• Circle
• Parabola