Trigonometry (KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math): Questions 6 - 9 of 10

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Question number: 6

» Trigonometry » Trigonometric Functions

Appeared in Year: 2012

MCQ▾

Question

The sum of all x[0,π] which satisfy the equation sinx+12cosx=sin2(x+π4) is –

Choices

Choice (4) Response

a.

π6

b.

π

c.

2π

d.

5π6

Question number: 7

» Trigonometry » Trigonometric Identities and Equations

Appeared in Year: 2015

MCQ▾

Question

The number of real numbers λ for which the equality

sin(λα)sinαcos(λα)cosα=λ1

Holds for all real α which are not integral multiple of π2 is –

Choices

Choice (4) Response

a.

Infinite

b.

3

c.

2

d.

1

Question number: 8

» Trigonometry » Trigonometric Functions

Appeared in Year: 2015

MCQ▾

Question

Let,

C(θ)=n=0cos(nθ)n!

Which of the following statement is FALSE?

Choices

Choice (4) Response

a.

C(0)+C(π)>2

b.

C(θ)0forallθR

c.

C(0)C(π)=1

d.

C(θ)>0forallθR

Question number: 9

» Trigonometry » Heights and Distances

Appeared in Year: 2016

MCQ▾

Question

A sphere with centre O sits atop of a pole as shown in figure. An observer on the ground is at a distance 50m from the foot of the pole. She notes that the angles of elevation from the observer to points P and Q on the sphere are 30° and 60° , respectively. Then, the radius of the sphere in meters is –

Circle d Circle d: Circle through E with center DEllipse e Ellipse e: Ellipse with foci G, H passing through IAngle α Angle α: Angle between H, C, BAngle β Angle β: Angle between A, C, BSegment c Segment c: Segment [A, B] of Triangle poly1Segment a Segment a: Segment [B, C] of Triangle poly1Segment b Segment b: Segment [C, A] of Triangle poly1Segment f Segment f: Segment [F, A] Segment g Segment g: Segment [G, H] Segment h Segment h: Segment [H, C] Vector u Vector u: Vector [J, K] Vector u Vector u: Vector [J, K] Vector v Vector v: Vector [J, L] Vector v Vector v: Vector [J, L] Point A A = (-2.16, 3.94) Point A A = (-2.16, 3.94) Point C C = (4.4, 0.1) Point C C = (4.4, 0.1) 50 m text1 = “50 m”50 m text1 = “50 m”50 m text1 = “50 m”60/degree text1_1 = “60/degree”60/degree text1_1 = “60/degree”60/degree text1_1 = “60/degree”30/degree text1_2 = “30/degree”30/degree text1_2 = “30/degree”30/degree text1_2 = “30/degree”P text1_3 = “P”O text1_4 = “O”Q text1_5 = “Q”

a Sphere Sits Atop of a Pole

In figure a sphere with centre O sits atop of a pole is shown. An observer on the ground is a t a distance 50 m from the foot of the pole.

Choices

Choice (4) Response

a.

100(113)

b.

50(113)

c.

5063

d.

10063

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