If cot2x3 + tanx3 = csckx3, then the val

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 Multiple Choice QuestionsMultiple Choice Questions

21.

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60o and when he retires 40 meters away from the tree the angle of elevation becomes 30o. The breadth of the river is

  • 20 m

  • 30 m

  • 40 m

  • 40 m

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22.

The equation sin x(sin(x) + cos(x)) = k has real solutions, where k is a real number. Then,

  • 0  k  1 + 22

  • 2 - 3  k  2 + 3

  • 0  k  2 - 3

  • 1 - 22  k  1 + 22


23.

The cosine of the angle between any two diagonals of a cube is

  • 13

  • 12

  • 23

  • 13


24.

The value of cos15°cos71°2sin71°2 is

  • 12

  • 18

  • 14

  • 116


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25.

If z = sinθ - icosθ, then for any integer n,

  • zn +1zn = 2cos2 - 

  • zn +1zn = 2sin2 - 

  • zn -1zn = 2isin  - 2

  • zn -1zn = 2icos2 - 


26.

The minimum value of cosθ + sinθ + 2sinθ for θ  0, π2

  • 2 + 2

  • 2

  • 1 + 2

  • 22


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27.

If cot2x3 + tanx3 = csckx3, then the value of k is

  • 1

  • 2

  • 3

  • - 1


B.

2

Given,

cot2x3 + tanx3 = csckx3Let θ = x3, then we getcot2θ + tanθ = csc cos2θsin2θ + sinθcosθ = csc

 2cos2θ - 12sinθcosθ + sinθcosθ = csc 2cos2θ - 1 + 2sin2θ2sinθcosθ = cscθ 12sinθcosθ = csc

 csc2θ = csc k = 2


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28.

If θ  π2, 3π2, then the value of 4cos4θ + sin22θ + 4cotθcos2π4 - θ2 is

  • - 2cotθ

  • 2cotθ

  • 2cosθ

  • 2sinθ


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29.

The number ofreal solutions of the equation sinx - xcosx - x2 = 0 is

  • 1

  • 2

  • 3

  • 4


30.

In ABC, if a2cos2A - b2 - c2 = 0 then

  • π4 < A < π2

  • π2 < A < π

  • A = π2

  • A < π4


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