Consider the following statements :1) If in a triangle ABC, A = 2

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 Multiple Choice QuestionsMultiple Choice Questions

91.

Let asin2(x) + bcos2(x) = c; bsin2(y) + acos2(y) = d and p tan(x) = qtan(y).

What is tan2(x) equal to ?

  • c - ba - c

  • a - cc - b

  • c - ac - b

  • c - bc - a


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92.

Consider the following statements :

1) If in a triangle ABC, A = 2B and b = c, then it must be an obtuse-angled triangle.

2) There exists no triangle ABC with A = 40o. B = 65o and ac = sin40°csc15°

Which of the above statements is/are correct ?

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


B.

2 only

We know sine rule,

asinA = bsinB = csinC1 We have, b = c sinB = sinCAnd, A = 2B sinA = sin2B sin180 - B + C = sin2B sinB + C = 2sinBcosB sinBcosC +cosBsinC = 2sinBcosB sinBcosC +cosBsinB = 2sinBcosB   sinB = sinC sinBcosC + cosB = 2sinBcosB cosC +cosB = 2cosB cosC = cosBIf sinB = sinC and cosC = cosBMeans, B = C = 45°Then A = 90°.So, in this triangle there is no obtuse angle. so this triangle ABC is not obtuse angle triangle.

This statement is wrong..

2 If A = 40° and B = 65°We know that A + B+ C = 180° C = 180 - 45 - 65 = 75°We know sine rule,asinA = bsinB = csinC asin40 = bsin65 = csin75 asin40 = csin75 ac = sin40csc75So here  ac  sin40csc15Then, this statement is right


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93.

What is the value of cos48° - cos12° ?

  • 5 - 14

  • 1 - 54

  • 5 + 12

  • 1 - 58


94.

Consider the following statements :

1) If ABC is a right-angled triangle, right-angled at A and if then cosec(C) = 3

2) If bcos(B) = ccos(C) and if the triangle ABC is not right-angled, then ABC must be isosceles.

Which of the above statements is/are correct ?

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


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95.

What is the value of 8cos10° . cos20° . cos40° ?

  • tan10°

  • cot10°

  • csc10°

  • sec10°


96.

What is sin(3x) + cos(3x) + 4sin(3x) – 3sin(x) + 3cos(x) – 4cos(3x) equal to ?

  • 0

  • 1

  • 2sin(2x)

  • 4cos(4x)


97.

A and B are positive acute angles such that cos(2B) = 3 sin(2A) and 3sin(2A) = 2sin(2B). What is the value of (A + 2B) ?

  • π6

  • π4

  • π3

  • π2


98.

ABC is a trapezium such that AB and CD are parallel and BC is perpendicular to them. Let ADB = θABD = α, BC = p and CD = q.

If tanθ = cos17° - sin17°cos17° + sin17° then what is the value of θ ?

  • 0°

  • 28°

  • 38°

  • 52°


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99.

ABC is a trapezium such that AB and CD are parallel and BC is perpendicular to them. Let ADB = θABD = α, BC = p and CD = q.

What is AB equal to ?

  • p2 - q2sinθpcosθ + qsinθ

  • p2 - q2cosθpcosθ + qsinθ

  • p2 + q2sinθpcosθ + qsinθ

  • p2 - q2cosθqcosθ + psinθ


100.

ABC is a trapezium such that AB and CD are parallel and BC is perpendicular to them. Let ADB = θABD = α, BC = p and CD = q.

Consider the following :

1) ADsin(θ) = ABsin(α)

2) BDsin(θ) = ABsin(θ + α)

Which of the above is/are correct ?

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


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