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 Multiple Choice QuestionsMultiple Choice Questions

61.

If 2 space sin space open parentheses πx over 2 close parentheses space equals space straight x squared space plus space 1 over straight x squared comma then the value of open parentheses straight x minus 1 over straight x close parentheses is

  • -1

  • 2

  • 1

  • 1

134 Views

62.

If 0 degree space less than space straight theta space less than space 90 degree, the value of sin θ + cos θ is

  • equal to 1

  • greater than 1

  • less than 1

  • less than 1

164 Views

63.

If θ is a positive acute angle and tan 2θ tan 3θ = 1, then the value of 
left parenthesis 2 space cos squared straight theta fraction numerator 5 straight theta over denominator 2 end fraction minus 1 right parenthesis is

  • negative 1 half
  • 1

  • 0

  • 0

188 Views

64.

If sin space 17 degree space equals space straight x over straight y comma then the value of left parenthesis sec space 17 degree space minus space sin space 73 degree right parenthesis is

  • fraction numerator straight y squared over denominator straight x square root of straight y squared minus straight x squared end root end fraction
  • fraction numerator straight x squared over denominator straight y square root of straight y squared minus straight x squared end root end fraction
  • fraction numerator straight x squared over denominator straight y square root of straight x squared minus straight y squared end root end fraction
  • fraction numerator straight x squared over denominator straight y square root of straight x squared minus straight y squared end root end fraction
124 Views

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65.

In a right-angled triangle, XYZ, right-angled at Y, If XY space equals space 2 square root of 6 and XZ - YZ = 2, then sec X + tan X is

  • fraction numerator 1 over denominator square root of 6 end fraction
  • square root of 6
  • 2 square root of 6
  • 2 square root of 6


B.

square root of 6

XZ - YZ =  2                  ...(i)
rightwards double arrow space space space space space space space XY squared space plus space YZ squared space equals space XZ squared
rightwards double arrow space space space space open parentheses 2 square root of 6 close parentheses squared space equals space XZ squared space minus space YZ squared
rightwards double arrow space space space space 24 space equals space left parenthesis XZ space minus space YZ right parenthesis space left parenthesis XZ space plus space YZ right parenthesis
rightwards double arrow space space space space space space XZ space plus space YZ space equals space 12 space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis ii right parenthesis
Adding both the equations, 
  2XZ = 14 ⟹  XZ = 7
 ∴     YZ = 7 - 2 = 5
therefore space space space space sec space straight X space equals space fraction numerator 7 over denominator 2 square root of 6 end fraction
tan space straight X space equals space fraction numerator 5 over denominator 2 square root of 6 end fraction
therefore space space sec space straight X space plus space tan space straight X space equals space fraction numerator 7 over denominator 2 square root of 6 end fraction space plus space fraction numerator 5 over denominator 2 square root of 6 end fraction space equals space fraction numerator 12 over denominator 2 square root of 6 end fraction space equals space square root of 6
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66.

If tan θ - cot θ = 0 and θ is positive acute angle, then the value of fraction numerator tan space left parenthesis straight theta space plus space 15 degree right parenthesis over denominator tan space left parenthesis straight theta space minus 15 degree right parenthesis end fraction is

  • 3

  • fraction numerator 1 over denominator square root of 3 end fraction
  • 1 third
  • 1 third
173 Views

67.

If sec space straight theta space minus space tan space straight theta space equals space fraction numerator 1 over denominator square root of 3 end fraction comma the value of sec space straight theta. space space tan space straight theta is

  • 2 over 3
  • fraction numerator 2 over denominator square root of 3 end fraction
  • fraction numerator 4 over denominator square root of 3 end fraction
  • fraction numerator 4 over denominator square root of 3 end fraction
359 Views

68.

If 5 space cos space straight theta space plus space 12 space sin space straight theta space equals space 13,  0 degree less than straight theta less than 90 degree comma then the value of sin space straight theta is

  • 5 over 13
  • negative 12 over 13
  • 6 over 13
  • 6 over 13
165 Views

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69.

If sin A + sin2A = 1,  then the value of cos2A + cos4A is

  • 2

  • 1 2 over 3
  • 1 1 half
  • 1 1 half
155 Views

70.

If 7 space sin squared straight theta space plus space 3 cos squared straight theta space equals space 4, then the value of tan θ is (θ is acute)

  • fraction numerator 1 over denominator square root of 3 end fraction
  • fraction numerator 1 over denominator square root of 2 end fraction
  • square root of 3
  • square root of 3
155 Views

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