In a right-angled triangle, XYZ, right-angled at Y, If  and XZ

Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

81.
The area of the square inscribed in a circle of radius 8 cm is
  • 256 sq. cm.

  • 250 sq. cm.

  • 128 sq. cm.

  • 128 sq. cm.

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82.

X and Y are centres of circles of radii 9cm and 2 cm respectively, XY = 17cm. Z is the centre of a circle of radius r cm which touches the above circles externally. Given that angle XZY space equals space 90 degree comma the value of r is

  • 13 cm

  • 6 cm

  • 9 cm

  • 9 cm

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83.

I is the incentre of a triangle ABC. If angle ABC space equals space 65 degree and angle ACB space equals space 55 degree comma then the value of angle BIC is

  • 130°

  • 120°

  • 140°

  • 140°

204 Views

84.

If the radii of two circles be 6 cm and 3 cm and the length of the transverse common tangent be 8 cm, then the distance between the two centres is

  • square root of 145 space cm
  • square root of 140 space cm
  • square root of 150 space cm
  • square root of 150 space cm
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85.

The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons is respectively.

  • 6, 12

  • 5, 10

  • 4, 8

  • 4, 8

371 Views

86.

Two posts are x metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in metres) of the shorter post is

  • fraction numerator straight x over denominator 2 square root of 2 end fraction
  • straight x over 4
  • straight x square root of 2
  • straight x square root of 2
145 Views

87.

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

88.

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
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89.

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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90.

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

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