Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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91.

If 2 straight y space cosθ space equals space straight x space sinθ and 2 straight x space sec space straight theta space minus space straight y space cosec space straight theta space equals space 3 comma then the value of open parentheses straight x squared space plus space 4 straight y squared close parentheses is

  • 1

  • 2

  • 3

  • 3


D.

3

2 straight y space cosθ space equals space straight x space sin space straight theta space space space space space space  ...(i)
rightwards double arrow space space space space straight x space equals space fraction numerator 2 straight y space cosθ over denominator sin space straight theta end fraction space space space space space... left parenthesis ii right parenthesis
2 straight x space sec space straight theta space minus space straight y space cosec space straight theta space equals space 3 
rightwards double arrow space space space 2. space fraction numerator 2 straight y space cosθ over denominator sin space straight theta end fraction. space sec space straight theta space minus space straight y space cosec space straight theta space space equals space 3 space space space space space left square bracket Using space left parenthesis ii right parenthesis right square bracket
rightwards double arrow space space space 4 straight y space cosec space straight theta space minus space straight y space coecθ space equals space 3
rightwards double arrow space space space 3 straight y space cosec space straight theta space equals space 3
rightwards double arrow space space space space space straight y space equals space fraction numerator 3 over denominator 3 cosec space straight theta end fraction equals space space sin space straight theta
From equation (i),
2 space sin space straight theta space. space cos space straight theta space equals space straight x space sin space straight theta
rightwards double arrow space space space space straight x space equals space 2 space cosθ
therefore space space space space space space straight x squared space plus space 4 straight y squared space equals space 4 space cos squared straight theta space plus space 4 space sin squared straight theta
space space space space equals space 4 left parenthesis cos squared straight theta space plus space sin squared straight theta right parenthesis
space space space space equals space 4
 
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92.

From the top of a cliff 100 metre high, the angles of depression of the top and bottom of a tower are 45° and 60° respectively. The height of the tower is

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93.

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of the bottom of the flag staff is α and that of the top of the flag staff is β. Then the height of the tower is

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94.

A man on the top of a tower, standing on the sea shore, finds that a boat coming towards him takes 10 minutes for the angle of depression to change from 30° to 60°. How soon the boat reach the sea-shore?

  • 5 minutes

  • 7 minutes

  • 10 minutes

  • 50 minutes

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95.

The expression of
fraction numerator cot space straight theta space plus space cosec space straight theta space minus space 1 over denominator cot space straight theta space minus space cosec space straight theta space plus space 1 end fraction is equal to

  • fraction numerator 1 plus cos space straight theta over denominator sin space straight theta end fraction
  • fraction numerator 1 minus cos space straight theta over denominator sin space straight theta end fraction
  • fraction numerator cot space straight theta space plus space 1 over denominator cosec space straight theta end fraction
  • fraction numerator cot space straight theta space plus space 1 over denominator cosec space straight theta end fraction
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96.

The following pie-chart shows the monthly expenditure of a family on various items. If the family spends Rs. 825 on clothing, answer the questions.

         

What is the total monthly income of the family?

  • Rs. 8025

  • Rs. 8250

  • Rs. 8520

  • Rs. 8520

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97.

The following pie-chart shows the monthly expenditure of a family on various items. If the family spends Rs. 825 on clothing, answer the questions.

         

What per cent of the total income does the family save?

  • 15%

  • 50%

  • 20%

  • 20%

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98.

The following pie-chart shows the monthly expenditure of a family on various items. If the family spends Rs. 825 on clothing, answer the questions.

         

What is the ratio of expenses on food and miscellaneous?

  • 3 : 4

  • 2 : 3

  • 3 : 2

  • 3 : 2

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99.

The following pie-chart shows the monthly expenditure of a family on various items. If the family spends Rs. 825 on clothing, answer the questions.

         

What is the average of expenses on clothing and rent?


  • Rs. 1443.75

  • Rs. 1344.57

  • Rs. 1574.34

  • Rs. 1574.34

172 Views

100.

The following pie-chart shows the monthly expenditure of a family on various items. If the family spends Rs. 825 on clothing, answer the questions.

         

The ratio of average of expenses on food, clothing and miscellaenous items to the average of expenses on savings and rent is

  • 3 : 2

  • 1 : 3

  • 2 : 1

  • 2 : 1

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