Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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61.

If straight alpha space plus space straight beta space equals space 90 degree and straight alpha space colon thin space straight beta space equals space 2 space colon space 1 comma then the ratio of cos space straight alpha space to space cos space straight beta is:

  • 1 space colon space square root of 3

  • 1 : 3

  • 1 colon square root of 2

  • 1 colon square root of 2


A.

1 space colon space square root of 3

 Let space space straight alpha space equals space 2 straight x
and space straight beta space equals space straight x

According to the question,

       straight alpha space plus space straight beta space equals space 90 degree
2 straight x space plus space straight x space equals space 90 degree
space space space space space space space 3 straight x space equals space 90 degree
space space space space space space space space straight x space equals space 30 degree

         straight alpha space equals space 2 straight x space equals space 2 space cross times space 30 degree space equals space 60 degree
straight beta space equals space 30 degree

fraction numerator cos space straight alpha over denominator cos space straight beta end fraction space equals space fraction numerator cos begin display style space end style begin display style 60 end style begin display style degree end style over denominator cos begin display style space end style begin display style 30 end style begin display style degree end style end fraction space equals space fraction numerator open parentheses begin display style 1 half end style close parentheses over denominator open parentheses begin display style fraction numerator square root of 3 over denominator 2 end fraction end style close parentheses end fraction space equals space 1 space colon space square root of 3

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62.

The least number to be added to 13851 to get a number which is divisible by 87 is

  • 18

  • 43

  • 54

  • 54

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63.

Two numbers are in the ratio 3 : 5. If 6 is added to both of them, the ratio becomes 2 : 3. The numbers are

  • 21 and 35

  • 30 and 50

  • 24 and 40

  • 24 and 40

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64.

The average weight of 10 parcels is 1.7 kg. Addition of another new parcel reduces the average weight by 60 gm. What is the weight, in kg, of the new parcel?

  • 1.04

  • 1.08

  • 1.4

  • 1.4

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65.

If x = 999, y = 1000, z = 1001, then the value of fraction numerator straight x cubed plus straight y cubed plus straight z cubed minus 3 xyz over denominator straight x minus straight y plus straight z end fraction is

  • 1000

  • 9000

  • 1

  • 1

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66.

If fraction numerator straight a over denominator 1 minus 2 straight a end fraction space plus space fraction numerator straight b over denominator 1 minus 2 straight b end fraction space plus space fraction numerator straight c over denominator 1 minus 2 straight c end fraction space equals space 1 half, then the value of fraction numerator 1 over denominator 1 minus 2 straight a end fraction space plus space fraction numerator 1 over denominator 1 minus 2 straight b end fraction space plus space fraction numerator 1 over denominator 1 minus 2 straight c end fraction is

  • 1

  • 2

  • 3

  • 3

51 Views

67.

In an isosceles triangle ABC, AB = AC and angle straight A space equals space 80 degree comma the bisector of angle straight B and angle straight C meet at D. The angle BDC is equal to

  • 90°

  • 100°

  • 130°

  • 80°

66 Views

68.

The length of the chord which is at distance of 12 cm from the centre of a circle of radius 13 cm is

  • 10 cm

  • 5 cm

  • 6 cm

  • 12 cm

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69.

If θ is a positive acute angle and 7 space cos squared straight theta space plus space 3 space sin squared straight theta space equals space 4 comma then the value of θ is

  • 60°

  • 30°

  • 45°

  • 45°

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70.

Radius cross section of a solid circular cylindrical rod is 3.2 dm. The rod is melted and 44 equal solid cubes of side 8 cm are formed. The length of the rod is left parenthesis Take space straight pi space equals space 22 over 7 right parenthesis

  • 56 cm

  • 7 cm

  • 5.6 cm

  • 5.6 cm

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