Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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61.

If straight x space equals space fraction numerator 2 plus square root of 3 over denominator 2 minus square root of 3 end fraction space comma then the value of straight x space plus space 1 over straight x ?

  • 14

  • 8 square root of 3

  • 0

  • 18


A.

14

Shortcut Method:
The space value space of space space space fraction numerator square root of straight a space plus space square root of straight b over denominator square root of straight a space minus space square root of straight b end fraction space plus space fraction numerator square root of straight a space minus square root of straight b over denominator square root of straight a space plus space square root of straight b end fraction space equals fraction numerator left parenthesis straight a space plus straight b right parenthesis over denominator left parenthesis straight a minus straight b right parenthesis end fraction space cross times space 2
straight i. straight e. space fraction numerator 4 space plus space 3 over denominator 4 space minus space 3 end fraction space cross times space 2 space equals space 14


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62.

If straight x space equals space 2 space plus space square root of 3 comma space then what is the value of square root of 2 straight x space plus space fraction numerator 1 over denominator square root of 2 straight x end root end fraction ?

  • 2 square root of 3

  • 3 square root of 3

  • fraction numerator left parenthesis 3 square root of 3 space plus space 1 right parenthesis over denominator 2 end fraction

  • 2 square root of 3 space plus space 1


63.

If straight x space plus space 1 over straight x space equals space 4 comma space then what is the value of straight x to the power of 6 space plus space 1 over straight x to the power of 6 ?

  • 52

  • 256

  • 1026

  • 2702


64.

If straight y space equals space fraction numerator 2 minus straight x over denominator 1 plus straight x end fraction comma then what is the value of fraction numerator 1 over denominator straight y space plus space 1 end fraction space plus space fraction numerator 2 straight y space plus space 1 over denominator straight y squared minus 1 end fraction ?

  • fraction numerator left parenthesis 1 space plus space straight x right parenthesis thin space left parenthesis 2 space minus space straight x right parenthesis over denominator 2 straight x minus 1 end fraction

  • fraction numerator left parenthesis 1 space minus space straight x right parenthesis thin space left parenthesis 2 space plus space straight x right parenthesis over denominator straight x space minus space 1 end fraction

  • fraction numerator left parenthesis 1 space plus space straight x right parenthesis thin space left parenthesis 2 space minus space straight x right parenthesis over denominator 1 space minus space 2 straight x end fraction

  • fraction numerator left parenthesis 1 plus straight x right parenthesis thin space left parenthesis 1 minus 2 straight x right parenthesis over denominator 2 minus straight x end fraction


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65.

In the ΔABC,  and the bisectors of  and  meets at P What is the value (in degrees) of 

  • 100°

  • 105°

  • 115°

  • 125°


66.

Two circles of same radius intersect each other at P and Q. If the length of the common chord is 30 cm and distance between the centres of the two circles is 40 cm, then what is the radius (in cm) of the circles?

  • 25 cm

  • 50 cm


67.

In the given figure, angle QRN space equals space 40 degree comma space space angle PQR space equals space 46 degree and MN is a tangent at R. What is the value (in degrees) of x,y and z respectively.

  • 40°, 46°,  94°

  • 40°, 50°,  90°

  • 46°, 54°,  80°

  • 50°, 40°,  90°


68.

In ΔPQR,  the perpendicular of PQ at S meets QR at T. If  then what is the value (in degrees) of ?

  • 25°

  • 40°

  • 50°

  • 60°


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69.

What is the simplified value of fraction numerator cot space straight A space plus space tan space straight B over denominator cot space straight B space plus space tan space straight A end fraction ?

  • tan B cot A

  • tan A cot B

  • tan A tan B

  • cot A cot B


70.

What is the simplified value of open parentheses fraction numerator 1 over denominator cosec space straight A space plus space cot space straight A end fraction close parentheses squared ?

  • sec A + tan A

  • fraction numerator open parentheses 1 space minus space cos space straight A close parentheses over denominator left parenthesis 1 space plus space cos space straight A right parenthesis end fraction

  • fraction numerator left parenthesis 1 minus cosec space straight A right parenthesis over denominator left parenthesis 1 space plus space cosec space straight A right parenthesis end fraction

  • sin A


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