Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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


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


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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


D.

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

straight y space equals space fraction numerator 2 space minus space straight x over denominator 1 space plus space straight x end fraction
rightwards double arrow space space space space fraction numerator 1 over denominator straight y space plus space 1 end fraction space plus space space fraction numerator 2 straight y space plus space 1 over denominator straight y squared space minus 1 end fraction space equals space fraction numerator 1 over denominator begin display style fraction numerator 2 minus straight x over denominator 1 plus straight x end fraction space plus space 1 end style end fraction space plus space fraction numerator begin display style 2 end style open square brackets begin display style fraction numerator 2 minus straight x over denominator 1 plus straight x end fraction end style close square brackets begin display style plus end style begin display style 1 end style over denominator begin display style open square brackets begin display style fraction numerator 2 minus straight x over denominator 1 plus straight x end fraction end style close square brackets squared end style begin display style minus end style begin display style 1 end style end fraction
rightwards double arrow space space space space space fraction numerator 1 plus straight x over denominator 2 minus straight x plus 1 plus straight x end fraction space plus space fraction numerator left parenthesis 4 minus 2 straight x plus 1 plus straight x right parenthesis over denominator left parenthesis 4 plus straight x squared space minus 4 straight x minus 1 minus straight x squared minus 2 straight x right parenthesis end fraction space cross times space fraction numerator left parenthesis 1 plus straight x right parenthesis squared over denominator left parenthesis 1 space plus space straight x right parenthesis end fraction
rightwards double arrow space space space space space fraction numerator 1 plus straight x over denominator 3 end fraction open square brackets fraction numerator 1 minus 2 straight x plus 5 minus straight x over denominator 1 minus 2 straight x end fraction close square brackets space equals space fraction numerator left parenthesis 1 plus straight x right parenthesis over denominator 3 end fraction fraction numerator left square bracket 6 minus 3 straight x right square bracket over denominator left parenthesis 1 minus 2 straight x right parenthesis end fraction
space space space space space space space space equals space fraction numerator left parenthesis 1 plus straight x right parenthesis left parenthesis 2 minus straight x right parenthesis over denominator left parenthesis 1 minus 2 straight x right parenthesis 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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