Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

102.

cube root of 1 minus 127 over 343 end root is equal to

  • 5 over 9

  • 1 minus 1 over 7

  • 4 over 7

  • 1 minus 2 over 7


B.

1 minus 1 over 7

cube root of 1 minus 127 over 343 end root space equals space cube root of fraction numerator 343 minus 127 over denominator 343 end fraction end root space equals space cube root of 216 over 343 end root space equals space 6 over 7 equals space space 1 minus 1 over 7

34 Views

106.

The square root of open parentheses fraction numerator square root of 3 space plus space square root of 2 over denominator square root of 3 space minus space square root of 2 end fraction close parentheses is

  • square root of 3 space plus space square root of 2

  • square root of 3 space minus space square root of 2

  • square root of 2 space plus-or-minus space square root of 3

  • square root of 2 minus square root of 3


A.

square root of 3 space plus space square root of 2

First solve: 
open parentheses fraction numerator square root of 3 space plus space square root of 2 over denominator square root of 3 minus square root of 2 end fraction close parentheses
space equals space fraction numerator straight S plus 2 square root of straight P over denominator straight D end fraction
equals space fraction numerator left parenthesis 3 plus 2 right parenthesis space plus space 2 square root of 3 space cross times space 2 end root over denominator left parenthesis 3 minus 2 right parenthesis end fraction
equals space fraction numerator 5 plus 2 square root of 6 over denominator 3 minus 2 end fraction
equals space 5 space plus space 2 square root of 6
∴   Required square root
           equals space square root of 5 plus 2 square root of 6 end root space equals space square root of left parenthesis square root of 3 space plus space square root of 2 right parenthesis squared end root space equals space square root of 3 space plus space square root of 2

31 Views

101.

If 9 square root of straight x space equals space square root of 12 space plus space square root of 147 comma then x = ?

  • 2

  • 3

  • 4

  • 5


B.

3

space 9 square root of straight x space equals space square root of 12 space plus space square root of 147
rightwards double arrow space space 9 square root of straight x space equals space 2 square root of 3 space plus space 7 square root of 3
rightwards double arrow space space 9 square root of straight x space equals space 9 square root of 3
rightwards double arrow space space space square root of straight x space equals space square root of 3 space space space space space space space space left square bracket Squaring space both space sides right square bracket
rightwards double arrow space space space space straight x space equals space 3

74 Views

105.

square root of 6 plus square root of 6 plus square root of 6 plus... end root end root end root space equals space ?

  • 2.3

  • 3

  • 6

  • 6.3


B.

3

Shortcut Method:
Find out two coprime numbers i.e whose HCF is 1. 
for ex. (3, 2) are coprime factors of 6.
In case of (+) symbol followed in the question, the large co-prime factor required answer i.e. 3. 

37 Views

103.

If the sum of two numbers be multiplied by each number separately, the products so obtained are 247 and 114. The sum of the numbers is

  • 19

  • 20

  • 21

  • 23


A.

19

Let two numbers be x and y respectively.
According to the question,
              (x)  x (x + y) = 247 
               x2 + xy = 247    ...(i)
And,      (y) x (x + y) = 114     
               y2 + xy = 114    ...(ii)
Adding (i) and (ii), we get
               x2  + y2 + 2xy = 361
⟹            (x + y)2 = 361
⟹             (x + y) = 19
∴  Sum of the numbers are 19.


50 Views

108.

The value of fraction numerator 2 begin display style 1 third end style minus 1 begin display style 2 over 11 end style over denominator 3 plus begin display style fraction numerator 1 over denominator 3 plus begin display style fraction numerator 1 over denominator 3 plus begin display style 1 third end style end fraction end style end fraction end style end fraction is

  • 38 over 109

  • 109 over 38

  • 1

  • 116 over 109


A.

38 over 109

fraction numerator 2 begin display style 1 third end style minus 1 begin display style 2 over 11 end style over denominator 3 plus begin display style fraction numerator 1 over denominator 3 plus begin display style fraction numerator 1 over denominator 3 plus begin display style 1 third end style end fraction end style end fraction end style end fraction space equals space fraction numerator begin display style 7 over 3 minus 13 over 11 end style over denominator 3 plus begin display style fraction numerator 1 over denominator 3 plus begin display style fraction numerator 1 over denominator begin display style 10 over 3 end style end fraction end style end fraction end style end fraction
equals space fraction numerator begin display style fraction numerator 77 minus 39 over denominator 33 end fraction end style over denominator 3 plus begin display style fraction numerator 1 over denominator 3 plus begin display style 3 over 10 end style end fraction end style end fraction space equals space fraction numerator begin display style 38 over 33 end style over denominator 3 plus begin display style fraction numerator 1 over denominator begin display style 33 over 10 end style end fraction end style end fraction
equals space fraction numerator 38 divided by 33 over denominator 3 plus begin display style 10 over 33 end style end fraction space equals space fraction numerator 38 divided by 33 over denominator 109 divided by 33 end fraction space equals space 38 over 109

30 Views

104.

Find a number, one-seventh of which exceeds its eleventh part by 100.

  • 1925

  • 1825

  • 1540

  • 1340


A.

1925

Let the number be x.
According to the question,
    straight x space cross times space 1 over 7 space minus space straight x over 11 space equals space 100
rightwards double arrow space space fraction numerator 11 straight x minus 7 straight x over denominator 77 end fraction space equals space 100
rightwards double arrow space space space 4 straight x space equals space 77 space cross times space 100
rightwards double arrow space space space space straight x space equals space fraction numerator 77 space cross times space 100 over denominator 4 end fraction
rightwards double arrow space space space straight x space equals space 1925

35 Views

109.

The last digit of (1001)2008 +  1002 is

  • 0

  • 3

  • 4

  • 6


B.

3

(1001)2008 + 1002 
Unit digit in 18  + 1002
 = 1 + 1002 = 1003
Hence, last digit is 3.

73 Views

107.

The remainder when 321 is divided by 5 is

  • 1

  • 2

  • 3

  • 4


C.

3

The unit digit of 321 is 3.
The remainder, when a number is divided by 5, always the unit digit itself. i .e. 3  is the right answer.

48 Views

110.

The value of 
fraction numerator 3 square root of 2 over denominator square root of 3 space plus space square root of 6 end fraction space minus space fraction numerator 4 square root of 3 over denominator square root of 6 space end root begin display style plus end style begin display style square root of 2 end style end fraction space plus space fraction numerator square root of 6 over denominator square root of 3 begin display style space end style begin display style plus end style begin display style space end style begin display style square root of 2 end style end fraction is

  • 4

  • 0

  • square root of 2

  • 3 square root of 6


B.

0

space space fraction numerator 3 square root of 2 over denominator square root of 3 space plus space square root of 6 end fraction space equals space fraction numerator 3 square root of 2 over denominator square root of 3 begin display style space end style begin display style plus end style begin display style space end style begin display style square root of 6 end style end fraction space cross times space fraction numerator square root of 3 begin display style minus end style begin display style square root of 6 end style over denominator square root of 3 begin display style minus end style begin display style square root of 6 end style end fraction
equals space space fraction numerator 3 square root of 6 space minus space 3 square root of 12 over denominator 3 minus 6 end fraction space equals space fraction numerator 3 square root of 6 minus 3 square root of 12 over denominator negative 3 end fraction
equals space square root of 12 space minus space square root of 6 space equals space 2 square root of 3 space minus space square root of 6 space space space space space space space space space space... left parenthesis straight i right parenthesis

fraction numerator 4 square root of 3 over denominator square root of 6 plus square root of 2 end fraction space equals space fraction numerator 4 square root of 3 over denominator square root of 6 begin display style plus end style begin display style square root of 2 end style end fraction space cross times space fraction numerator square root of 6 begin display style minus end style begin display style square root of 2 end style over denominator square root of 6 begin display style minus end style begin display style square root of 2 end style end fraction
space equals space fraction numerator 4 square root of 18 minus 4 square root of 6 over denominator 6 minus 2 end fraction space equals space square root of 18 minus square root of 6 space equals 3 square root of 2 space minus space square root of 6 space space space space space space space space space... left parenthesis ii right parenthesis

fraction numerator square root of 6 over denominator square root of 3 space plus space square root of 2 end fraction space equals space fraction numerator square root of 6 over denominator square root of 3 begin display style space end style begin display style plus end style begin display style space end style begin display style square root of 2 end style end fraction space cross times fraction numerator square root of 3 begin display style space end style begin display style minus end style begin display style space end style begin display style square root of 2 end style over denominator square root of 3 begin display style minus end style begin display style square root of 2 end style end fraction space equals space fraction numerator square root of 18 begin display style minus end style begin display style square root of 12 end style over denominator 3 minus 2 end fraction
space space equals space square root of 18 space minus space square root of 12 space equals space 3 square root of 2 space minus space 2 square root of 3 space space space space space space space space space... left parenthesis iii right parenthesis

therefore space space space fraction numerator 3 square root of 2 over denominator square root of 3 space plus space square root of 6 end fraction space minus space fraction numerator 4 square root of 3 over denominator square root of 6 space plus space square root of 2 end fraction space plus space fraction numerator square root of 6 over denominator square root of 3 space plus space square root of 2 end fraction
space equals space 2 square root of 3 space minus space square root of 6 space minus space 3 square root of 2 space plus space square root of 6 space plus space 3 square root of 2 space minus space 2 square root of 3 space equals space 0

33 Views