Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

3.

A number, when divided by 296, gives 75 as the remainder. If the same number is divided by 37 then the remainder will be

  • 1

  • 2

  • 19

  • 31


A.

1

Shortcut Method:
In all such questions, divide the remainder by new number.
i.e on dividing 75 by 37 we get 1 as remainder.

245 Views

7.

If open parentheses straight x plus 1 over straight x close parentheses squared space equals space 3, then open parentheses straight x cubed space plus space 1 over straight x cubed close parentheses is equal to

  • 3

  • 2

  • 1

  • 0


D.

0

If straight x space plus space 1 over straight x space equals space straight a comma space then straight x cubed space plus space 1 over straight x cubed space equals space straight a cubed space minus space 3 straight a
open parentheses straight x plus 1 over straight x close parentheses squared space equals space 3
space space space
straight x plus 1 over straight x space equals space square root of 3
therefore space space straight x cubed space plus space 1 over straight x cubed space equals space open parentheses square root of 3 close parentheses cubed space minus space 3 square root of 3 space equals space 3 square root of 3 space minus space 3 square root of 3 space equals space 0

153 Views

5.

The sum and product of two numbers are 12 and 35 respectively. The sum of their reciprocals will be

  • 1 third
  • 1 fifth
  • 12 over 35
  • 35 over 12

C.

12 over 35

Sum of reciprocals =  fraction numerator Sum space of space numbers over denominator Product space of space numbers end fraction equals space 12 over 35

186 Views

4.

The square root of
fraction numerator left parenthesis 0.75 right parenthesis cubed over denominator 1 minus 0.75 end fraction space plus space open square brackets 0.75 space plus space left parenthesis 0.75 right parenthesis squared space plus space 1 close square brackets is

  • 1

  • 2

  • 3

  • 4


B.

2

fraction numerator left parenthesis 0.75 right parenthesis cubed over denominator 1 minus 0.75 end fraction plus space open square brackets open parentheses 0.75 close parentheses squared space plus space 0.75 space cross times space 1 space plus space 1 close square brackets
equals space open square brackets fraction numerator left parenthesis 0.75 right parenthesis cubed space plus space left parenthesis 1 minus 0.75 right parenthesis open square brackets left parenthesis 0.75 right parenthesis squared space plus space 0.75 space cross times space 1 space plus space 1 squared close square brackets over denominator 1 minus 0.75 end fraction close square brackets
equals space fraction numerator left square bracket left parenthesis 0.75 right parenthesis cubed space plus space left parenthesis 1 right parenthesis cubed space minus space left parenthesis 0.75 right parenthesis cubed over denominator 0.25 end fraction space equals space fraction numerator 1 over denominator 0.25 end fraction space equals space 100 over 25 space equals space 4
∴  Square root space equals space square root of 4 space equals space 2
157 Views

9.

If straight x plus 1 over straight x space equals space 2, then the value of straight x to the power of 100 space plus space 1 over straight x to the power of 100 is

  • 2

  • 0

  • 1

  • -1


A.

2

Shortcut Method:
Put x = 1 as it balances the equation
therefore space space space straight x to the power of 100 space plus space 1 over straight x to the power of 100 space equals space 1 space plus space 1 space space equals space 2

129 Views

6.

If straight a squared space plus space straight b squared space plus space 1 over straight a squared space plus space 1 over straight b squared space equals space 4 comma then the value of straight a squared space plus space straight b squared will be

  • 1

  • 1 1 half
  • 2

  • 2 1 half

C.

2

Shortcut Method:
Put a = 1,  b = 1 , as it balances the equation.
rightwards double arrow space space space space straight a squared space plus straight b squared space plus space 1 over straight a squared space plus 1 over straight b squared space equals space 4
rightwards double arrow space space space 1 squared space plus space 1 squared space plus space 1 over 1 squared space plus space 1 over 1 squared space equals space 4
∴ the value of a2 + b2 is open square brackets left parenthesis 1 right parenthesis squared space plus space left parenthesis 1 right parenthesis squared space equals space 2 close square brackets

142 Views

10.

If straight x cubed plus 3 straight x squared plus 3 straight x space equals space 7 comma then x is equal to

  • 2

  • cube root of 6
  • 1

  • -1


C.

1

straight x cubed plus 3 straight x squared space plus space 3 straight x space equals space 7
rightwards double arrow space space space straight x cubed space plus space 3 straight x squared space plus space 3 straight x plus 1 space equals space 7 plus space 1 space equals space 8
rightwards double arrow space left parenthesis straight x space plus space 1 right parenthesis cubed space equals space 2 cubed
rightwards double arrow space space straight x space plus space 1 space equals space 2
rightwards double arrow space space space straight x space equals space 1
165 Views

8. fraction numerator 0.1 space cross times space 0.1 space cross times space 0.1 space plus space 0.02 space cross times space 0.02 space cross times space 0.02 over denominator 0.2 space cross times space 0.2 space cross times space 0.2 space plus space 0.04 space cross times space 0.04 space cross times space 0.04 end fraction is equal to
  • 0.125

  • 0.250

  • 0.500

  • 0.855


A.

0.125

Let 0.1 = a ,    then 0.2 = 2a
and 0.02 = b,  then 0.04 = 2b
∴  Expression
     equals space fraction numerator straight a space cross times space straight a space cross times space straight a space plus space straight b space cross times space straight b space cross times space straight b over denominator 2 straight a space cross times space 2 straight a space cross times 2 straight a space plus space 2 straight b space cross times space 2 straight b space cross times space 2 straight b end fraction
equals space fraction numerator straight a cubed space plus space straight b cubed over denominator 8 straight a cubed space plus space 8 straight b cubed end fraction space equals space fraction numerator straight a cubed space plus space straight b cubed over denominator 8 left parenthesis straight a cubed space plus space straight b cubed right parenthesis end fraction space equals space 1 over 8 space equals space 0.125

153 Views

2.

A number, when divided successively by 4, 5 and 6 leaves remainders 2, 3 and 4 respectively. The least such number is

  • 50

  • 53

  • 58

  • 214


D.

214

216 Views

1.

A General, while arranging his men, who were 6000 in number, in the form of a square, found that there were 71 men left over. How many were arranged in each row?

  • 73

  • 77

  • 87

  • 93


B.

77

Number of men arranged in the form of square
    = 6000 - 71 = 5929
∴   Number of men arranged in each row
      equals space space square root of 5929 space equals space 77

723 Views