Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

107.

The rate of simple interest at which a sum of money becomes three times in 25 yr is

  • 8%

  • 5%

  • 4%

  • 6%


A.

8%

Let principal  = ₹ P
∴    S.I. = 3P - P = ₹ 2P
According to the question,
    rightwards double arrow space space space 2 straight P space equals space fraction numerator straight P space cross times space 25 space cross times space straight r over denominator 100 end fraction
rightwards double arrow space space space space space straight r space equals space fraction numerator 100 space cross times space 2 over denominator 25 end fraction space equals space 8 percent sign

29 Views

105.

The value of x when 5% of square root of 2 straight x end root is 0.01 will be

  • 0.02

  • 0.01

  • 0.05

  • 0.03


A.

0.02

5 percent sign space of space square root of 2 straight x end root space equals space 0.01
rightwards double arrow space space square root of 2 straight x space cross times space space 5 over 100 space equals space 0.01
rightwards double arrow space space square root of 2 straight x end root space equals space 1 fifth
rightwards double arrow space space space 2 straight x space space equals space 1 over 25
therefore space space space space straight x space equals space 1 over 50 space equals space 0.02

39 Views

103.

The distance between the points (0, 0) and the intersecting point of the graph of x = 3 and y = 4 is

  • 3 units

  • 2 units

  • 5 units

  • 4 units


C.

5 units

Coordinate of intersection point of x = 3 and y = 4 is (3, 4).
∴   Required distance:
       equals space square root of left parenthesis 3 space minus space 0 right parenthesis squared space plus space left parenthesis space 4 space minus 0 right parenthesis squared end root
equals space square root of 9 space plus space 16 end root
equals space square root of 25
space equals space 5 space space unit

60 Views

110.

A container has 80 L of milk. From this container, 8 L of milk was taken out and replaced by water. The process was further repeated twice. The volume of the milk in the container after that is

  • 58.23 L

  • 85.23 L

  • 58.32 L

  • 85.32 L


C.

58.32 L

Shortcut Method:
Volume of milk left after 3 operations:
    equals space 80 open parentheses 1 minus 8 over 80 close parentheses cubed space equals space 80 open parentheses 1 minus 1 over 10 close parentheses cubed
equals space fraction numerator 80 space cross times space 9 space cross times space 9 space cross times space 9 over denominator 10 space cross times space 10 space cross times space 10 end fraction space equals space 58.32 space straight L

97 Views

109.

The odd element in the sequence
3, 7, 13, 21, 33, 43, 57, ............ is

  • 33

  • 43

  • 7

  • 21


A.

33

3 rightwards arrow with plus 4 on top 7 rightwards arrow with plus 6 on top 13 rightwards arrow with plus 8 on top 21 rightwards arrow with plus 10 on top stack box enclose 31 with 33 on top rightwards arrow with plus 12 on top 43 rightwards arrow with plus 14 on top 57

27 Views

108.

A and B can separately do a piece of work in 20 and 15 days respectively. They worked together for 6 days after which B was replaced by C. The work as finished in next 4 days. The number of days in which C alone could do the work is

  • 30 days

  • 45 days

  • 40 days

  • 35 days


C.

40 days

Work done by A and B together in 6 days:
   equals space 6 open parentheses 1 over 20 space plus space 1 over 15 close parentheses space equals 6 space open parentheses fraction numerator 3 plus space 4 space over denominator 60 end fraction close parentheses space equals space 7 over 10
Remaining work:
                equals space open parentheses 1 minus 7 over 10 close parentheses space
equals space 3 over 10
Now, this remaining work open parentheses 3 over 10 close parentheses done by A and C in 4 days
∴    The whole work will be completed by A and C in:
                           equals space 4 space cross times space 10 over 3 space space equals space 40 over 3 space days
∴   Net work done by C in 1 day:
                      equals space open parentheses 3 over 40 space minus space 1 over 20 close parentheses space equals space open parentheses fraction numerator 3 minus 2 over denominator 40 end fraction close parentheses space equals space 1 over 40
∴ The no of days in which c alone could do the work is 40 days.
  



   

37 Views

104.

The value of 
(1 + sec 20° + cot 70°) (1 - cosec 20° + tan 70°) is

  • -1

  • 2

  • 1

  • 0


B.

2

(1 + sec 20° + cot 70°) (1 - cosec 20° + tan 70°)
equals space open curly brackets 1 plus space sec space left parenthesis 90 degree space minus space 70 degree right parenthesis space plus space cot space 70 degree right parenthesis close curly brackets space open curly brackets 1 space minus space cosec space left parenthesis 90 degree space minus space 70 degree right parenthesis plus space tan space 70 degree close curly brackets
equals space open curly brackets 1 space plus space cosec space 70 degree space plus space cot space 70 degree close curly brackets space open curly brackets 1 space minus space sec space 70 degree space plus space tan space 70 degree close curly brackets
equals space open square brackets 1 plus fraction numerator 1 over denominator sin space 70 degree end fraction space plus space fraction numerator cos space 70 degree over denominator sin space 70 degree end fraction close square brackets space open square brackets 1 minus fraction numerator 1 over denominator cos space 70 degree end fraction space plus space fraction numerator sin space 70 degree over denominator cos space 70 degree end fraction close square brackets
equals space fraction numerator left parenthesis sin space 70 degree space plus space cos space 70 degree plus 1 right parenthesis thin space left parenthesis sin space 70 degree space plus space cos space 70 degree space minus space 1 right parenthesis over denominator sin space 70 degree space cos space 70 degree end fraction
equals space fraction numerator sin squared 70 degree space plus space cos squared 70 degree space plus space 2 space sin space 70 degree space cos space 70 degree space minus space 1 over denominator sin space 70 degree space cos space 70 degree end fraction
equals space fraction numerator 2 space sin space 70 degree space cos space 70 degree over denominator sin space 70 degree space cos space 70 degree end fraction space space open square brackets because sin squared 70 degree space plus space cos squared 70 degree space equals space 1 close square brackets
equals space space space 2

 

37 Views

101.

The value of square root of negative square root of 3 space plus space square root of 3 space plus space 8 square root of 7 space plus space 4 square root of 3 end root end root end root is

  • 3

  • 4

  • 1

  • 2


D.

2

square root of negative square root of 3 space plus space square root of 3 plus space 8 space square root of 7 space plus space 4 square root of 3 end root end root end root
            equals space square root of negative square root of 3 space plus space square root of 3 space plus space 8 left parenthesis 2 space plus space square root of 3 right parenthesis end root end root
equals space square root of negative square root of 3 space plus space 4 space plus space square root of 3 end root
equals space square root of 4 space equals space 2
         open curly brackets because space space space square root of 7 space plus space 4 square root of 3 end root space equals space fraction numerator square root of 6 space end root space over denominator square root of 2 end fraction plus space fraction numerator square root of 8 over denominator square root of 2 end fraction space equals space left parenthesis space 2 space plus space square root of 3 right parenthesis close curly brackets

65 Views

102.

The tangents drawn at the points A and B of a circle centred at O meet at P. If angle AOB space equals space 120 degree comma then angle APB space colon thin space angle APO is

  • 3 : 2

  • 4 : 1

  • 2 : 1

  • 2 : 5


C.

2 : 1



space space angle APB space equals space 360 degree space minus space 90 degree space minus space 90 degree space minus space 120 degree
therefore space angle APB space equals space 60 degree
As, Δ PAO and Δ PBO are similar, 
therefore space space angle APO space equals space angle OPB space equals space fraction numerator 60 degree over denominator 2 end fraction equals space space 30 degree
therefore space angle APB space colon space angle APO space equals space 60 degree space colon space 30 degree space equals space 2 space colon space 1
    

40 Views

106.

If square root of fraction numerator straight x minus straight a over denominator straight x minus straight b end fraction end root space plus space straight a over straight x space equals space square root of fraction numerator straight x minus straight b over denominator straight x minus straight a end fraction end root space plus space straight b over straight x comma space space straight b not equal to straight a comma space then the value of x is

  • fraction numerator ab over denominator straight a plus straight b end fraction

  • 1

  • fraction numerator straight a over denominator straight a space plus space straight b end fraction

  • fraction numerator straight b over denominator straight a space plus space straight b end fraction


A.

fraction numerator ab over denominator straight a plus straight b end fraction

rightwards double arrow space space space space space square root of fraction numerator straight x minus straight a over denominator straight x minus straight b end fraction end root space plus space straight a over straight x space equals space square root of fraction numerator straight x minus straight b over denominator straight x minus straight a end fraction end root space plus space straight b over straight x
rightwards double arrow space space space space square root of fraction numerator straight x minus straight a over denominator straight x minus straight b end fraction end root space minus space square root of fraction numerator straight x minus straight b over denominator straight x minus straight a end fraction end root space equals space straight b over straight x space minus space straight a over straight x
rightwards double arrow space space space space fraction numerator straight x space minus space straight a space minus space straight x space plus space straight b over denominator square root of left parenthesis straight x minus straight b right parenthesis thin space left parenthesis straight x minus straight a right parenthesis end root end fraction space equals fraction numerator straight b minus straight a over denominator straight x end fraction

rightwards double arrow space space straight x space equals space square root of left parenthesis straight x minus straight a right parenthesis thin space left parenthesis straight x minus straight b right parenthesis end root
rightwards double arrow space space straight x squared space equals space left parenthesis straight x space minus space straight a right parenthesis thin space left parenthesis straight x space minus space straight b right parenthesis
rightwards double arrow space space straight x squared space equals space straight x squared space minus space left parenthesis straight a space plus straight b right parenthesis straight x space plus space ab
rightwards double arrow space space space straight x left parenthesis straight a space plus space straight b right parenthesis space equals space ab
therefore space space space space straight x space equals space fraction numerator ab over denominator straight a plus straight b end fraction

31 Views