SSCCGL quantitative aptitude

Question
SSCCGLENQA12043158

If 7 space sin squared straight theta space plus space 3 cos squared straight theta space equals space 4, then the value of tan θ is (θ is acute)

  • fraction numerator 1 over denominator square root of 3 end fraction
  • fraction numerator 1 over denominator square root of 2 end fraction
  • square root of 3
  • 1

Solution

A.

fraction numerator 1 over denominator square root of 3 end fraction 7 space sin squared straight theta space plus space 3 left parenthesis 1 minus sin squared straight theta right parenthesis space equals space 4
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∴  The value of tan space straight theta space equals space tan space 30 degree space equals space fraction numerator 1 over denominator square root of 3 end fraction

Question
SSCCGLENQA12043159

The value of :
    4 minus fraction numerator 1 over denominator 1 plus begin display style fraction numerator 1 over denominator 3 plus begin display style fraction numerator 1 over denominator begin display style fraction numerator 8 plus 1 over denominator 4 end fraction end style end fraction end style end fraction end style end fraction is 

  • 1 over 8
  • 1 over 64
  • 1 over 16
  • 1 over 32

Solution

A.

1 over 8

Expression
  equals space space 4 minus fraction numerator 5 over denominator 1 plus begin display style fraction numerator 1 over denominator 3 plus begin display style fraction numerator 1 over denominator begin display style fraction numerator 8 plus 1 over denominator 4 end fraction end style end fraction end style end fraction end style end fraction
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Question
SSCCGLENQA12043160

300 grams of sugar solution has 40% of sugar in it. How much sugar should be added to make it 50% in the solution?

  • 40 gram

  • 10 gram

  • 60 gram

  • 80 gram

Solution

C.

60 gram

In 300 gm of solution,
Percentage of sugar = 40%
∴  Sugar = fraction numerator 300 space cross times space 40 over denominator 100 end fraction space equals space 120 space gm.
Let x gm of sugar be added.
Now, according to the question
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Question
SSCCGLENQA12043161

A boat moves downstream at the rate of 1 km in 7 1 half space minutes and upstream at the rate of 5 km an hour. what is the speed of the boat in the still water?

  • 3 1 half space km divided by hour
  • 6 1 half space km divided by hour
  • 4 km/hour

  • 8 km/hour

Solution

B.

6 1 half space km divided by hour

Rate downstream of boat
 WiredFaculty
Rate downstream of boat = 5 kmph
Speed of boat in still water = 1 half left parenthesis Rate space downstream space plus space Rate space upstream right parenthesis
      equals space 1 half left parenthesis 8 plus 5 right parenthesis space equals space 13 over 2 space equals space 6 1 half space kmph

Question
SSCCGLENQA12043162

In an office, 40% of the staff is female. 70% of the female staff and 50% of the male staff are married. The percentage of the unmarried staff in the office is

  • 64

  • 60

  • 54

  • 42

Solution

D.

42

Let the strength of total staff be 100.
∴     Female  = 40% = 40
       Males = 60
Married females = fraction numerator 40 space cross times space 70 over denominator 100 end fraction space equals space 28
Unmarried females = 40 - 28 = 12
Unmarried males = 50% of 60 = 30
∴  Unmarried staff = 30 + 12 = 42 i.e. 42%