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SSCCHSL quantitative aptitude

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Question
SSCCGLENQA12042138
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In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and DE are 10 cm, 5 cm and 6 cm respectively. What is the length of BC?

  • 9 cm

  • 2 cm

  • 3 cm

  • 11 cm

Solution

A.

9 cm

As space increment ADE space tilde space increment ABC comma
  rightwards double arrow space space space AD over AB space equals space DE over BC rightwards double arrow space space fraction numerator 10 over denominator 10 plus 5 end fraction space equals space 6 over BC therefore space space space space BC space equals space fraction numerator 6 space cross times space 15 over denominator 10 end fraction space equals space 9 space cm
                 

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Question
SSCCGLENQA12042139
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A carpenter can build a cupboard in 60 hours. After 15 hours he takes a break. What fraction of the cupboard is yet to be built?

  • 0.5

  • 0.9

  • 0.75

  • 0.25

Solution

C.

0.75

Carpenter takes break after 15 hours
∴  45 hours of work is left
∴ Fraction of work left
                  equals space 45 over 60 space equals space 9 over 12 space equals space 3 over 4 space equals space 0.75
               

 

Question
SSCCGLENQA12042140
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Which of the following equations has the sum of its roots?

  • x2 - 5x + 6 = 0

  • x2 - 5x - 6 = 0

  • x2 + 5x + 6 = 0

  • x2 + 5x - 6 = 0

Solution

A.

x2 - 5x + 6 = 0

x2 - 5x + 6 = 0
The sum of roots open parentheses straight alpha space plus space straight beta close parentheses is given by,
                         equals negative straight b over straight a space equals space fraction numerator negative left parenthesis negative 5 right parenthesis over denominator 1 end fraction space equals space 5

Question
SSCCGLENQA12042141
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If Girilal's salary is 11 over 7 times of Hariram's and Shekhar's is 3 over 4 times of Hariram's, What is the ratio of Girilal's salary to Shekhar's salary.

  • 44 : 21

  • 28 : 33

  • 33 : 28

  • 21 : 44

Solution

A.

44 : 21

Girilal = 11 over 7 space cross times space Hariram
7Girilal = 11 Hariram
∴   Girilal : Hariram = 11 : 7    ...(i)

Hariram : Shekhar = 4 : 3       ...(ii)
∴  Girilal : Hariram : Shekhar = 11 x 4 : 7 x 4 : 7 x 3
                                           = 44 : 28 : 21

Question
SSCCGLENQA12042142
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(cos A + sin A)2 + (cos A - sin A)2 equals to

  • 1

  • 1 half

  • 2

  • 0

Solution

C.

2

[cos A + sin A]2 + [cos A - sin A]2
   = cos2A + sin2A + 2cosAsinA + cos2A  +sin2A - 2cosA sinA
   = 1 + 1 = 2

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