SSCCHSL quantitative aptitude

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Question
SSCCGLENQA12042138

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

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As space increment ADE space tilde space increment ABC comma
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Question
SSCCGLENQA12042139

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

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

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

(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