Subject

Quantitative Aptitude

Class

SSCCHSL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

The base angle of an isosceles trapezium is 45°. If the shorter side and both the equal sides are 10 cm each, what is the area of the trapezium?

  • left parenthesis 50 square root of 2 space plus space 50 right parenthesis cm

  • left parenthesis 50 square root of 2 space plus space 100 right parenthesis cm

  • left parenthesis 100 square root of 2 space plus space 50 right parenthesis cm

  • left parenthesis 100 square root of 2 space plus space 100 right parenthesis cm


A.

left parenthesis 50 square root of 2 space plus space 50 right parenthesis cm

In Δ ADE, 
cos space 45 degree equals space space AE over AD
fraction numerator 1 over denominator square root of 2 end fraction space equals space AE over 10
rightwards double arrow space space AE space equals space fraction numerator 10 over denominator square root of 2 end fraction space equals space 5 square root of 2

Similarly, 
BF space equals space 5 square root of 2 space cm
Now again in Δ ADE, 
sini space 45 degree space equals space DE over AD
rightwards double arrow space fraction numerator 1 over denominator square root of 2 end fraction space equals space DE over 10
rightwards double arrow space space space DE space equals space fraction numerator 10 over denominator square root of 2 end fraction space equals space 5 square root of 2
rightwards double arrow space space AB space equals space AE space plus space EF space plus space BF space equals space 5 square root of 2 space plus space 10 space plus space 5 square root of 2 space equals space 10 space plus space 10 square root of 2
Now, 
Area of trapezium  = 1/2 x (sum of parallel sides) x height
             = 1/2 x (CD + AB) x DE
              space equals space 1 half cross times space left parenthesis 10 space plus space 10 space plus space 10 square root of 2 right parenthesis space cross times space 5 square root of 2
space equals space left parenthesis 10 space plus space 5 square root of 2 right parenthesis space cross times space 5 square root of 2
space equals space left parenthesis 50 square root of 2 space plus space 50 right parenthesis space sq. space cm.
             


22.

If the radius of a circle is increased by 27%, then its area will increase by

  • 61.29%

  • 54%

  • 27%

  • 30.645%


A.

61.29%

Shortcut Method:

space equals space open parentheses straight x space plus space straight y space plus space xy over 100 close parentheses percent sign
equals space open parentheses 27 space plus space 27 space plus space fraction numerator 27 space cross times space 27 over denominator 100 end fraction close parentheses percent sign
equals space 54 space plus space 729 over 100
equals space 54 space plus space 7.29 space equals space 61.29 percent sign


23.

Refer the below data table and answer following question.

Company 2011 2012 2013 2014 2015
Company A 4000 3000 3000 1000 2000
Company B 1000 1000 1000 5000 4000
Company C 1000 1000 4000 2000 1000

For which of the following pairs of years the total exports from the three companies together are equal?
(Note: Figures given are in ₹ lakh)

  • 2013 and 2014

  • 2013 and 2015

  • 2011 and 2012

  • 2014 and 2015


A.

2013 and 2014

Total exports in 2013 for all companies together = 3000 + 1000 + 4000 = 8000
Total exports in 2014 for all companies together = 1000 + 5000 + 2000 = 8000
Thus, total exports for all companies together are equal in 2013 and 2014.


24.

What would be the equation of the line, which intercepts x-axis at -5 and perpendicular to the line y = 2x - 3?

  • x - 2y = -5

  • x + 2y = 5

  • x + 2y = -5

  • x - 2y = 5


C.

x + 2y = -5


25.

To travel 816 km, an Express train takes 9 hours more than Rajdhani. If however, the speed of the Express train is doubled, it takes 4 hours less than Rajdhani. What is the speed of Rajdhani?

  • 48 km/h

  • 62.8 km/h

  • 33.2 km/h

  • 77.5 km/h


A.

48 km/h

Let the speed of Rajdhani  = x km/hr
Speed of Express Train = y km/hr
According to the question,
rightwards double arrow space space 816 over straight y space minus 816 over straight x space equals space 9 space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis straight i right parenthesis
rightwards double arrow space space space 816 over straight x space minus fraction numerator 816 over denominator 2 straight y end fraction space equals space 4 space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis ii right parenthesis
Solving (i) and (ii), we get,
  x = 48 km/hr.