Which one among the following is indicated by the following figure?

F1 Shailesh.Y 17-09-20 Savita D1

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UPSC CAPF Previous Year Paper 6 (Held on: 13 July 2014)
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  1. \(a+ab+ab^2+........=\frac{a}{1-b} \ for \ b < 1\)
  2. \(a>b \ \rightarrow \ a^3 > a^3\)
  3. \((a+b)^2 = a^2 + 2ab + b^2\)
  4. \(a > b \rightarrow - a < - b\)

Answer (Detailed Solution Below)

Option 3 : \((a+b)^2 = a^2 + 2ab + b^2\)
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Detailed Solution

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Concept:

Area of rectangle = Length × Width

 

Calculation:

Given Figure:

F1 Shailesh.Y 23-11-20 Savita D1

As we can see side length of the figure is (a + b) and width is (a + b) 

Area of figure = Length × width = (a + b) × (a + b) = (a + b)2         ..... (1)

Now,

Area of figure = Area of section 1 + Area of section 2 + Area of section 3 + Area of section 4

= a × a + a × b + b × a + b × b

=  a2 + 2ab + b2

∴ (a + b)2 = a2 + 2ab + b2

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