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Solved Examples

Question 1: Solve (x - 2)(x - 4)2
Solution:
Given, (x - 2)(x - 4)2

=> (x - 2)(x - 4)2  = (x - 2)(x2 + 16 - 8x)

[Using identity, (a - b)2 = a2 + b2 - 2ab]

=> (x - 2)(x2 + 16 - 8x) = x(x2 + 16 - 8x) - 2(x2 + 16 - 8x)

= x3 + 16x - 8x2 - 2x2 - 32 + 16x

= x- 10x2 + 32x - 32

=> (x - 2)(x - 4)2 = x- 10x2 + 32x - 32
 

Question 2: The perimeter of a rectangle is 50 inch. The length of the rectangle is 5 inch less than twice the width. Find the length and width of the rectangle.

Solution:
Given
Perimeter of rectangle = 50

Let width of the rectangle = x

Then length of rectangle = 2x - 5

[Perimeter of rectangle = 2(Length + Breadth)]

=> 50 = 2(2x - 5 + x)

=> 50 = 2(3x - 5)

=> 50 = 6x - 10

=> 50 + 10 = 6x

=> 60 = 6x

=> x = 10

So length of rectangle = 2x - 5 = 2 * 10 - 5

= 20 - 5 = 15

=> Width of the rectangle = 10 inch

and length of rectangle = 15 inch

 

Question 3: A pair of dice is rolled. What is the probability of getting a sum of 2 ?
Solution:
Sample Space = {(1, 1), (1, 2), .......(1, 6), (2, 1), (2, 2),......,(2, 6), (3, 1), (3, 2),.........., (3, 6), (4, 1), (4, 2), .............., (4, 6), (5, 1), (5, 2), ......, (5, 6), (6, 1), (6, 2), .........., (6, 6)}

Total number of possible outcomes = 36

Possible outcomes getting sum of 2 = {(1,1)}

Number of favorable outcomes = 1

P(getting sum of 2) = $\frac{Number   of   Favorable   Outcomes}{Number   of   Possible    Outcomes}$

= $\frac{1}{36}$

=> P(getting sum of 2) = $\frac{1}{36}$.