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UPTET Paper 1 Model Test 1

Section: Mathematics

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Question : 102 of 150

Marks: +1, -0

Simplify:

\frac{(7.3)^{3}-(4.7)^{3}}{(7.3)^{2}+7.3\times 4.7+(4.7)^{2}}

12
3.2
2.6
11

Solution:

Concept:

This uses the algebraic identity:

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

.

Explanation:

Let

a = 7.3

and

b = 4.7

.

The numerator is

a^3 - b^3

.

The denominator is

a^2 + ab + b^2

.

Using the identity, the numerator becomes

(a - b)(a^2 + ab + b^2)

.

Cancel the common factor

(a^2 + ab + b^2)

from numerator and denominator.

We are left with

a - b

.

Substitute values:

7.3 - 4.7 = 2.6

.

Answer:

2.6

(Option C)

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