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UPTET Paper 1 2013 Solved Paper

Question : 94 of 150

Marks: +1, -0

\frac{5.47\times 5.47-4.53\times 4.53}{0.94}-\frac{14.50}{7.25}

Solution:

Concept:

Use the identity

a^{2} - b^{2} = (a - b)(a + b)

to simplify the numerator, then cancel common factors.

Explanation:

First, rewrite the expression:

\frac{5.47^2 - 4.53^2}{0.94} - \frac{14.50}{7.25}

Calculate the second fraction:

\frac{14.50}{7.25} = 2

Apply the identity:

5.47^2 - 4.53^2 = (5.47 - 4.53)(5.47 + 4.53)

This simplifies to

(0.94) \times (10) = 9.4

Now the first term becomes

\frac{9.4}{0.94} = 10

Subtract the 2:

10 - 2 = 8

Answer:

C. 8

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