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CTET Paper II (Mathematics and Science) 29 Jan 2023 Solved Paper

Question : 38 of 150

Marks: +1, -0

If x =

\frac{(1.75)^{2}-(1.62)^{2}}{0.13}

, then x is equal to

Solution:

Concept:

Use the algebraic identity

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

to simplify the numerator before dividing.

Explanation:

First, rewrite the numerator:

(1.75)^2 - (1.62)^2 = (1.75 - 1.62)(1.75 + 1.62)

Calculate the differences:

1.75 - 1.62 = 0.13

and

1.75 + 1.62 = 3.37

So the expression becomes

\frac{0.13 \times 3.37}{0.13}

Cancel the common factor

0.13

from numerator and denominator, leaving

x = 3.37

Answer:

A. 3.37

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