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NCHMCT JEE 2023 Solved Paper

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Question : 8 of 200

Marks: +1, -0

Simplify

\frac{\frac{7}{8} \times \frac{7}{8}+\frac{5}{6} \times \frac{5}{6}+\frac{7}{8} \times \frac{5}{3}}{\frac{7}{8} \times \frac{7}{8}-\frac{5}{6} \times \frac{5}{6}}

41
40
38
35

Solution:

Concept:

Recognize the numerator as

(a+b)^2

and denominator as

a^2-b^2

, where

a=\frac{7}{8}

and

b=\frac{5}{6}

.

Explanation:

Let

a=\frac{7}{8}

and

b=\frac{5}{6}

.

Also,

\frac{5}{3}=2b

.

So numerator:

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

.

Denominator:

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

.

Thus, expression

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

.

Now,

a+b=\frac{7}{8}+\frac{5}{6}=\frac{21+20}{24}=\frac{41}{24}

.

And

a-b=\frac{7}{8}-\frac{5}{6}=\frac{21-20}{24}=\frac{1}{24}

.

Therefore,

\frac{a+b}{a-b}=\frac{41/24}{1/24}=41

.

Answer:

41

, i.e., option A.

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