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UPTET Paper 2 Math and Science Model Test 3

Section: Mathematics and Science

Question : 130 of 150

Marks: +1, -0

\frac{762\times 762\times 762+316\times 316\times 316}{762\times 762-762\times 316+316\times 316}

Solution:

Concept:

The expression matches the algebraic identity for sum of cubes:

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

. The denominator is exactly

a^2 - ab + b^2

, so the fraction simplifies to

a + b

Explanation:

Let

a = 762

and

b = 316

The numerator becomes

a^3 + b^3

. The denominator is

a^2 - ab + b^2

Apply the identity:

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

Therefore, the fraction is

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

Cancel the common term

a^2 - ab + b^2

from numerator and denominator.

We are left with

a + b = 762 + 316 = 1078

Answer:

D. 1078

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