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Maths Fundamental of Mathematics General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Consider the statement : x ( α – x) < y ( α – y) for all x, y with 0 < x < y < 1. The statement is true

if and only if α ≥ 2

if and only if α > 2

if and only if α < –1

for no values of α

Text Solution

Verified by Experts

The correct answer is:

For 0 < x < y < 1 f(x) = x ( α – x) = –x 2 + x

f(x) < f(1)

so f(x) should be increasing in (0, 1) and one root is 0 so vertex should be ≥ 1

⇒ ≥ 1, α ≥ 2

0 < x < y < 1 f(x) = x ( α – x) = –x 2 + x

f(x) < f(1)

⇒ ≥ 1, α ≥ 2

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