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Given that a, b, c, d are non-negative real numbers satisfying a + b + c + d = 9 and a² + b² + c² + d² = 27: Statement-1: d belongs to the interval [0, 9/2]. Statement-2: ((a + b + c) / 3)² <= (a² + b² + c²) / 3.

1. Statement-1 is True, Statement-2 is True
2. Statement-1 is False, Statement-2 is False
3. Statement-1 is True, Statement-2 is False
4. Statement-1 is False, Statement-2 is True

Correct answer: Statement-1 is True, Statement-2 is True

Solution

Statement-2 is the well-known Cauchy-Schwarz / QM-AM inequality and is always true. Use it on a, b, c to bound d from Statement-1's constraints.

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