Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide to work independently. After trying all possible combination of elements, they conclude that the spell does not work. How many attempts does each wizard make before coming to this conclusion, independently?

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Solution

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Official answer: A) 24

Quantitative Aptitude

The problem asks for the number of attempts made by each wizard independently.

There are $4$ distinct elements: *water*, *air*, *fire*, and *earth*. Mixing all four elements in all possible orders corresponds to the number of permutations of $4$ distinct items:

\text{Number of attempts} = 4! = 4 \times 3 \times 2 \times 1 = 24

Since each wizard independently tests all possible orders, each wizard makes $24$ attempts.

Therefore, the correct option is (A).

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This Quantitative Aptitude previous year question is Q2 of the GATE CSE 2024 Set 2 paper. Find more GATE CSE PYQs on Quantitative Aptitude in General Aptitude, or browse all GATE CSE PYQs.

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Quantitative Aptitude in GATE CSE

Quantitative Aptitude has 53 GATE CSE PYQs across 13 papers from 2011 to 2026. 26 of them are 1-mark MCQs like this one, and GATE CSE 2024 Set 2 has 5.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.