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GATE 2025 EE – Question 9

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 2 marks · Multiple choice

Spheres of unit diameter are centered at $(l,m,n)$ where $l$, $m$, and $n$ take every possible integer values.

The distance between two spheres is computed from the center of one sphere to the center of the other. For a given sphere, $x$ is the distance to its nearest sphere and $y$ is the distance to its next nearest sphere. The value of $\dfrac yx$ is:

  1. $2\sqrt2$
  2. $\dfrac1{\sqrt2}$
  3. $\sqrt2$
  4. 2

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Show answer and explanation

Correct answer: (C) $\sqrt2$

Explanation

The centres form the integer lattice. The nearest neighbours are at distance $x=1$ (along an axis). The next nearest are at $\sqrt2$ (along a face diagonal). So $y/x=\sqrt2$.