GATE DA 2026 Q43: Number of cuboids from three concept hierarchies

Consider the concept hierarchies as shown in the figure.

Which of the following options denotes the total number of possible data cuboids from these concept hierarchies?

Try it: multiple choice: exactly one correct option

Wrong answer costs 2/3 mark in GATE.

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Answer: A (official GATE 2026 final answer key)

Concept used: With hierarchies, total cuboids $= \prod_i (L_i + 1)$ , where $L_i$ is the number of levels of dimension $i$ (the $+1$ is "all").

First step: Each dimension has 3 levels plus "all", so 4 choices for each of the 3 dimensions.

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key