GATE DA 2026 Q11: Angle between two principal components

For a classification problem, Principal Component Analysis (PCA) has been used to reduce the dimensionality of a feature space from 100 to 10.

Which of the following options is true about the angle $\theta$ between the first and the tenth principal components?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: B (official GATE 2026 final answer key)

Concept used: Principal components are eigenvectors of a symmetric covariance matrix, so they are orthogonal.

First step: Distinct principal components are mutually perpendicular.

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