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Principal Component Analysis (PCA) MCQs

Prepare for Principal Component Analysis (PCA) MCQs with verified questions, past-paper solutions, and conceptual explanations for CSS, PMS, FPSC, PPSC, and NTS examinations.

15 Solved Questions • 12 Mins Practice • Updated for 2026 Competitive Exams
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Direct Definition & Conceptual Scope

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Principal Component Analysis (PCA) constitutes an essential examination topic within Statistics, evaluating theoretical principles, historical context, and practical problem-solving applications. On MCQsMind, candidates practice verified past-paper solutions, conceptual breakdowns, and syllabus-aligned questions tailored for CSS, PMS, and competitive screening examinations.

Welcome to the verified preparation module for Multivariate Statistics on McqsMind. This comprehensive set offers solved multiple-choice questions with answers, detailed explanations, and authentic past-paper style questions aligned with the latest syllabus of Multivariate Statistics (Statistics).

100% Verified Answer Keys CSS, PMS, FPSC, PPSC, NTS Ready 2026/2027 Syllabus Guidelines

Solved Questions

Practice with answers, explanations, and exam-focused revision notes.

15 MCQs Page 1

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Topic Notes: Principal Component Analysis (PCA)

Quick Revision 3 min read 16 key points
Section 1 of 4

1 1. Fundamental Concepts of PCA

4 points
  • Definition
    Principal Component Analysis (PCA): A dimensionality reduction technique that transforms a set of correlated variables into a smaller set of uncorrelated variables called principal components, while retaining maximum variance.
  • Theory
    Objective: The primary goal is to simplify high-dimensional data by projecting it onto a lower-dimensional subspace, minimizing information loss by capturing the directions of greatest variance.
  • Fact
    Linear Combination: Each principal component is a linear combination of the original variables, defined by weights known as loadings or eigenvectors.
  • Fact
    Orthogonality: By construction, principal components are orthogonal to each other, meaning the correlation between any two components is zero.
Section 1 / 4
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1
Which of the following is a common application of PCA in data preprocessing?
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2
In PCA, what is the 'score' of an observation?
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3
What is the sum of the eigenvalues in a PCA performed on a correlation matrix equal to?
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4
What is the primary limitation of PCA when applied to real-world data?
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5
Which mathematical decomposition is the foundation of PCA?
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6
If all variables in a dataset are perfectly correlated, how many principal components are needed to explain 100% of the variance?
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7
What does a 'Scree Plot' visualize in the context of PCA?
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8
What are the coefficients that define the linear combination of original variables to form a principal component called?
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9
Which criterion is commonly used to decide the number of principal components to retain?
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10
What is the maximum number of principal components that can be extracted from a dataset with 'p' variables?
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Pedagogical Syllabus Blueprint

Principal Component Analysis (PCA) MCQs: Preparation Strategy & Exam Blueprint

Examination Weightage & Commission Distribution

In Pakistan's premier competitive examinations—including the Federal Public Service Commission (FPSC General Recruitment & CSS MPT), Punjab Public Service Commission (PPSC Lecturer, Tehsildar & PMS Screening), KPPSC, SPSC, and BPSC—questions derived from Principal Component Analysis (PCA) MCQs consistently constitute a decisive 10% to 25% weightage of the Multivariate Statistics paper. Testing agencies frequently evaluate both foundational factual recall and deeper analytical comprehension, requiring aspirants to master key dates, statutory articles, constitutional clauses, and thematic definitions.

High-Yield Conceptual Pillars & Distractor Analysis

Historical trend analysis across past five-year examination cycles demonstrates that examiner traps frequently involve closely matched numerical alternatives, chronologically contiguous treaties, and semantic subtleties in statutory phraseology. When preparing Principal Component Analysis (PCA) MCQs, candidates must deliberately review the underlying rationale provided for every question rather than merely memorizing raw answer options. Understanding why incorrect distractors fail is the most reliable predictor of achieving top percentiles in computerized and optical mark recognition (OMR) screening tests.

Negative Marking Mitigation & Time Management Protocol

For examinations enforcing negative marking penalties (such as PPSC's 0.25-mark deduction per erroneous response or NTS gatekeeper quotas), an aggressive elimination technique must be deployed. Candidates should systematically rule out improbable options first to elevate probability thresholds from 25% to 50% or 100%. Allocating an average of 45 to 60 seconds per item during mock trials builds the psychological stamina and cognitive precision required to complete 100-question papers within official 90-minute time limits.

Recommended Reference Sources & Statutory Reading

To achieve definitive conceptual mastery in Statistics, candidates are advised to cross-reference our solved explanations with primary gazettes, statutory texts, and canonical academic textbooks. Verifying controversial questions against authentic official repositories guarantees that prospective civil servants and professional candidates present incontestable answers during both optical paper evaluations and viva voce departmental interviews.