Exercise 7.2 Class 11 Math Solutions - Unit 7 Permutations and Combinations, Punjab Board

Step-by-step solutions to Exercise 7.2, Unit 7: Permutations and Combinations, for Class 11 Punjab Board students. Covers the definition and algebraic evaluation of linear permutations ⁿPᵣ = n! / (n - r)!, solving for unknown n or r in permutation equations, and solving restricted arrangement word problems worked out question by question.

This page provides complete, step-by-step solved solutions for Exercise 7.2 of Unit 7: Permutations and Combinations for Class 11 Mathematics under the Punjab Board (PCTB / PECTAA). All questions on applying the permutation formula ⁿPᵣ = n!/(n - r)!, solving algebraic equations to find unknown values of n and r, evaluating word formation arrangements, digit orderings with and without repetition, and constrained seating arrangements are thoroughly worked out for HSSC Part 1 board exam preparation.
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Exercise Overview

Exercise 7.2 in Unit 7 of Class 11 Mathematics develops the mathematical framework of Permutations. An arrangement of n distinct objects in a definite linear order taken r at a time is called a permutation, designated by ⁿPᵣ = n! / (n - r)! = n(n - 1)(n - 2)...(n - r + 1). Students learn both the algebraic and practical applications of this fundamental combinatorial operator.

The exercise features diverse problem categories: algebraic equations where students determine unknown values of n or r from permutation ratios (e.g., ⁿP₅ : ⁿ⁻¹P₄ = 6 : 1), and word problem arrangements under various geometric and positional constraints. These constraints include arranging letters of words such that particular vowels or consonants always sit together (the "tie-together" grouping method) or never occur consecutively, as well as digit permutations forming numbers greater than or less than given thresholds.

In Punjab Board HSSC Part 1 examinations, Exercise 7.2 is one of the most reliable sources for Section B short questions (algebraic n evaluations) and Section C long questions (constrained permutations word problems) across Lahore, Rawalpindi, Gujranwala, Faisalabad, and Multan boards. Practicing these step-by-step solutions ensures students develop rigorous analytical reasoning and foolproof exam execution.

FAQs

Are these Exercise 7.2 solutions according to the Punjab Board syllabus?
Yes, these solutions strictly follow the official Punjab Curriculum and Textbook Board (PCTB / PECTAA) syllabus for Class 11 Mathematics, covering linear permutations and arrangement problems for the 2026-2027 academic session.
Do these solutions cover every question in Exercise 7.2?
Yes, every textbook problem from Exercise 7.2 is completely solved with step-by-step working, including evaluating ⁿPᵣ, solving equations involving permutation ratios, and calculating constrained word/digit arrangements.
What is the formula for the permutation of n distinct objects taken r at a time?
The number of permutations of n distinct objects taken r at a time is given by ⁿPᵣ = n! / (n - r)!, where 0 ≤ r ≤ n.
What is the difference between a permutation and the fundamental counting principle?
A permutation is a specific application of the Fundamental Principle of Counting applied to ordering distinct objects without replacement, where order of arrangement matters.
Can students read these solutions online?
Yes, students can read all Exercise 7.2 solutions directly online through MaryamNotes.pk on any web browser without needing to download external files or install third-party apps.
Are these solutions useful for Punjab Board exams?
Yes, solving for n in equations like ⁿP₄ = 20 x ⁿP₂ and word arrangement problems with vowel restrictions are high-frequency questions in Section B short questions and Section C long questions.
Are these solutions based on the latest PCTB / PECTAA syllabus?
Yes, they are fully aligned with the updated Student Learning Outcomes (SLO) mandated by the Punjab Curriculum and Textbook Board (PECTAA) for the 2026-2027 academic year.
Are these solutions free for students?
Yes, all Class 11 Mathematics Exercise 7.2 solutions on MaryamNotes.pk are available entirely free of cost for students and teachers across Punjab.