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Permutations & combinations

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Q. How many ways can 5 different letters be selected from the alphabet?
  • A. 26
  • B. 3003
  • C. 156
  • D. 120
Q. How many ways can 5 different prizes be awarded to 3 students?
  • A. 60
  • B. 100
  • C. 150
  • D. 200
Q. How many ways can 6 different books be arranged on a shelf if 2 specific books must be together?
  • A. 120
  • B. 720
  • C. 240
  • D. 480
Q. How many ways can 6 people be arranged in a circle?
  • A. 720
  • B. 120
  • C. 60
  • D. 30
Q. How many ways can 6 people be divided into 2 groups of 3?
  • A. 20
  • B. 30
  • C. 10
  • D. 15
Q. How many ways can a committee of 3 be formed from 5 people?
  • A. 10
  • B. 15
  • C. 20
  • D. 5
Q. How many ways can you arrange the letters of the word 'BANANA'?
  • A. 60
  • B. 30
  • C. 20
  • D. 10
Q. How many ways can you choose 3 fruits from a basket of 5 different fruits?
  • A. 10
  • B. 15
  • C. 20
  • D. 5
Q. How many ways can you form a committee of 3 from a group of 10 people?
  • A. 120
  • B. 90
  • C. 80
  • D. 100
Q. How many ways can you select 2 fruits from 5 different fruits?
  • A. 10
  • B. 15
  • C. 20
  • D. 5
Q. How many ways can you select 2 students from a group of 8?
  • A. 28
  • B. 56
  • C. 36
  • D. 8
Q. In how many ways can 3 boys and 2 girls be seated in a row?
  • A. 30
  • B. 60
  • C. 120
  • D. 24
Q. In how many ways can 3 different colored balls be arranged in a line?
  • A. 6
  • B. 3
  • C. 9
  • D. 12
Q. In how many ways can 3 different colored balls be chosen from a set of 7?
  • A. 35
  • B. 21
  • C. 42
  • D. 56
Q. In how many ways can 3 men and 2 women be arranged in a line if the men must be together?
  • A. 60
  • B. 120
  • C. 30
  • D. 24
Q. In how many ways can 3 red balls and 2 blue balls be arranged in a row?
  • A. 10
  • B. 15
  • C. 20
  • D. 25
Q. In how many ways can 3 red, 2 blue, and 1 green balls be arranged in a line?
  • A. 60
  • B. 120
  • C. 30
  • D. 10
Q. In how many ways can 4 different books be chosen from a shelf of 10 books?
  • A. 210
  • B. 120
  • C. 240
  • D. 300
Q. In how many ways can 4 different books be selected from a shelf of 10 books?
  • A. 210
  • B. 120
  • C. 240
  • D. 300
Q. In how many ways can 4 different colored balls be arranged in a line?
  • A. 16
  • B. 24
  • C. 32
  • D. 48
Q. In how many ways can 4 different colored balls be placed in 3 different boxes?
  • A. 81
  • B. 64
  • C. 27
  • D. 12
Q. In how many ways can 4 different prizes be awarded to 3 students?
  • A. 12
  • B. 24
  • C. 36
  • D. 48
Q. In how many ways can 4 different prizes be distributed among 3 students?
  • A. 81
  • B. 64
  • C. 27
  • D. 12
Q. In how many ways can 4 students be selected from a group of 10?
  • A. 210
  • B. 120
  • C. 240
  • D. 300
Q. In how many ways can 5 different colored balls be arranged in a box?
  • A. 60
  • B. 120
  • C. 100
  • D. 80
Q. In how many ways can 5 different flags be arranged on a pole?
  • A. 120
  • B. 60
  • C. 30
  • D. 24
Q. In how many ways can 5 different items be selected from 10 items?
  • A. 252
  • B. 120
  • C. 200
  • D. 300
Q. In how many ways can 5 different objects be selected from 10 objects?
  • A. 252
  • B. 120
  • C. 10
  • D. 100
Q. In how many ways can 6 different objects be selected and arranged in a line?
  • A. 720
  • B. 600
  • C. 840
  • D. 960
Q. In how many ways can 6 people be divided into 2 groups of 3?
  • A. 20
  • B. 30
  • C. 10
  • D. 15
Showing 31 to 60 of 63 (3 Pages)

Permutations & Combinations MCQ & Objective Questions

Understanding permutations and combinations is crucial for students preparing for various exams in India. This topic not only enhances problem-solving skills but also plays a significant role in scoring well in objective questions. By practicing MCQs and other practice questions, students can grasp important concepts and improve their exam readiness.

What You Will Practise Here

  • Basic definitions and differences between permutations and combinations
  • Formulas for calculating permutations and combinations
  • Applications of permutations and combinations in real-life scenarios
  • Solving problems involving arrangements and selections
  • Understanding the concept of factorials and their role in calculations
  • Common theorems related to permutations and combinations
  • Practice with solved examples and objective questions

Exam Relevance

Permutations and combinations are integral parts of the mathematics syllabus for CBSE, State Boards, NEET, and JEE. Students can expect questions that test their understanding of these concepts in various formats, such as direct calculations, word problems, and application-based scenarios. Familiarity with common question patterns will help students tackle these problems with confidence during exams.

Common Mistakes Students Make

  • Confusing permutations with combinations, especially in word problems
  • Incorrectly applying formulas, particularly in complex scenarios
  • Neglecting to account for restrictions or conditions in a problem
  • Overlooking the importance of factorial notation in calculations

FAQs

Question: What is the difference between permutations and combinations?
Answer: Permutations refer to arrangements where order matters, while combinations refer to selections where order does not matter.

Question: How can I improve my skills in permutations and combinations?
Answer: Regular practice of MCQs and solving important questions will enhance your understanding and problem-solving abilities.

Start solving practice MCQs on permutations and combinations today to test your understanding and boost your confidence for the upcoming exams!

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