Quantitative Aptitude

Permutation and Combination

609 Questions
All Vowels or Objects Together 139 Restricted Group Selection 135 Objects Never Together 98 Fundamental Counting Principle 96 Objects with Repetitions Arrangement 72 Rank or Dictionary Word 20 Selection With Identical Items 15 Pairing or Grouping 10 Distributing Distinct Objects 9 Distributing Identical Objects 9 Circular Ring Arrangement 5 Circular Necklace Arrangement 1

Permutation and Combination Questions

Multiple choice

There are 20 questions in a question paper. If no two students solve the same combination of questions but solve equal number of questions then the maximum number of students who appeared in the examination is
  1. $\displaystyle ^{20}C_9$
  2. $\displaystyle ^{20}C_{11}$
  3. $\displaystyle ^{20}C_{10}$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To have the maximum number of students solving an equal number of questions with unique combinations, we look for the maximum value of nCr, which occurs at the middle term. For n=20, this is 20C10.

Multiple choice

An examination consists of $10$ multiple choice questions, where each question has $4$ options, only one of which is correct. In every question, a candidate earns $3$ marks for choosing the correct option, and $-1$ for choosing a wrong option. Assume a candidate answers all questions by choosing exactly one option for each. Then the number of distinct combinations of answers which can earn the candidate a score from the set $\left {15, 16, 17, 18, 19, 20\right }$ is
  1. $27$
  2. $120$
  3. $3240$
  4. $6480$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let c be correct answers, w be wrong answers. c + w = 10. Score = 3c - w = 3c - (10-c) = 4c - 10. We want 4c - 10 in {15, 16, 17, 18, 19, 20}. 4c in {25, 26, 27, 28, 29, 30}. Since c must be an integer, 4c = 28, so c = 7. Number of ways to get 7 correct = 10C7 * 3^3 = 120 * 27 = 3240.

Multiple choice

The number of different ways in which five 'alike dashes' and eight 'alike dots' can be arranged using only seven of these 'dashes' and 'dots' is
  1. $350$
  2. $120$
  3. $1287$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We need to choose 7 items from 5 dashes and 8 dots. This is equivalent to finding the number of combinations of dashes (d) and dots (t) such that d + t = 7, where 0 <= d <= 5 and 0 <= t <= 8. Summing the combinations for each valid (d, t) pair gives the total arrangements.

Multiple choice

In an examination, the question paper consists of $10$ questions which are equally divided into two sections $a$ and $b$. A student has to attempt a total of six questions by attempting at least two from each section. In how many ways can the student select the questions?
  1. $200$
  2. $180$
  3. $300$
  4. $360$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Section A has 5 questions, Section B has 5. Need 6 questions total, at least 2 from each. Cases: (2A, 4B) = 5C2 * 5C4 = 10 * 5 = 50. (3A, 3B) = 5C3 * 5C3 = 10 * 10 = 100. (4A, 2B) = 5C4 * 5C2 = 5 * 10 = 50. Total = 50 + 100 + 50 = 200.