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

Directions: Study the following set of questions carefully and answer the questions given below. Using all the letters of the word LINEAR.How many different words can be formed that start and end with vowel?

  1. 126

  2. 108

  3. 144

  4. 216

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The word LINEAR has 6 letters: 3 vowels (I, E, A) and 3 consonants (L, N, R). To start and end with a vowel, choose 2 vowels for the ends (3 * 2 = 6 ways) and arrange the remaining 4 letters in the middle (4! = 24 ways). Total = 6 * 24 = 144.

Multiple choice

In how many ways the letters of the word 'PLUMBER' be arranged such that U, M always come together and P and R always come at end places?

  1. 2520

  2. 240

  3. 120

  4. 96
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Word PLUMBER (7 letters). P and R at ends: (P _ _ _ _ _ R) or (R _ _ _ _ _ P). 2 ways. Remaining letters: L, U, M, B, E. U and M must be together. Treat (UM) as one unit. We have 4 units: L, B, E, (UM). They can be arranged in 4! = 24 ways. Within (UM), 2! = 2 ways. Total = 2 * 24 * 2 = 96.

Multiple choice

Direction(19-20) :- In each of the following Questions, five words are given. Which of them will come arrange the following words according to English dictionary order. प्रत्येक प्रश्न में पांच शब्द दिए गए है। कौन-सा शब्द निम्नलिखित शब्दों को अंग्रेजी शब्दकोश के अनुसार व्यवस्थित करेगा ? 1. Storm 2. Strap 3. Strangle 4. Stamped 5. Satire

  1. 51432

  2. 51342

  3. 54132

  4. 53412

  5. 0
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Alphabetical order: 1. Satire (Sa), 2. Stamped (Sta-m), 3. Storm (Sto), 4. Strangle (Str-a), 5. Strap (Str-p). Order: 5, 4, 1, 3, 2.

Multiple choice

Direction(18-19) :- In each of the following Questions, five words are given. Which of them will come arrange the following words according to English dictionary order. प्रत्येक प्रश्न में पांच शब्द दिए गए है। कौन-सा शब्द निम्नलिखित शब्दों को अंग्रेजी शब्दकोश के अनुसार व्यवस्थित करेगा ? 1. Cough 2. Council 3. Couch 4. Count 5. Counsel

  1. 13425

  2. 31425

  3. 32145

  4. 31254

  5. 0
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Let E denote the set of letters of the English alphabet, V = {a, e, i, o, u}, and C be the complement of V in E. Then the number of four-letter words (where repetitions of letters are allowed) having at least one letter from V and at least one letter from C is

  1. 2,61,870

  2. 3,14,160

  3. 4,25,880

  4. 8,51,760
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total 4-letter words with 26 letters = 26^4 = 456,976. Words with no vowels (all consonants) = 21^4 = 194,481. Words with no consonants (all vowels) = 5^4 = 625. Words with at least one vowel and at least one consonant = Total - (All Vowels) - (All Consonants) = 456,976 - 625 - 194,481 = 261,870.