Permutation Test

Result

Permutation Test - 2

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

The number of words which can be made out of the letters of the word ‘MOBILE’ when consonants always occupy odd places is

A
20

B
36

C
30

D
720

Solution

The word ‘MOBILE’ has three even places and three odd places. It has 3 consonants and 3 vowels. In three odd places we have to fix up 3 consonants which can be done in ³ P₃ ways. Now remaining three places we have to fix up remaining three places which can be done in ³ P₃ ways.

The total number of ways =³ P₃× ³ P₃ = 36.
Question 2
1 / -0

The number of 4 digit number that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contain digit 1 is

A
1225

B
1252

C
1522

D
480

Solution

After fixing 1 at one position out of 4 places, 3 places can be filled by ⁷P₃ ways. But some numbers whose fourth digit is zero, so such type of ways = ⁶ P₂

∴ Total ways = ⁷ P₃– ⁶ P₂= 480.
Question 3
1 / -0

If the letters of the word ‘KRISNA’ are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word ‘KRISNA’ is

A
324

B
341

C
359

D
None of these

Solution

Words starting from A are 5 ! = 120;    Words starting from I are 5 ! = 120

Words starting from KA are 4 ! = 24;                    Words starting from KI are 4 ! = 24

Words starting from KN are 4 ! = 24;                     Words starting from KRA are 3 ! = 6

Words starting from KRIA are 2 ! = 2;                   Words starting from KRIN are 2 ! = 2

Words starting from KRIS are 1 ! = 1                    Words starting from KRISNA are 1 ! = 1

Hence rank of the word KRISNA is 324
Question 4
1 / -0

An n digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of n for which this is possible is

A
6

B
7

C
8

D
9

Solution

Since at any place, any of the digits 2, 5 and 7 can be used total number of such positive n-digit numbers are 3ⁿ. Since we have to form 900 distinct numbers, hence 3ⁿ ≥ 900 ⇒ n = 7 .