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__MOST IMPORTANT QUESTIONS__ __FOR GRADE 12 ENTRANCE EXAM__** **__SET-1__

__MOST IMPORTANT QUESTIONS__

__FOR GRADE 12 ENTRANCE EXAM__

__SET-1__

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https://educationgalaxies.blogspot.com

https://educationgalaxies.blogspot.com |

__Permutation__**Q.1**

**.How many ways can 4 students from a group of 15 be lined up for a photograph?**

**solution :**

There are 15 P 4 possible permutations of 4 students from a group of 15.

15 P 4 =

This is asking for the number of permutations, since we don't want repetitions. The number of ways is:

5 P 3 =

There are 4 letters in the word love and making making 3 letter words is similar to arranging these 3 letters and order is important since LOV and VOL are different words because of the order of the same letters L, O and V. Hence it is a permutation problem. The number of words is given by:

4 P 3 =

Given words: BANANA.

Total number of letters in "BANANA" = 6

Total number of "A" in the word "BANANA" = 3

Total number of "N" in the word "BANANA" = 2

so, the permutation =

3 red, 4 yellow and 2 blue bulbs can be arranged in a string of Christmas tree lights with 9 sockets given by:

= 1260

Since there are 5 objects, the number of ways is =5!=120

Number of words we can make using the letters A, B, E, H and L with repetition not allowed given by:5 ! = 5 × 4 × 3 × 2 × 1

= 120

Since there are three "m"s, two "a"s and one "l" in the word "mammal", we have for the number of ways we can arrange the letters in the word "mammal":

The number of ways three alphabets can be chosen from five will be,

5 P 3 =

Here total number of lettersn = 26 . Chosen number of letters r = 4 .

So, The number of different ways of arranging 4 letters of 26-letter alphabet with repetition is given by:26 4 = 456 , 976

=

=

= 15 × 14 × 13 × 12

= 32760 different lineups

**Q.2.In how many ways can a supermarket manager display 5 brands of cereals in 3 spaces on a shelf?****Solution:**This is asking for the number of permutations, since we don't want repetitions. The number of ways is:

=

=

= 5 × 4 × 3

= 60

**Q.3.How many 3 letter words can we make with the letters in the word LOVE?****Solution:**There are 4 letters in the word love and making making 3 letter words is similar to arranging these 3 letters and order is important since LOV and VOL are different words because of the order of the same letters L, O and V. Hence it is a permutation problem. The number of words is given by:

=

= 4 × 3 × 2

= 24

Q.4.Find how many ways you can rearrange the word "BANANA" all at a time?Solution: Given words: BANANA.

Total number of letters in "BANANA" = 6

Total number of "A" in the word "BANANA" = 3

Total number of "N" in the word "BANANA" = 2

so, the permutation =

=

= 60

Q.5.How **ny ordered arrangements are****there of the letters in the word****PHILIPPINES?**Solution:

*The number of ordered arrangements of the letters in the word PHILIPPINES is:*

= 1 , 108 , 800

**Q.6.How many different ways can 3 red, 4 yellow and 2 blue bulbs be arranged in a string of Christmas tree lights with 9 sockets?**Solution: 3 red, 4 yellow and 2 blue bulbs can be arranged in a string of Christmas tree lights with 9 sockets given by:

**Q.7.In how many ways can 5 bulbs be arranged****in series?****Solution:**Since there are 5 objects, the number of ways is =5!=120

**Q.8.How many different words can we make using the letters A, B, E, H and L where repetition is not allowed?****Solution:**Number of words we can make using the letters A, B, E, H and L with repetition not allowed given by:

**Q.9.In how many ways can the six letters of the word "mammal" be arranged in a row?****Solution:**Since there are three "m"s, two "a"s and one "l" in the word "mammal", we have for the number of ways we can arrange the letters in the word "mammal":

=

=

= 2 |

= 60 **Q.10.If three alphabets are to be chosen from A, B, C, D and E such that repetition is not allowed then in how many ways it can be done?****Solution:**The number of ways three alphabets can be chosen from five will be,

=

=

= 60

**Q.11.How many three digit numbers can be formed with the digits: 1, 2, 3, 4, 5 with repetition allowed.**

**Solution:**

**Here total number of digits n = 5.**

Number of digits taken each time r = 3. We know that the number of permutations of r objects taken from n objects with repetition allowed is =n r . So number of permutations here is = 5 3 = 125

Number of digits taken each time r = 3. We know that the number of permutations of r objects taken from n objects with repetition allowed is =

**Q.12.Find the number of different ways of arranging 4 letters of 26-letter alphabet with repetition.**

**Solution**

__:__Here total number of letters

So, The number of different ways of arranging 4 letters of 26-letter alphabet with repetition is given by: