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Maths XI C, D

Mrs. G.R. Valsala

Date of submission : 26/10/09

 

(Maths optional)

 

PERMUTATIONS AND COMBINATIONS

  1. How many words, with or without meaning each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
  1. How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
  1. A committee of 7 has to be formed from nine boys and four girls.  In how many ways can this be done when the committee consists of:
      1. Exactly 3 girls? (ii) At least 3 girls? (iii) Almost 3 girls?

BINOMIAL THEOREM

Using Binomial Theorem, evaluate each of the following:

4.   (96)3

5.   (102)5

6. (101)4

7. Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.

8. Find (x+1)6 + (x-1)6. Hence or otherwise evaluate (√2 + 1)6 + (√2 – 1)6.

9. Show that 9 n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.

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