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Let n1<n2<n3<n4<n5 be positive intege...

Let `n_1

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MOTION-THEORY AND EXERCISE BOOK-EXERCISE - 4 (LEVEL -II)
  1. Using permutation or otherwise, prove that (n^2)!/(n!)^n is an integer...

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  2. r, s, t are prime numbers and p, q are natural numbers such that LCM o...

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  3. The letters of the word COCHIN are permuted and all the permutation...

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  4. Consider all possible permutations of the letters of the word ENDEANOE...

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  5. The number of seven digit integers, with sum of the digits equal to 10...

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  6. Let S={1,,2,34} . The total number of unordered pairs of disjoint s...

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  7. The total number of ways in which 5 balls of differ- ent colours can b...

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  8. Let a(n) denote the number of all n-digit numbers formed by the digits...

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  9. Let a(n) denote the number of all n-digit numbers formed by the digits...

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  10. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

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  11. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

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  12. Let ngeq2 be integer. Take n distinct points on a circle and join each...

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  13. Let n1<n2<n3<n4<n5 be positive integers such that n1+n2+n3+n4+n5=20...

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  14. Let n be the number of ways in which 5 boys and 5 girls can stand in a...

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  15. A debate club consists of 6 girls and 4 boys. A team of 4 members is t...

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  16. How many 3xx3 matrices M with entries from {0,1,2} are there, for whic...

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  17. Word of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J....

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  18. In a high school, a commintee has to be formed from a group of 6 boys ...

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  19. The number of 5 digit numbers which are divisible by 4, with digits ...

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  20. Let X=(\ ^(10)C1)^2+2(\ ^(10)C2)^2+3(\ ^(10)C3)^2+\ ddot\ +10(\ ^(10)C...

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