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A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then `k-20` is equal to

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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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