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If P(5, r)=P(6, r-1),\ fin d\ rdot...

If `P(5, r)=P(6, r-1),\ fin d\ rdot`

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To solve the equation \( P(5, r) = P(6, r-1) \), we will follow these steps: ### Step 1: Write the permutation formulas The permutation formula \( P(n, r) \) is given by: \[ P(n, r) = \frac{n!}{(n-r)!} \] Using this, we can express \( P(5, r) \) and \( P(6, r-1) \): ...
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RD SHARMA-PERMUTATIONS-Solved Examples And Exercises
  1. Evaluate each of the following: \ ^(10)P4

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  2. Evaluate each of the following: P(6,4)

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  3. If P(5, r)=P(6, r-1),\ fin d\ rdot

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  4. If \ ^n P4=360 ,\ find the value of ndot

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  5. If P(9, r)=3024 ,\ find rdot

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  6. If P(11 , r)=P(12 , r-1) find ndot

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  7. If P(n-1,\ 3): P(n ,4)=1:9 find n

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  8. If ""^(2n-1)P(n): ""^(2n+1)P(n-1)=22:7, find n.

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  9. If P(n ,5): P(n ,3)=2:1 find n

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  10. Prove that: P(1,1)+2. P(2,2)+3. P(3,3)++ndotP(n , n)=P(n+1,\ n+1)-1.

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  11. In how many ways can five children stand in a queue?

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  12. From among the 36 teachers in a school, one principal and one vice ...

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  13. Four letters E, K, S an V, one in each, were purchased from a plastic ...

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  14. Four books, one each in Chemistry, Physics, Biology and Mathematics, ...

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  15. Find the number of different 4-leter words, with or without meaning, ...

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  16. How many 3 digit numbers are there, with distinct digits, with each ...

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  17. How many words, with or without meaning, can be formed by using all th...

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  18. There are two works each of 3 volumes and two works each of 2 volumes;...

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  19. There are 6 items in column A and 6 items in column B. A student is ...

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  20. How many three digit numbers are there, with no digit repeated.

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