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If ""^(n)P(4) =2xx""^(5)P(3), find n....

If ` ""^(n)P_(4) =2xx""^(5)P_(3)`, find n.

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To solve the equation \( nP_4 = 2 \times 5P_3 \), we will follow these steps: ### Step 1: Write the formula for permutations The formula for permutations is given by: \[ nP_r = \frac{n!}{(n-r)!} \] So, we can express \( nP_4 \) and \( 5P_3 \) using this formula. ...
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(i) If ""^(n)P_(5)=20xx""^(n)P_(3) , find n. (ii) If 16xx""^(n)P_(3)=13xx""^(n+1)P_(3) , find n. (iii) If ""^(2n)P_(3)=100xx""^(n)P_(2) , find n.

(i) If ""^(n)P_(4): ""^(n)P_(5)=1:2 , find n. (ii) If ""^(n-1)P_(3): ""^(n+1)P_(3)=5:12 , find n.

Find the value of n such that "(i) "^(n)P_(5) =42 xx ""^(n)P_(3), n gt 4 " (ii) "(""^(n)P_(4))/(" "^(n-1)P_(4))=(5)/(3), n gt 4.

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RS AGGARWAL-PERMUTATIONS-SOLVED EXAMPLES
  1. Find the value of n such that "(i) "^(n)P(5) =42 xx ""^(n)P(3), n g...

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  2. Find r if (i) .^(5)P(r) = 2 .^(6)P(r-1) (ii) .^(5)P(r) =^(6)P(r-1).

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  3. If ""^(n)P(4) =2xx""^(5)P(3), find n.

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  4. (i) If ""^(15)P(r)=2730, find the value of r. (ii) If ""^(10)P(r)=5...

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  5. If .^56 P(r+6):^(54)P(r+3)=30800 :1, findr

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  6. If ^2n+1P(n-1):^(2n-1)Pn=3:5,fin dndot

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  7. If ""^(22)P(r+1):""^(20)P(r+2)=11:52, find r.

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  8. Prove that: (i) ""^(n)P(n)=""^(n)P(n-1) " (ii) "^(n)P(r)=n* ""^...

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  9. If r lt s le n " then prove that " ^(n)P(s) " is divisible by "^(n)P(r...

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  10. Find the number of permutations of 7 objects, taken 3 at a time.

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  11. Find the number of different permutations of the letters of the word ...

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  12. How many words can be formed using the letter A thrice, the letter B ...

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  13. (i) Find how many arrangements can be made with the letters of the wo...

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  14. Find the number of arrangements of the letters of the INDEPENDENCE....

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  15. How many different words can be formed by using all the letters of the...

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  16. In how many of the distinct permutations of the letters in MISSISSIPPI...

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  17. (i) How many words can be formed with the letters of the word, 'HARYAN...

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  18. In how many ways can the letters of the word 'PERMUTATIONS' be arrang...

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  19. If the different permutations of all the letter of the word EXAMINATIO...

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  20. Find the number of words with or without meaning which can be made ...

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