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Prove that "^nCr + 2. ^nC(r-1) + ^nC(r-2...

Prove that `"^nC_r + 2. ^nC_(r-1) + ^nC_(r-2) = ^(n+2)C_r`

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Prove that ^nC_(r)+^(n-1)C_(r)+...+^(r)C_(r)=^(n+1)C_(r+1)

Prove that: .^nC_rxx^rC_s=^nC_sxx^(n-s)C_(r-s)

Prove that two +ive integers n,r cannot be found such that ^nC_r ,^nC_(r+1),^nC_(r+2) and ^nC_(r+3) are in A.P.

nCr + 2.nC (r-1) + nC (r-2) = (n + 2) Cr (2 <= r <= n)

If n and r are positive integers such that 0ltrltn then roots of the equation ^nC_r x^2+2.^nC_(r+1)x+^nC_(r+2)=0 are necessarily (A) imaginary (B) real and equal (C) real and unequal (D) real but may be equal or unequal

Prove that ""^nC_0-2*""^nC_1+3*""^nC_2-...+(-1)""^n(n+1)""^nC_n=0

If n and r are positive integers such that 0ltrltn then show that the roots of the quadratic equation nC_r x^2+2. ^nC_(r+1)x+^nC_(r+2)=0 are real.

^nC_r+^nC_(r+1)+^nC_(r+2) is equal to (2lerlen) (A) 2^nC_(r+2) (B) 2^(n+1)C_(r+1) (C) 2^(n+2)C_(r+2) (D) none of these

Prove that ^nC_0-^nC_1+^nC_2-^nC_3+....+(-1)^r ^C_r+....=(-1)^(r-1) ^(n-1)C_(r-1)

MAHAVEER PUBLICATION-PERMUTATIONS AND COMBINATIONS -QUESTION BANK
  1. Find n if "^nP3 : ^(n+1)P3 = 5:12

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  2. If "^nC10 = ^nC5 find "^nC14

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  3. Find the value of r if "^nPr = 3024 and "^nCr = 126

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  4. Find the value of r if "^(n-1)Pr : ^nPr = 2:3 and "^nCr :^(n+1)Cr = 9:...

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  5. If show that "^(n-1)Pr = (n-r).^(n-1)P(r-1)

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  6. Prove that "^nCr + 2. ^nC(r-1) + ^nC(r-2) = ^(n+2)Cr

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  7. How many odd numbers of 5 district significatcant digits can be formed...

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  8. Find how many word can be formed of the letters in the word "FAILURE" ...

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  9. How many ways the letters of the word "RUBBER" can be arranged ?

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  10. In how many ways can be letters of the word "MULTIPLE" be arranged wit...

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  11. How many numbers of five digits can be formed without repetition if 2,...

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  12. How many numbers of five digits can be formed without repetition if 0 ...

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  13. Six different colours are chosen to make a tri-colour fiag. How many ...

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  14. How many chords can be drawn through 11 points on a circle?

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  15. How many numbers of 4 digits can be formed with the odd digits without...

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  16. How many words can be formed with the letters of the word 'PENCIL' beg...

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  17. In how many ways 7 books can be arranged from 10 books?

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  18. From 50 students how many ways a group of 3 repesentative can be selec...

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  19. In how many different ways can 8 examination papers be arranged...

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  20. In how many ways a committee of 5 is to be formed from 6 boys and 4 gi...

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