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If ([""^(n)C(r) + 4*""^(n)C(r+1) + 6*""...

If ` ([""^(n)C_(r) + 4*""^(n)C_(r+1) + 6*""^(n)C_(r+2)+ 4*""^(n)C_(r+3) + ""^(n)C_(r+4)])/([""^(n)C_(r) + 3. ""^(n)C_(r+1)+ 3*""^(n)C_(r+2) + ""^(n)C_(r +3)])=(n + lambda)/(r+lambda)`
the value of ` lambda ` is

A

1

B

2

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
C
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The expression ""^(n)C_(r)+4.""^(n)C_(r-1)+6.""^(n)C_(r-2)+4.""^(n)C_(r-3)+""^(n)C_(r-4)

""^(n)C_(n-r)+3.""^(n)C_(n-r+1)+3.""^(n)C_(n-r+2)+""^(n)C_(n-r+3)=""^(x)C_(r)

Prove that ""^(n)C_(r )+2""^(n)C_(r-1)+ ""^(n)C_(r-2)= ""^(n+2)C_(r ) .

""^(n)C_(r+1)+^(n)C_(r-1)+2.""^(n)C_(r)=

"^(n)C_(r)=^(n)C_(n-r)

""^(n-2)C_(r)+2""^(n-2)C_(r-1)+""^(n-2)C_(r-2) equals :

ML KHANNA-PERMUTATIONS AND COMBINATIONS -SELF ASSESSMENT TEST
  1. If ([""^(n)C(r) + 4*""^(n)C(r+1) + 6*""^(n)C(r+2)+ 4*""^(n)C(r+3) + "...

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  2. sum(r=0)^m "^(n+r) Cn is equal to

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  3. A polygon has 44 diagonals , then the number of its sides is

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  4. If 7 points out of 12 are in the same straight line, then what is the ...

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  5. All the letters of the word EAMCET are arranged in all possible ways. ...

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  6. Out of 10 red and 8 white balls , 5 red and 4 white balls can be drawn...

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  7. 7 men and 7 women are to sit round a table so that there is a man on e...

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

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

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  10. Assuming the balls to be identical except for difference in colours, t...

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  11. How many different words can be formed by jumbling the letters of the ...

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  12. The number of numbers, that can be formed by using all digits 1,2, 3, ...

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  13. How many words can be formed with the letters o the word MATHEMATICS b...

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  14. In how many ways 7 men and 7 women can sit on a round table such that ...

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  15. If ^15 C(3r)=^(15)C(r+3) , then find rdot

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  16. IF ""^n C12=""^nC6 then "^n C2=

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  17. There are n points in a place in which p point are collinear. How many...

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  18. There are 10 points in a plane, out of these 6 are collinear. The numb...

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  19. IF x,y,r are positive integers then ""^x Cr+""^x C(r-1) . ""^ y C1+ ...

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  21. Let Tn be the number of all possible triangles formed by joining ve...

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