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Let ((n),(k)) represents the combination...

Let `((n),(k))` represents the combination of 'n' things taken 'k' at a time, then the value of the sum
`((99),(97))+((98),(96))+((97),(95))+......+((3),(1))+((2),(0))` equals:

A

`((99),(97))`

B

`((100),(98))`

C

`((99),(98))`

D

`((100),(97))`

Text Solution

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The correct Answer is:
D
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VK JAISWAL ENGLISH-BIONMIAL THEOREM-Exercise-4 : Subjective Type Problems
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  2. The sum of series 3*""^(2007)C(0)-8*""^(2007)C(1)+13*""^(2007)C(2)-18...

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  3. In the polynomial (x-1)(x^(2)-2)(x^(3)-3)…(x^(11)-11), the coefficient...

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  4. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

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  5. If 3^(101)-2^(100) is divided by 11, the remainder is

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  6. Find the hundred's digit in the co-efficient of x^(17) in the expansio...

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  7. Let x=(3sqrt(6)+7)^(89). If {x} denotes the fractional part of 'x' the...

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  8. Let n in N, S(n)=sum(r=0)^(3n)(""^(3n)C(r )) and T(n)=sum(r=0)^(n)(""^...

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  9. Find the sum of possible real values of x for which the sixth term of ...

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  10. Let q be a positive with q le 50. If the sum ""^(98)C(30)+2" "^(97)C...

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  11. The remainder when (sum(k=1)^(5) ""^(20)C(2k-1))^(6) is divided by 11,...

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  12. Let a=3^(1/(223))+1 and for all geq3,l e tf(n)=^n C0dota^(n-1)-^n C1do...

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  13. In the polynomial (x-1)(x^(2)-2)(x^(3)-3)…(x^(11)-11), the coefficient...

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  14. Let the sum of all divisiors of the form 2^(p)*3^(q) (with p, q posit...

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  15. about to only mathematics

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  16. Let 1+sum(r=1)^(10)(3^r.^(10)Cr+r.^(10)Cr)=2^(10)(alpha. 4^5+beta) whe...

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  17. Let S(n)=""^(n)C(0)""^(n)C(1)+""^(n)C(1)""^(n)C(2)+…..+""^(n)C(n-1)""^...

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