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The number N=""^(20)C(7)-""^(20)C(8)+""^...

The number `N=""^(20)C_(7)-""^(20)C_(8)+""^(20)C_(9)-""^(20)C_(10)+….. -""^(20)C_(20)` is not divisible by :

A

3

B

7

C

11

D

19

Text Solution

Verified by Experts

The correct Answer is:
C
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The number N=""^(20)C_(7)-""^(20)C_(8)+""^(20)C_(9)-""^(20)C_(10)+….. -""^(20)C_(20) is divisible by :

1.^(20)C_(1)-2.^(20)C_(2)+3.^(20)C_(3)-...-20.^(20)C_(20)

The sum ""^(20)C_(0)+""^(20)C_(1)+""^(20)C_(2)+……+""^(20)C_(10) is equal to :

The sum of the series .^(20)C_(0)-.^(20)C_(1)+ .^(20)C_(2)-.^(20)C_(3)+...-.+ .^(20)C_(10) is -

The sum S = ""^(20)C_(2) + 2*""^(20)C_(3) + 3 *""^(20)C_(4) + ...+ 19 * ""^(20)C_(20) is equal to

The sum of the series 20C_(0)-^(20)C_(1)+^(20)C_(2)-^(20)C_(3)+...-...+^(20)C_(10) is:

If ""^(20)C_(r)=""^(20)C_(r-10) , then ""^(18)C_(r) is equal to

Evaluate: .^(20)C_(5)+^(20)C_(4)+^(21)C_(4)+^(22)C_(4)

VK JAISWAL-BIONMIAL THEOREM-Exercise-4 : Subjective Type Problems
  1. The number N=""^(20)C(7)-""^(20)C(8)+""^(20)C(9)-""^(20)C(10)+….. -""^...

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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 function f(x)=(x-1)(x^(2)-2)(x^(3)-3)……..(x^(11)-11...

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  4. If sum(r=0)^(3n)a(r)(x-4)^(r )=sum(r=0)^(3n)A(r)(x-5)^(r ) and a( k)=1...

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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 n in N, Sn=sum(r=0)^(3n)^(3n)Cr and Tn=sum(r=0)^n^(3n)C(3r), then ...

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

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

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

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

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  12. In the polynomial function f(x)=(x-1)(x^(2)-2)(x^(3)-3)……..(x^(11)-11...

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

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  14. For what value of x is the ninth term in the expansion of (3^(log3 sqr...

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  15. Let 1+ sum(r=1)^10 (3^r C(10,r) + r C(10,r))=2^10 (alpha 4^5+beta) whe...

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

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