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The coefficient of x^(n) in the polynomi...

The coefficient of `x^(n)` in the polynomial `(x+.^(n)C_(0))(x+3.^(n)C_(1))(x+5.^(n)C_(2))(x+7.^(n)C_(3)) . . .(x+(2n+1).^(n)C_(n))` is

A

`2^(2n)`

B

`2^(2n+1)-1`

C

`2^(n+1)`

D

None of these

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The correct Answer is:
D
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VMC MODULES ENGLISH-BINOMIAL THEOREM-LEVEL 1
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  2. The coefficient of x^(28) in the expansion of (1+x^3-x^6)^(30) is 1 b....

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  3. The coefficient of x^(n) in the polynomial (x+.^(n)C(0))(x+3.^(n)C(1))...

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  4. If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,then ar is a.(.^nC2)^2 b. .^n ...

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  5. The value of sum(r=0)^nsum(s=0)^nsum(t=0)^nsum(u=0)^n(1) is

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  6. If n is an even natural number , find the value of sum(r=0)^(n) ((...

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  7. sum(r=0)^n(-2)^r*(nCr)/((r+2)Cr) is equal to

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  8. If (1+2x+3x^2)^(10)=a0+a1x+a2x^2++a(20)x^(20),t h e na1 equals 10 b. 2...

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  9. The remainder, if 1+2+2^2++2^(1999) is divided by 5 is.

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  10. The value of ((""^(50)C(0))/(1)+(""^(50)C(2))/(3)+(""^(50)C(4))/(5)+…....

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  11. In the expansion of (1+x+x^3+x^4)^10, the coefficient of x^4 is ^40C4 ...

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  12. Let S1=sum(j=1)^(10)j(j-1)^(10)Cj ,""S2=sum(j=1)^(10)j""^(10)Ci "andS"...

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  13. Find underset(r=0) overset(10)sumr^ (10)C(r).3^(r).(-2)^(10-r)

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  14. Prove that ^100 C0^(100)C2+^(100)C2^(100)C4+^(100)C4^(100)C6++^(100)C(...

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  15. Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...

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  16. The digit at the unit place in the number 19^(2005)+11^(2005)-9^(2005)...

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  17. If (1!)^(2) + (2!)^(2) + (3!)^(2) + "…….." + (99!)^(2) is divided by 1...

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  18. In the expansion of (1+3x+2x^2)^6 , the coefficient of x^(11) is a. 14...

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  19. The value of underset(r=0)overset(40)sumr.^(40)C(r).^(30)C(r) is

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  20. The value of ( .^7C0 + ^7C1)+( .^7C1+ ^7C2)+....+(.^7C6+ ^7C7) is (A...

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