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Find the coefficient of x^7 in the expan...

Find the coefficient of `x^7` in the expansion of `(1 - x -x^2 + x^3)^(6)dot`

A

-132

B

-144

C

132

D

144

Text Solution

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The correct Answer is:
B
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VMC MODULES ENGLISH-BINOMIAL THEOREM-LEVEL 1
  1. Let (1 + x)^(n) = sum(r=0)^(n) a(r) x^(r) . Then ( a+ (a(1))/(a(0))...

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  2. sum(r=0)^(n-1) (""^(n)C(r))/(""^(n)C(r) + ""^(n)C(r+1)) is equal to

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  3. Find the coefficient of x^7 in the expansion of (1 - x -x^2 + x^3)^(6)...

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  4. Statement - 1 sum(r=0)^(n) (r + 1) ""^(n)C(r) = (n+2)*2^(n-1) Stat...

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  5. if n>=2, ""^(n+1)C(2)+2(""^(2)C(2)+""^(3)C(2)+""^(4)C(2)+....+""^(n)...

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  6. In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binom...

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  7. If s(n)=sum(r=0)^(n)(1)/(.^(n)C(r))and t(n)=sum(r=0)^(n)(r)/(.^(n)C(r)...

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  8. The sum ""^(20)C(0)+""^(20)C(1)+""^(20)C(2)+……+""^(20)C(10) is equal t...

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  9. Find the coefficient of x^5 in (1+2x+3x^2...........)^(-3/2)

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  10. The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (20 !)/(...

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  11. The coefficient of x^(10) in the expansion of (1+x^2-x^3)^8 is 476 b. ...

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  12. The reamainder left out when 8^(2n) - (62)^(2n+1) is divided by 9 is

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  13. If ak is the coefficient of x^k in the expansion of (1+x+x^2)^n for k ...

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  14. The coefficient of x^(28) in the expansion of (1+x^3-x^6)^(30) is 1 b....

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

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

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

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

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  20. 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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