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The coefficient of x^n in the expansio...

The coefficient of `x^n` in the expansion of `(1+x)(1-x)^n` is

A

`(-1)^(n-1) n`

B

`( -1)^(n) ( 1-n)`

C

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

D

`( n - 1)`

Text Solution

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The correct Answer is:
B
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DISHA PUBLICATION-BINOMIAL THEOREM -EXERCISE-1 (CONCEPT BUILDER )
  1. The coefficient of x^n in the expansion of (1+x)(1-x)^n is

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  2. If pa n dq are ositive, then prove that the coefficients of x^pa n dx^...

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  3. After simplification, what is the number of terms in the expansion of ...

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  4. If x = ( 2 + sqrt( 3))^(n), then find the value of x( 1- { x} ), where...

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  5. Prove that (n !) is divisible by (n !)^(n-1)!

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  6. If x + y = 1, then sum(r-0)^n r nCr x^r y^(n-r) equals

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  7. The coefficient of x^3 in the expansion of (3-2x)/((1+3x)^3) is

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  8. The number of dissimilar terms in the expansion of (a+b)^(n) is n+1, t...

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

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  10. If sum(r=0)^(10)((r+2)/(r+1))^^n Cr=(2^8-1)/6 , then n is 8 b. 4 c. 6 ...

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  11. The total number of terms in the expansion of (x+a)^(51) - ( x-a)^(51)...

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  12. If |x| lt 1 then 1+n ((2x)/(1+x))+(n(n+1))/(2!) ((2x)/(1=x))^2 + ….......

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  13. When 2^(1505) is divided by 9, the remainder is

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  14. The minimum positive integral value of m such that ( 1073)^(71)-m may ...

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  15. If n is a positive integer and C(k)=""^(n)C(k), then the value of sum(...

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  16. I three consecutive coefficients in the expansion of (1+x)^n are in th...

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  17. If I is integral part of (2+ sqrt(3))^n and f is its fractional part....

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  18. The greatest integer less than or equal to (sqrt2 + 1)^6 is

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  19. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

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  20. If (+x)^n=sum(r=0)^n ar x^r&br=1+(ar)/(a(r-1))&prod(r=1)^n br=((101)^...

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