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Coefficient of x^3 in 1+(1+x) +(1 +x)^2 ...

Coefficient of `x^3` in `1+(1+x) +(1 +x)^2 +…..+(1+x)^n` is

A

`""^nC_4`

B

`""^((n+1))C_4`

C

`""^((n+2))C_4`

D

`""^((n+1))C_2`

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
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  2. Binomial coefficients which are in decreasing order are

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  3. Coefficient of x^3 in 1+(1+x) +(1 +x)^2 +…..+(1+x)^n is

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  4. Sum of the coefficients of (1+2x-4x^2)^(2003)

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  5. Sum of coefficients of terms of even powers of x in (1 + x + x^2 + x^...

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  6. Sum of coefficients of terms of odd powers of in (1+x - x^2 -x^3)^8is

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  7. If (1+x -2x^2)^8 =1 -a1x + a2x^2+……+a16x^16, then a2+a4+a6+……+a16 =

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  8. If (1+x-2x^2)^8 = 1 + a1x + a2x^2 + ……+ a16 x^16, then a1 +a3 + a5 + …...

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  9. (1+x)^25 = sum(r = 0)^(25) Cr x^r then C1 - C3 + C5 - C7 + ……-C25 =

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  10. The sum of the coefficients in the expansion of (1+x-3x^2)^(171) is

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  11. If the sum of all the binomial coefficients in (x+y)^n is 512 , then t...

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  12. The coefficient of x^(-n) in (1+x)^n (1+(1)/(x))^n is

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  13. If n is a positive integer then 2^(4n) - 15n - 1 is divisible by

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  14. Smaller of (19^10 + 20^10) and 21^10 is

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  15. 9^11 + 11^9 is divisible by

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  16. Integral part of (8 + 3sqrt7)^n is

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  17. If n = (sqrt2 +1)^6. Then the integer just greater than n is

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  18. 1.C0 + 3.C1+ 3^2.C2+….+3^n.Cn =

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  19. C0 + (C1)/(2) + (C2)/(2^2) + (C3)/(2^3)+…..+(Cn)/(2^n)=

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  20. ""^11C0 + ""^11C1 + ""^11C2 + ……+ ""^11C5 =

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