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Let n be a positive integer such that (1...

Let n be a positive integer such that `(1+x+x^2)^n=a_0+a_1x+a_2x^2+…….+a_(2n)x^(2n)` then `sum_(r=0)^(2n) a_r`is

A

`a_(2n) , 0gere2n`

B

`a_(2n-r),0lerle2n`

C

`a_(2n-r),0lerle2n`

D

none of these

Text Solution

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The correct Answer is:
B
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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. Find the coefficient of x^20 in the expression of (1+x^2)^40(x^2+2+1/x...

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  2. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

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  3. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

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  4. The greatest integer which divides the number 101^(100)-1 is

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  5. Coefficient of x^(11) in the expansion of (1+3x+2x^2)^6 is equal to

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  6. Show that 101^(50)gt 99^(50)+100^(50)

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  7. The greatest term (numerically) in the expansion of (2+3x)^9 when x=3/...

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  8. If agt0 and coefficients of x^5 and x^(15) in the expansion of (x^2+a/...

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  9. 1/(n!)+1/(2!(n-2)!)+1/(4!(n-4)!)+ …… is equal to

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  10. The coefficients of x^n in (1+x/(1!)+x^2/(2!)+……+x^n/(n!))^2 is

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  11. The sum of the coefficients of all the integral powers of x in the exp...

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  12. The coefficient of x^m in (1+x)^r+ (1+x)^(r+1)+(1+x)^(r+2)+………+(1+x)^n...

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  13. The coefficient of x^ny^n in the expansion of {(1+x)(1+y)(x+y)}^n is

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  14. If log(1-x+x^2)=a1x+a2x^2+a3x^3+……… then a3+a6+a9+……… is equal to

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  15. The greatest term in the expansion of (1+x)^(10) when x=2/3 is

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  16. The number of integral terms in the expansion of (3^(1/2)+2^(1/2))^(50...

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  17. The least (positive) remainder when 17^(30) is divided by 5 is

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  18. The coefficient of x^(17) in the expansion of (x-1)(x-2)……..(x-18) is

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  19. The number of terms in the expansion of (a+b+c)^n where ninN is

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  20. The sum of the rational terms in the expansion of (sqrt2+3^(1/5))^(10)...

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