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Let a=3^(1/(223))+1 and for all geq3,l e...

Let `a=3^(1/(223))+1` and for all `geq3,l e tf(n)=^n C_0dota^(n-1)-^n C_1dota^(n-2)+^n C_2dota^(n-3)-+(-1)^(n-1)dot^n C_(n-1)dota^0` . If the value of `f(2007)+f(2008)=3^k w h e r ek in N ,` then the value of `k` is.

A

2187

B

1987

C

3232

D

4187

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The correct Answer is:
A
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DISHA PUBLICATION-BINOMIAL THEOREM -EXERCISE-1 (CONCEPT BUILDER )
  1. The coefficient of x^3 in the expansion of (3-2x)/((1+3x)^3) is

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

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

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

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

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

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

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

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

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

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

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

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  14. 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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  15. The expression (1)/( sqrt( 3x +1)) [ ( ( 1+ sqrt( 3x + 1))/(2))^(7) -...

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  16. If z = 1/3 + (1.3)/(3.6) + (1.3.5)/(3.6.9) + .... then

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  17. If the sum of the coefficients in the expansion of (1 + 2x)^(n) is...

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  18. The coefficient of the term independent of x in the exampansion of ((x...

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  19. If the coefficient of (r +1)^(th) term in the expansion of (1 +x)^...

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  20. In the binomial expansion of (a - b)^(n) , n ge 5 , the sum of the ...

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