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Let f(n)=10^n+3 . 4^(n+2)+5, n in N. The...

Let `f(n)=10^n+3 . 4^(n+2)+5, n in N`. The greatest integer which divides f(n) for all n is

A

27

B

9

C

3

D

None of these

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The correct Answer is:
B
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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. If an=sum(r=0)^n1/(^nCr) , then sum(r=0)^nr/(^nCr) equals

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  2. The number of real negative terms in the binomial expansion of (1+ix)^...

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  3. Let f(n)=10^n+3 . 4^(n+2)+5, n in N. The greatest integer which divide...

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  4. The value of the sum of the series 3cdot^nC0+8cdot^nC1+13cdot^nC2-18cd...

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  5. For natural numbers m, n if (1-y)^m(1+y)^n=1+a1y+a2y^2+.... and a1=a2=...

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  6. The coefficient of the term independent of x in the expansion of [((x+...

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  7. The coefficient of a^3b^4c in the expansion of (1+a-b+c)^9 is equal to

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  8. The remainder when 9^(103) is divided by 25 is equal to

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  9. If (3+x^(2008)+x^(2009))^(2010)=a0+a1x^2+....+anx^n, a0-1/2 a1-1/2 a2+...

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

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  11. The remainder when x=5^(5^(5^(......))) (23 times 5) is divided by 24 ...

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  12. For integer n gt 1, the digit at units place in the number sum(r=0)^(1...

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  13. In the expansion of (1+x+x^2+x^3)^6, the coefficient of x^(14) is

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  14. The coefficient of x^(3l+2) in the expression (a+x)^l(b+x)^(l+1)(c+x)^...

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  15. The interval in which x must lie so that greatest term in the expansio...

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  16. The digit in the unit place in the number (19)^(2005)+(11)^(2005)-(9)^...

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  17. If n lt p lt 2n and p is prime and N = .^(2n)Cn, then

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  18. If absx lt 2/3 then the 4^(th) term in the expansion of (1+3/2x)^(1/2)...

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  19. The sum of rational in (sqrt2+root(3)(3)+root(6)(5))^10 is equal to

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  20. Let f(x)=a0+a1x+a2x^2+.....+anx^n+....and f(x)/(1-x)=b0+b1x+b2x^2+.......

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