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The greatest integer which divides the n...

The greatest integer which divides the number `101^100 - 1 ` is

A

`10^2`

B

`10^3`

C

`10^4`

D

`10^5`

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The correct Answer is:
C
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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - II
  1. The coefficient of x^9 in (x - 1)(x - 4) ( x- 9) ……. ( x -100) is

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  2. The term in (x + y)^50 which is greatest in absolute value if |x| = sq...

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  3. The greatest integer which divides the number 101^100 - 1 is

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  4. 9^7 + 7^9 is divisible by

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  5. Larger of 99^50+100^50 and 101^50

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  6. The remainder left out when 8^(2n) - 6(2)^( 2n+1) is divided by 9 is

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  7. Integral part of 7 + 4sqrt3)^n is (n in N)

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  8. Integral part of (7 + 5sqrt2)^(2n+1) is (n in N)

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  9. If (6 sqrt6+14)^(2n+1)=R and F=[R], where [R] denotes the greatest int...

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  10. The integral part of (sqrt2+1)^6 is

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  11. ""^(n) C(r+1)+2""^(n)C(r) +""^(n)C(r-1)=

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  12. If Ck is the coefficient of x^k in the expansion of (1 + x)^2005 and i...

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  13. The sum of the series ""^20C0 - ""^20C1 + ""^20C2 - ""^20C3 +…….""^20C...

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  14. If S(n) = underset (r=0) overset( n) sum (1) /(""^(n) C(r)) and T...

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  15. C0 - [C1 -2.C2+ 3.C3-……..+(-1)^(n-1).n.Cn] =

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  16. C0+4. C1 + 7. C2+…...(n+1) terms =

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  17. 2. C2 + 6. C3 + 12. C4 +….. + n (n-1) . Cn=

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  18. Sum of last 8 coefficients in (1 + x)^16 is

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  19. C0 + (C1)/(2) (4) + (C2)/(3) (16) + …………..+(Cn)/(n + 1) (2^(2n))

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  20. (1 +x)^15 = a0 + a1x +…..+a15 x^15 rArr sum(r = 1)^15 r (ar)/(a(r - 1)...

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