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

Show that `101^(50)gt 99^(50)+100^(50)`

A

`xgty`

B

'xlty`

C

x=y

D

x=2y

Text Solution

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The correct Answer is:
B
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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. The greatest integer which divides the number 101^(100)-1 is

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

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

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

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

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  6. 1/(n!)+1/(2!(n-2)!)+1/(4!(n-4)!)+ …… is equal to

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

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

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

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

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

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

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

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

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

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

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  18. The greatest coefficient iin the expansion of (x+y+z+t)^(15) is

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  19. If (1+x)^n=sum(r=0)^n .^nCr x^r then sum(r=m)^n .^rCm is equal to

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

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