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Statement 1: If p is a prime number (p!=...

Statement 1: If `p` is a prime number `(p!=2),` then `[(2+sqrt(5))^p]-2^(p+1)` is always divisible by `p(w h e r e[dot]` denotes the greatest integer function). Statement 2: if `n` prime, then `^n C_1,^n C_2,^n C_2 ,^n C_(n-1)` must be divisible by `ndot`

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. 1+(1/4)+((1*3)/(4*8))+((1*4*7)/(4*8*12))+....=

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  2. If |x|<1,then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+...... is eq...

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  3. Statement 1: If p is a prime number (p!=2), then [(2+sqrt(5))^p]-2^(p+...

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  4. Statement 1: The total number of dissimilar terms in the expansion of ...

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  5. Statement 1: In the expansion of (1+x)^(41)(1-x+x^2)^(40), the coeffic...

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  6. Statement 1: The coefficient of x^n in (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^...

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  7. Evaluate 3C2

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  8. Evaluate 5C2

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  9. Find underset(r=0) overset(10)sumr^ (10)C(r).3^(r).(-2)^(10-r)

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  10. Find n if nP1=2

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  11. Evaluate 5P2

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  12. The value of ("^n C0)/n+("^nC1)/(n+1)+("^nC2)/(n+2)+....+("^nC n)/(2n)...

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  13. The value of "^20 C0+^(20)C1+^(20)C2+^(20)C3+^(20)C4+^(20)C 12+^(20)C ...

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  14. If (3+x^(2008)+x^(2009))^(2010)=a0+a1x+a2x^2++an x^n , then the value ...

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  15. hat A hat A 404 C4 hatA hat aprime hat A hat A 4C1 hat A hat A hat A 3...

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  16. The sum of series ""^(20)C0-""^(20)C1+""^(20)C2-""^(20)C3+...............

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  17. If (1+x)^n=C0+C1x+C2x^2+...+Cn x^n , then C0C2+C1C3+C2C4+...+C(n-2)Cn=...

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  18. The value of lim(n-&gt;oo)sum(r=0)^(n)(sum(t=0)^(r-1)1/(5^n)*"^n Cr*"^...

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  19. Prove that C0-2^2C1+3^2C2-4^2C3++(-1)^n(n+1)^2xxCn=0w h e r eCr=^n Cr ...

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  20. The remainder, if 1+2+2^2+.......+2^(1999) is divided by 5 is.

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