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For which of the following value of x, 5...

For which of the following value of `x, 5^(th)` term is the numerically greatest term in the expansion of `(1+x//3)^(10)`:

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. If (1+2x +3x^2)^10 = a0 +a1x +a2x^2 + ……+a20x^20 then a1 = ?

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  2. In the expansion of (5^(1//2)+7^(1//8))^(1024), the number of integral...

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  3. For which of the following value of x, 5^(th) term is the numerically ...

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

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  5. If the middle term in the expansion of (x/2+2)^8 is 1120, then find t...

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  6. If (1+x)^n=C0+C1x+C2x^2+...+Cn x^n , t h e n C0-(C0+C1)+(C0+C1+C2)-(C0...

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  7. In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N,

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  8. The value of ^n C1+^(n+1)C2+^(n+2)C3++^(n+m-1)Cm is equal to

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  9. If (1+x)^n=C0+C1x+C2x2++Cn x^n , n in N ,t h e nC0-C1+C2-+(-1)^(n-1)C...

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  10. The 10th term of (3-sqrt((17)/4+3sqrt(2)))^(20) is (a) a irrational nu...

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  11. For the expansion (xsinp+x^(-1)cosp)^(10),(p in R), The greatest v...

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  12. Let (1+x^2)^2(1+x)^n=sum(k=0)^(n+4)ak x^k. If a1, a2 and a3 are in ari...

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  13. The middle term in the expansion of (x//2+2)^8 is 1120, then x in R i...

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  14. If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,then ar is a.(.^nC2)^2 b. .^n ...

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  15. [(^nC0+^n C3+)-1/2(^n C1+^n C2+^n C4+^n C5]^2 + 3/4(^n C1-^n C2+^n C4 ...

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  16. If sum(r=0)^(n)((r+2)/(r+1)).^n Cr=(2^8-1)/6 , then n is (A) 8 (B...

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

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  18. If (1+x^(2))^(n) = underset(r=0)overset(n)suma(r)x^(r )= (1+x+x^(2)+x^...

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  19. The value of sum(r=1)^(n+1)(sum(k=1)^n "^k C(r-1))( where r ,k ,n in ...

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  20. If (x^2+x+1)/(1-x)=a0+a1x+a2x^2+ ,t h e nsum(r=1)^(50)ar is equal to 1...

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