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Expand : ( y+2)^6...

Expand : `( y+2)^6`

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`""^6C_(0)y^6+""^6C_(1)y^(5).2+""^(6)C_(2)y^(4).2^2+""^(6)C_(3)y^(3)+""^6C_(4)y^(2).2^(4)+""^6C_(5)y^(1).2^(5)+""^6C_(6).2^6`
`= y^(6)+12y^(5)+60y^(4)+160y^(3)+240y^(2)+192y+64`
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ALLEN-Solutions of Triangle & Binomial Theorem-Illustration
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  2. Write first 4 terms of (1-(2y^2)/(5))^7

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  3. if in the expansion of (1+x)^m (1-x)^n the cofficients of x and x^2 ar...

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  4. Find (a) the coefficient of x^7 in the epansion of (ax^2+1/(bx))^11...

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  5. Find the number of reational is exponets of (9^(1//4)+8^(1//6))^(1000)

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  6. Find the middle term in the expansion of (3x-(x^3)/6)^9

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  7. Find the term independent of x in the expansion of (i) [sqrt(x/3)+sqr...

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  8. Find numerically greatest term is the expansion of (3-5x)^11 "when " x...

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  9. Given T(3) in the expansion of (1-3x)^6 has maximum numerical value .F...

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  10. Prove that : ""^(25)C(10)+""^(24)C(10)+……..+""^(10)C(10)=""^(26)C(11)

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  11. A student is allowed to select at most n books from a collection of (...

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  12. Prove that (i) C(1)+2C(2)+3C(3)+……+nC(n)=n.2^(n+1) (ii) C(0)+(C(1)...

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  13. If (1+x)^n=underset(r=0)overset(n)C(r)x^r then prove that C(1)^2+2.C(2...

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  14. Prove that :C(0)-3C(1)+5C(2)- ………..(-1)^n(2n+1)C(n)=0

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  15. Prove that (""^(2n)C(0))^2-(""^(2n)C(1))^2+(""^(2n)C(2))^2-.....+(-1)^...

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  16. Prove that : ""^(n)C(0).""^(2n)C(n)-""^(n)C(1).""^(2n-2)Cn(n)+""^(n)...

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  17. If (1+x)^n=C(0)C1c+C(2)x^2+…..+C(n)x^n then show that the sum of the p...

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  18. If (1+x)^n=C(0)+C(1)x+C(2)x^2+….+C(n)x^n then prove that (SigmaSigma)...

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  19. Find the coffiecient of x^2 y^3 z^4 w in the expansion of (x-y-z+w)^(...

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  20. Find the total number of terms in the expansion of 1(1+x+y)^(10) and c...

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