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Find a positive value of m for which the...

Find a positive value of m for which the coefficient of `x^(2)` in the expansion of `(1+x)^(m)`, is 6.

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The correct Answer is:
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`(1+x)^(m)=^(m)C_(0).1+^(m)C_(1).x+^(m)C_(2).x^(2)`
`+......+^(m)C_(m).x^(m)`
According to the problem
`.^(m)C_(2)=6`
`rArr " "(m(m-1))/(2)=6`
`rArr " "(m(m-1)=12 =4.3`
`rArr " "m=4`
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NAGEEN PRAKASHAN ENGLISH-BINOMIAL THEOREM-Exericse 8.2
  1. Find the 4^(t h)term in the expansion of (x-2y)^(12).

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  2. Find 13th term in the expansion of (9x-1/(3x))^(18),\ x!=0.

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  3. Find the middle terms in the expansion of (3 - (x^3)/( 6) )^7.

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  4. Find the middle term in the expansion of :\ (x/3+9y)^(10)

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  5. In the binomial expansion of (1+a)^(m+n) , prove that the coefficient ...

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  6. The coefficients of the (r-1)^(th),r^(th) and (r+1)^(th) terms in the ...

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  7. The coefficient of x^(n) in the expansion of (1 + x)^(2n) " and " (1 +...

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  8. Find a positive value of m for which the coefficient of x^(2) in the e...

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  9. Find the coefficient of x^5""in(x+3)^8

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  10. Find the coefficient of a^5b^7in(a-2b)^(12)

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  11. Write the general term in the expansion of (x^2-y)^6dot

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  12. Write the general term in the expansion of (x^2-y x)^(12),x!=0

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  13. Find the 4^(t h)term in the expansion of (x-2y)^(12).

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  14. Find the 13^(t h)term in the expansion of (9x-1/(3sqrt(x)))^(18),x!=0

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  15. Find the middle term in the expansion of (3-(x^(3))/(6))^(7)

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  16. Find the middle term in the expansion of :\ (x/3+9y)^(10)

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  17. In the expansion of (1+a)^(m+n) ,prove that coefficients of a^(m) and ...

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  18. The coefficients of the (r-1)^(th),r^(th) and (r+1)^(th) terms in the ...

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  19. prove that the coefficient of x^n in the expansion of (1+x)^(2n) is tw...

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  20. Find a positive value of m for which the coefficient of x^2 in the ex...

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