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If the 17th and 18th terms in the expans...

If the 17th and 18th terms in the expansion of `(2+a)^(50)` are equal , find the value of a.

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Verified by Experts

The correct Answer is:
a=1
`T_(r+1) = .^(50)C_(r) xx 2^((50-r)) xx a^(r).`
Now, `T_(17) = T_(18) rArr T_(16 + 1) = T _(17 + 1)`
` rArr .^(50)C_(16) xx 2 ^(34) xx a^(16) = .^(50)C_(17) xx 2^(33) xx a^(17)`
`rArr a = (2 xx .^(50)C_(16))/(.^(50C_(17)))=(2xx7)/((50-17+10))=1." "[:' (.^(n)C_(r-1))/(.^(n)C_(r))=r/(n-r+1)]`
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RS AGGARWAL-BINOMIAL THEOREM-EXERCISE 10A
  1. Find the coefficient of :\ x\ in the expansion of (1-3x+7x^2)(1-x)^(1...

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  2. Find the coefficient of (i) x^(5)" in the expansion of "(x+3)^(8) (...

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  3. Show that the term containing to does not exist in the expansion of (3...

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  4. Does the expansion of (2x^2-1/x)^(20) contain any term involving x^9?

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  5. Show that the expansion of (x^2+1/x)^1 does not contain any term invol...

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

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  7. Find the 5th term from the end in the expansion of (x-1/x)^(12).

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  8. Find the 4th term from the end in the expansion of ((4x)/5-5/(2x))^9do...

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  9. If the 7th terms from the beginning and end in the expansion of ( root...

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  10. Find the middle term in the expansion of : (i) 3+x)^(6) (ii)(...

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  11. Find the two middle terms in the expansion of : (i) (x^(2)+a^(2))^(5) ...

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  12. Find the term independent of x in the expansion of : (i) (2x+1/(3x^(...

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  13. Find the coefficent of x^(5) in the expansion of (1+x)^(3)(1-x)^(6).

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  14. Find numerically greatest term in the expansion of (2 + 3 x)^9, when x...

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  15. 17. If the coefficients of 2nd, 3rd and 4th terms in the expansion of ...

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  16. Find the 6th term of the expansion (y^(1//2) + x^(1//3))^(n) , if the ...

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  17. If the 17th and 18th terms in the expansion of (2+a)^(50) are equal ,...

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  18. Find the coefficient of x^(4) in the expansion of (1+x)^(n)(1-x)^(n). ...

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  19. Prove that the coefficient of x^(n) in the binomial expansion of (1+x...

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  20. If the middle term in the expansion of (p/2+2)^(8) is 1120, find p.

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