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Find the coefficient of :\ x\ in the ex...

Find the coefficient of :`\ x\ ` in the expansion of `(1-3x+7x^2)(1-x)^(16)dot`

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Verified by Experts

The correct Answer is:
-19
In the expansion of `E=(1-x)^(16),` we have
`T_(r+1) = (-1)^(r)*^(16) C_(r)x^(r).`
Product of given expressions `=( 1- 3x + 7x^(2))(1-16x + …)`.
Terms containing `x= [1 xx (-16x)+ (-3x) xx 1] = ( -19x).`
`:. " coefficient of " x= -19.`
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RS AGGARWAL-BINOMIAL THEOREM-EXERCISE 10A
  1. Prove that the ratio of the coefficient of x^10 in (1 - x^2)^10 & the ...

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

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  3. Find the coefficient of :\ x\ in the expansion of (1-3x+7x^2)(1-x)^(1...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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