Home
Class 12
MATHS
If the coefficients of x^3 and x^4 in th...

If the coefficients of `x^3` and `x^4` in the expansion of `(1""+a x+b x^2)""(1-2x)^(18)` in powers of x are both zero, then (a, b) is equal to (1) `(16 ,(251)/3)` (3) `(14 ,(251)/3)` (2) `(14 ,(272)/3)` (4) `(16 ,(272)/3)`

A

`(16,251/3)`

B

`(14,251/3)`

C

`(14, 272/3)`

D

`(16,272/3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(1+ax+bx^(2))(1-2x)^(18)`
`= 1(1-2x)^(18)+ax(1-2x)^(18)+bx^(2)(1-2x)^(18)` ltbr gt Coefficient of `x^(3) : (-2)^(3) .^(18)C_(3) + a(-2)^(2).^(18)C_(2)+b(-2).^(18)C_(1)=0`
`(4xx(17xx16))/((3xx2)) - 2a.(17)/(2)+b = 0" "(1)`
Coefficient of `x^(4) : (-2)^(4).^(18)C_(4)6+a(-2)^(3).^(18)C_(3)+b(-2)^(2).^(18)C_(2) = 0`
`(4 xx 20 ) - 2a . (16)/(3) + b = 0`
From equation (1) and (2) , we get
`4((17xx8)/(3)-20)+2a(16/3-17/2) = 0`
`rArr a = 16`
`rArr b = (2xx16xx16)/(3) - 80 = 272/3`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Single correct Answer|62 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Numerical)|25 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

The coefficient of x^(4) in the expansion of (1 + x + x^(2) + x^3)^(11) is

The coefficient of x^(4) in the expansion of (1 + x + x^(2))^(3) is

The coefficient of x^(4) in the expansion of (x/2-3/x^(2))^(10) is

Find the coefficient of x^7 in the expansion of (1+3x-2x^3)^(10)dot

The coefficient of x in the expansion of (1 + x)(1 + 2x)(1 + 3x) ... (1 + 100x) is

Find the coefficient of x^(13) in the expansion of (1-x)^5xx(1+x+x^2+x^3)^4dot

The coefficient of x^9 in the expansion of (1+x)(1+ x^2)(1+x^3)....(1+x^(100)) is

If |x|<1, then find the coefficient of x^n in the expansion of (1+2x+3x^2+4x^3+)^(1//2)dot

If |x|<1, then find the coefficient of x^n in the expansion of (1+x+x^2+x^3+....)^2dot