Find the coefficient of a^(2)b^(3)c^(4)d...

Find the coefficient of `a^(2)b^(3)c^(4)d` in the expansion of `(a-b-c+d)^(10)`.

Text Solution

AI Generated Solution

To find the coefficient of \( a^2 b^3 c^4 d \) in the expansion of \( (a - b - c + d)^{10} \), we can use the multinomial theorem. The multinomial expansion of \( (x_1 + x_2 + x_3 + x_4)^n \) is given by: \[ \sum \frac{n!}{k_1! k_2! k_3! k_4!} x_1^{k_1} x_2^{k_2} x_3^{k_3} x_4^{k_4} \] where \( k_1 + k_2 + k_3 + k_4 = n \). ...

Topper's Solved these Questions

BIONOMIAL THEOREM
ARIHANT MATHS ENGLISH|Exercise JEE Type Solved Example : (Matching Type Questions )|2 Videos
BIONOMIAL THEOREM
ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|7 Videos
AREA OF BOUNDED REGIONS
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|23 Videos
CIRCLE
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

Similar Questions

Explore conceptually related problems

Statement-1: The coefficient of a^(3)b^(4)c^(3) in the expansion of (a-b+c)^(10) is (10!)/(3!4!3!) Statement-2: The coefficient of x^(p)y^(q)z^(r) in the expansion of (x+y+z)^(n) is (n!)/(p!q!r!) for all integer n.

Find the coefficient of a^3b^4c in the expansion of (1+a+b-c)^9dot

Find the coefficient of a^3b^4c in the expansion of (1+a-b+c)^9dot

Find the coefficient of a^3b^4c^5 in the expansion of (b c+c a+a b)^6dot

Find the coefficient of x^2 y^3 z^4 in the expansion of (ax -by +cz)^9 (b) a^2 b^3 c^4 d in the expansion of (a -b-c +d)^10

The coefficient of a^(-6) b^(4) in the expansion of ((1)/(a) - (2b)/(3))^(10) is......

The coefficient of (x^(3)* b^(6) * C^(8) *d^(9) *e *f) in the expansion of (a + b + c - d - e - f)^(31) is

The coefficient of a^3b^6c in the expansionof (2a-b+c)^10 is (A) 6720 (B) 840 (C) 10 (D) none of these

ARIHANT MATHS ENGLISH-BIONOMIAL THEOREM-Exercise (Questions Asked In Previous 13 Years Exam)

Find the coefficient of a^(2)b^(3)c^(4)d in the expansion of (a-b-c+d)...
01:53
|
The value of ((30), (0))((30), (10))-((30), (1))((30),( 11)) +(30 2)(3...
06:07
|
If the coefficient of the rth, (r+1)th and (r+2)th terms in the expans...
04:24
|
If the coefficient of x^(7)in [ax^(2) + (1/bx)]^(11) equals the coeffi...
06:02
|
For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a1y+a2y^2+... , and a1=a2...
04:14
|
In the binomial expansion of (a - b)^n , n ge 5 the sum of the 5th ...
02:47
|
The sum of series ^^(20)C0-^^(20)C1+^^(20)C2-^^(20)C3++^^(20)C 10 is 1...
04:46
|
Statement-1: sum(r =0)^(n) (r +1)""^(n)C(r) = (n +2) 2^(n-1) Stat...
05:16
|
The reamainder left out when 8^(2n) - (62)^(2n+1) is divided by 9 is
04:51
|
For r = 0, 1,"…..",10, let A(r),B(r), and C(r) denote, respectively, t...
03:41
|
Let S(1) = sum(j=1)^(10) j(j-1).""^(10)C(j), S(2) = sum(j=1)^(10)j."...
07:00
|
Find the coefficient of x^7 in the expansion of (1 - x -x^2 + x^3)^(6)...
02:16
|
If n is a positive integer, then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is ...
03:41
|
The term independent of x in expansion of ((x+1)/(x^(2/3)-x^(1/3)+1)-(...
07:18
|
The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...
06:59
|
If the coefficient of x^(3) and x^(4) in the expansion of (1+ax+bx^(2)...
05:36
|
Coefficient of x^(11) in the expansion of (1+x^2)(1+x^3)^7(1+x^4)^(12)...
04:09
|
The sum of coefficient of integral powers of x in the binomial expansi...
04:12
|
The coefficient of x^9 in the expansion of (1+x)(16 x^2)(1+x^3)(1+x^(1...
01:59
|
If the number of terms in the expansion of (1-2/x+4/(x^(2))) x ne 0, i...
03:22
|
Let m be the smallest positive integer such that the coefficient of x^...
02:48
|

Home

Profile