If coefficient of a^2b^3c^4in(a+b+c)^m(w...

If coefficient of `a^2b^3c^4in(a+b+c)^m(w h e r em in N)i sL(L!=0)` , then in same expansion coefficient of `a^4b^4c^1` will be `L` b. `L/3` c. `(m L)/4` d. `L/2`

`L/3`

`(mL)/(4)`

`L/2`

Text Solution

Verified by Experts

The correct Answer is:

As `L ne 0`
`:. M = 2+3+4=9`
`:. L = (9!)/(2!3!4!)`
Now, coefficient of `a^(4)b^(4)c = (9!)/(4!4!1!) = L/2`

Topper's Solved these Questions

BINOMIAL THEOREM
CENGAGE|Exercise Exercise (Multiple)|27 Videos
BINOMIAL THEOREM
CENGAGE|Exercise Exercise (Comprehension)|20 Videos
BINOMIAL THEOREM
CENGAGE|Exercise Exercise 8.8|10 Videos
AREA UNDER CURVES
CENGAGE|Exercise Question Bank|20 Videos
BINOMIAL THEORM
CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

If coefficient of a^(2)b^(3)c^(4)in(a+b+c)^(m) (where n in N) is L(L!=0), then in same expansion coefficient of a^(4)b^(4)c^(1) will be (A) L(B)(L)/(3) (C) (mL)/(4)(D)(L)/(2)

In A=2h(l+b) , if A=54m^(2) , l=5m, and b=4m, then find h.

Let lines L_(1):y+6=m_(1)(x+4) and L_(2):y+6=m_(2)(x+4) touching parabola y^(2)=4ax(a>0) at points A and B respectively where A lies in 1 quadrant and (1)/(m_(1))+(1)/(m_(2))=-(3)/(2) then (A) Length of latus rectum of parabola is 12 (B) L_(1) and L_(2) are perpendicular (C) m_(1)>|m_(2)|" " (D) Slope of normal at point B on parabola is 2

If quad vec r=l(vec b xxvec c)+m(vec c xxvec a)+n(vec a xxvec b) and [vec a,vec b,vec c]=2, then l+m+n is equal to

In a multi - electron atom , which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic and electric fields ? (A) n=l, l=0,m=0 (B) n = 2, l =0 , m= 0 (C) n = 2 , l = 1 , m = 1 (D) n = 3, l =2 , m=1 (E) n=3,l=2,m=0.

A B C is a right-angled triangle in which /_B=90^0 and B C=adot If n points L_1, L_2, ,L_nonA B is divided in n+1 equal parts and L_1M_1, L_2M_2, ,L_n M_n are line segments parallel to B Ca n dM_1, M_2, ,M_n are on A C , then the sum of the lengths of L_1M_1, L_2M_2, ,L_n M_n is (a(n+1))/2 b. (a(n-1))/2 c. (a n)/2 d. none of these

If the dimensions of B^(2)l^(2)C are [M^(a)L^(b)T^(c)] , then the value of a+b+c is [Here B,l and C represent the magnitude of magnetic field, length and capacitance respectively]

CENGAGE-BINOMIAL THEOREM-Exercise (Single)

Sum of the coefficients of terms of degree 13 in the expansion of(1+x)...
Text Solution
|
The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (20 !)/(...
Text Solution
|
If coefficient of a^2b^3c^4in(a+b+c)^m(w h e r em in N)i sL(L!=0) , t...
Text Solution
|
The coefficient of x^r[0lt=rlt=(n-1)] in lthe expansion of (x+3)^(n-1)...
Text Solution
|
If (1+2x+3x^2)^(10)=a0+a1x+a2x^2++a(20)x^(20),t h e na1 equals 10 b. 2...
Text Solution
|
If f(x)=1-x^2-x^3++^(15)+x^(16)-x^(17) , then the coefficient of x^2in...
Text Solution
|
Let f(x0=a0+a1x+a2x^2++an x^n+ and (f(x))/(1-x)=b0+b1x+b2x^2++bn x^n+ ...
Text Solution
|
Statement 1: The coefficient of x^n is (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^...
Text Solution
|
In the expansion of (3^(-x//4)+3^(5x//4))^n the sum of binomial coeffi...
Text Solution
|
The sum of the coefficients of even power of x in the expansion of (1+...
Text Solution
|
Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is ...
Text Solution
|
If the sum of the coefficients in the expansion of (a+b)^n is 4096, th...
Text Solution
|
The value of .^(20)C(10)+.^(20)C(1)+.^(20)C(2)+.^(20)C(3)+.^(20)C(4)+....
Text Solution
|
The sum of the series C 20()0-C 20()1+C 20()2-C 20()3+...-...+C 20()(1...
Text Solution
|
If (3+x^(2008)+x^(2009))^(2010)=a0+a1x+a2x^2++an x^n , then the value ...
Text Solution
|
Value of sum(k=1)^(oo) sum(r=0)^(k) (1)/(3^(k)) (""^(k)C(r)) is
Text Solution
|
The value of sum(r=0)^(10) (r)""^(20)C(r) is equal to
Text Solution
|
[(^n C0+^n C3+)1//2(^n C1+^n C2+^n C4+^n C5]^2+3//4(^n C1-^n C2+^n C4-...
Text Solution
|
The value of sum(r=1)^(n+1) (sum(k=1)^(n) ""^(k)C(r-1)) (where r,k, n ...
Text Solution
|
The sum sumsum(0leilejle10) (""^(10)C(j))(""^(j)C(r-1)) is equal to
Text Solution
|