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 PUBLICATION|Exercise Multiple Correct Answer Type|27 Videos
BINOMIAL THEOREM
CENGAGE PUBLICATION|Exercise Linked Comphrension|20 Videos
BINOMIAL THEOREM
CENGAGE PUBLICATION|Exercise Concept Application Exercise 8.8|10 Videos
AREA
CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos
CIRCLE
CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 Videos

Similar Questions

Explore conceptually related problems

The coefficient of a^8b^4c^9d^9 in (a b c+a b d+a c d +b c d)^(10) is

The coefficient of a^3b^4c in the expansion of (1+a-b+c)^9 is equal to

In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be a. 4n b. 4n-3 c. 4n+1 d. none of these

In the expansion of (1+x+x^3+x^4)^10, the coefficient of x^4 is a. .^40C_4 b. .^10 C_4 c. 210 d. 310

If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the minimum value of a+b+c is (a) 1 (b) 3 (c) 5 (d) 9

An aluminium rod (coefficient of linear expansion alpha_(1) ) of length l_(1) " at " 0^(@)C is welded with a steel rod (coefficient of linear expansion alpha_(2) ) of length l_(2) to form a composite rod of length (l_(1)+l_(2)) . If, when heated through t^(@)C , each rod increases in length by the same amount, then the value of l_(1)/(l_(1)+l_(2)) will be

Explain the statement- "The coefficient of real expansion of mercury is 0.00018l^@C . "

If alpha,beta,gamma,delta are the roots of the equation x^4-K x^3+K x^2+L x+m=0,w h e r eK ,L ,a n dM are real numbers, then the minimum value of alpha^2+beta^2+gamma^2+delta^2 is a. 0 b. -1 c. 1 d. 2

Let's find L.C.M. of 4a^2b^4c , 12a^3bc^3 and 18a^2 b^3 c^2

Let's find the L.C.M of the following algebraic expressions. ab^4 - 8ab, a^2b^4+8a^2b, ab^4 - 4ab

CENGAGE PUBLICATION-BINOMIAL THEOREM-Single Correct Answer

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 (a)(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 the 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 a....
Text Solution
|
If f(x)=1-x+x^2-x^3+. . -x^(15)+x^(16)-x^(17) , then the coefficient o...
Text Solution
|
Let f(x)=a0+a1x+a2x^2+...+an x^n and (f(x))/(1-x)=b0+b1x+b2x^2+...+bn ...
Text Solution
|
Statement 1: The coefficient of x^n in (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 coef...
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(0)+.^(20)C(1)+.^(20)C(2)+.^(20)C(3)+.^(20)C(4)+.^...
Text Solution
|
The sum of series .^(20)C0-^(20)C1+^(20)C2-^(20)C3++^(20)C10 is 1/2 .^...
Text Solution
|
If (3+x^(2008)+x^(2009))^(2010)=a0+a1x^2+....+anx^n, a0-1/2 a1-1/2 a2+...
Text Solution
|
Value of sum(k=1)^oosum(r=0)^k1/(3^k)(^k Cr) is 2/3 b. 4/3 c. 2 d. 1
Text Solution
|
The value of sum(r=0)^(10)(r)^(20)Cr is equal to 20(2^(18)+^(19)C(10))...
Text Solution
|
[(. ^nC0+^n C3+)-1/2(.^n C1+^n C2+^n C4+^n C5]^2 + 3/4(.^n C1-^n C2+^n...
Text Solution
|
The value of sum(r=1)^(n+1)(sum(k=1)^n^kC(r-1)) (where r, k, n in N) i...
Text Solution
|
The sum sumsum(0leilejle10) (""^(10)C(j))(""^(j)C(i-1)) is equal to
Text Solution
|