Advertisements
Advertisements
Question
Find the coefficient of x4 in the expansion of (1 + x + x2 + x3)11.
Advertisements
Solution
Given expression is (1 + x + x2 + x3)11
= [(1 + x) + x2 (1 + x)]11
= [(1 + x)(1 + x2)]11
= (1 + x)11 · (1 + x2)11
Expanding the above expression, we get
(11C0 + 11C1x + 11C2x2 + 11C3x3 + 11C4x4 + …) · (11C0 + 11C1x2 + 11C2x4 +)
= (1 + 11x + 55x2 + 165x3 + 330x4 …) · (1 + 11x2 + 55x4 + …)
Collecting the terms containing x4, we get
(55 + 605 + 330)x4 = 990x4
Hence, the coefficient of x4 = 990
APPEARS IN
RELATED QUESTIONS
Expand the expression: (1– 2x)5
Expand the expression: (2x – 3)6
Expand the expression: `(x + 1/x)^6`
Using Binomial Theorem, evaluate the following:
(96)3
Using Binomial Theorem, evaluate of the following:
(102)5
Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.
Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.
Find a, b and n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively.
Find the value of `(a^2 + sqrt(a^2 - 1))^4 + (a^2 - sqrt(a^2 -1))^4`
Find an approximation of (0.99)5 using the first three terms of its expansion.
Expand using Binomial Theorem `(1+ x/2 - 2/x)^4, x != 0`
Find the value of (1.01)10 + (1 − 0.01)10 correct to 7 places of decimal.
Find the rth term in the expansion of `(x + 1/x)^(2r)`
Expand the following (1 – x + x2)4
Find the 4th term from the end in the expansion of `(x^3/2 - 2/x^2)^9`
Evaluate: `(x^2 - sqrt(1 - x^2))^4 + (x^2 + sqrt(1 - x^2))^4`
Find the coefficient of x11 in the expansion of `(x^3 - 2/x^2)^12`
Find the term independent of x in the expansion of `(sqrt(x)/sqrt(3) + sqrt(3)/(2x^2))^10`.
Show that `2^(4n + 4) - 15n - 16`, where n ∈ N is divisible by 225.
Which of the following is larger? 9950 + 10050 or 10150
If a1, a2, a3 and a4 are the coefficient of any four consecutive terms in the expansion of (1 + x)n, prove that `(a_1)/(a_1 + a_2) + (a_3)/(a_3 + a_4) = (2a_2)/(a_2 + a_3)`
The total number of terms in the expansion of (x + a)51 – (x – a)51 after simplification is ______.
If (1 – x + x2)n = a0 + a1 x + a2 x2 + ... + a2n x2n , then a0 + a2 + a4 + ... + a2n equals ______.
If z = `sqrt(3)/2 + i^5/2 + sqrt(3)/2 - i^5/2`, then ______.
Find the coefficient of x in the expansion of (1 – 3x + 7x2)(1 – x)16.
In the expansion of (x + a)n if the sum of odd terms is denoted by O and the sum of even term by E. Then prove that 4OE = (x + a)2n – (x – a)2n
The total number of terms in the expansion of (x + a)100 + (x – a)100 after simplification is ______.
Given the integers r > 1, n > 2, and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x)2n are equal, then ______.
The two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1:4 are ______.
The coefficient of a–6b4 in the expansion of `(1/a - (2b)/3)^10` is ______.
Number of terms in the expansion of (a + b)n where n ∈ N is one less than the power n.
The sum of the last eight coefficients in the expansion of (1 + x)16 is equal to ______.
