Advertisements
Advertisements
Question
Find a if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.
Advertisements
Solution


RELATED QUESTIONS
Expand the expression: (1– 2x)5
Expand the expression (1– 2x)5
Expand the expression: `(2/x - x/2)^5`
Expand the expression: (2x – 3)6
Expand the expression: `(x + 1/x)^6`
Using Binomial Theorem, evaluate of the following:
(102)5
Using binomial theorem, evaluate the following:
(99)5
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.
If a and b are distinct integers, prove that a – b is a factor of an – bn, whenever n is a positive integer.
[Hint: write an = (a – b + b)n and expand]
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.
If n is a positive integer, prove that \[3^{3n} - 26n - 1\] is divisible by 676.
Using binomial theorem determine which number is larger (1.2)4000 or 800?
Show that \[2^{4n + 4} - 15n - 16\] , where n ∈ \[\mathbb{N}\] is divisible by 225.
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`
Find the term independent of x in the expansion of `(sqrt(x)/sqrt(3) + sqrt(3)/(2x^2))^10`.
Which of the following is larger? 9950 + 10050 or 10150
Find the coefficient of x50 after simplifying and collecting the like terms in the expansion of (1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + ... + x1000 .
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)`
If the coefficients of x7 and x8 in `2 + x^n/3` are equal, then n is ______.
The coefficient of xp and xq (p and q are positive integers) in the expansion of (1 + x)p + q are ______.
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 O2 – E2 = (x2 – a2)n
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 number of terms in the expansion of (x + y + z)n ______.
Number of terms in the expansion of (a + b)n where n ∈ N is one less than the power n.
Let the coefficients of x–1 and x–3 in the expansion of `(2x^(1/5) - 1/x^(1/5))^15`, x > 0, be m and n respectively. If r is a positive integer such that mn2 = 15Cr, 2r, then the value of r is equal to ______.
If the coefficients of (2r + 4)th, (r – 2)th terms in the expansion of (1 + x)18 are equal, then r is ______.
Let `(5 + 2sqrt(6))^n` = p + f where n∈N and p∈N and 0 < f < 1 then the value of f2 – f + pf – p is ______.
