Find the coefficient of x18 in (x2 + \(\frac{3a}{x}\))15 – InterviewSolution

InterviewSolution

1.

Find the coefficient of x18 in (x2 + \(\frac{3a}{x}\))15

Answer»

Here x → x² a → \(\frac{3a}{x}\), n =15

∴ T_r+1 = ¹⁵C_r.(x²)^15-r(\(\frac{3a}{x}\))^r

= ¹⁵C_rx^30-2r.(3a)^rx^r

= ¹⁵C_r .3^r .a^r .x^30-3r

To find the coefficient of x¹⁸, we get 30 – 3r = 18

12 = 3r ⇒ r =4

∴ T₄₊₁ = ¹⁵C₄.3⁴ .a⁴ .x¹⁸

∴ coefficient of x¹⁸ is ¹⁵C₄.(3a)⁴

Discussion

No Comment Found

Related InterviewSolutions

Construct the composition table for ×5 on set Z5 = {0, 1, 2, 3, 4}
If C0, C1, C2,… Cn are coefficients of expansion (1 + x)n then find the value of :(i) 8C1 + 8C2 + 8C3 + … + 8C8(ii) 8C1+ 8C3 + 8C5 + 8C7
Class 11 Maths MCQ Questions of Binomial Theorem with Answers?
How to join and Practice Online Class 11 Binomial Theorem Mock Test?
Write the first six terms of the sequences given by (i) a1 = a2 = 1 = an - 1 + an - 2 (n ≥ 3)(ii) a1 = 4, an + 1 = 2nan
If a is the arithmetic mean and g is the geometric mean of two numbers, then ...(a) a ≤ g (b) a ≥ g (c) a = g (d) a > g
If (1 + x) n = C0 + C1x + C2x2 + .... + Cnxn, then C0 + 3 . C1 + 5 . C2 + .... + (2n + 1) . Cn equals(a) 22n–1 (b) (n + 1) 2n (c) n . 2n+1 (d) (n – 1) 2n–1
If a and b denote the sum of the coefficients in the expansions of (1-3x+10x2)n and (1 + x2)n respectively, then write the relation between a and b.
Write the number of terms in the expansion of (1-3x+3x2-x3)8.
47C4 + \(\sum_{r=1}^{5}\) \(^{52-r}C_3\) is equal to (a) 47C6 (b) 52C5 (c) 52C4 (d) None of these