Question

Find the coefficient of x⁵y¹⁰ in the expansion of (3x + 2y)¹⁵
1. ¹⁵C₁₀ 3⁵ 2¹⁰
2. 15C10 35 25
3. 15C10 310 210
4. 15C5 310 210
5. None of these

Answer 1

Correct Answer - Option 1 : ¹⁵C₁₀ 3⁵ 2¹⁰

Concept:

The general term of the expansion of (x + a)n is usually denoted by Tr+1 =  nCr xn-r ar

Calculation:

For the given expression (3x + 2y)15  ,  n = 15

(r + 1)th term

\(\rm T_{r+1}=^{15}\textrm{C}_{r}{(3x)}^{15-r}(2y)^r\)

For the coefficient of x⁵y¹⁰, r must be 10.

\(\rm T_{10+1}=^{15}\textrm{C}_{10}(3x)^{15-10}(2y)^{10}\)
\(\rm T_{10+1}=^{15}\textrm{C}_{10}(3x)^{5}(2y)^{10}\)

\(\rm T_{10+1}=^{15}\textrm{C}_{10}3^5 2^{10} x^{5}y^{10}\)

So the coefficient of x⁵y¹⁰ is equal to the 15C10 35 210