Question

The two consecutive terms in the expansion of (3 + 2x)⁷⁴, whose coefficients are equal are

(a) 11, 12 

(b) 7, 8 

(c) 30, 31 

(d) None of these

Answer 1

Answer : (c) 30 , 31

General term of (3 + 2x)⁷⁴ is T_{r + 1} = ⁷⁴C_r (3)^{74 – r} (2x)^r 

= ⁷⁴C_r (3)^{74 – r} 2^r . x^r

Let the two consecutive terms be (r + 1)th term and (r + 2)th term.

Then, T_{r + 2} = ⁷⁴C_{r + 1} (3)^{74 – (r + 1)} 2^{r + 1} x^{r + 1} 

Given, Coefficient of T_{r + 1} = Coefficient of T_{r + 2}

⇒ ⁷⁴C_r (3)^{74 – r} . 2r = ⁷⁴C_{r + 1} (3)^{73 – r} . 2^{r + 1}

⇒ \(\frac{74-r}{r+1} = \frac{3}{2}\) ⇒ 148 - 2r = 3r +3

⇒ 5r = 145 ⇒ r = 29.

 ∴ The two consecutive terms are 30th and 31st.