Answer : (b) 21
In the expansion of (3 + 7x)29
Tr+1 = 29Cr (3)29–r (7x)r = 29Cr 329–r . 7r . xr
\(\therefore\) Coefficient of (r + 1)th term = 29Cr 329–r 7r
\(\therefore\) Coefficient of rth term = 29Cr–1 329–(r–1) 7r–1
= 29Cr–1 330–r 7r–1
Given, 29Cr × 329–r × 7r = 29Cr–1 × 330–r × 7r–1
\(\implies
\) \(\frac{^{29}C_r}{^{29}C_{r-1}} = \frac{3}{7}\)
⇒ \(\frac{30-r}{r} = \frac{3}{7}\)
⇒ 210 – 7r = 3r
⇒ 210 = 10r
⇒ r = 21.