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If the coefficient of rth and (r + 1)th terms in the expansion of (3 + 7x)29 are equal, then r equals

(a) 15 

(b) 21 

(c) 14 

(d) None of these

1 Answer

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Best answer

Answer : (b) 21

In the expansion of (3 + 7x)29 

Tr+1 = 29Cr (3)29–r (7x)r = 29Cr 329–r . 7r . x

\(\therefore\) 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.

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