First slide

Binomial theorem for positive integral Index

Question

If $^{n + 1} C_{r + 1} :^{n} C_{r} : {}^{n - 1}C_{r - 1} = 11 : 6 : 3$ , then nr =

Moderate

A

20
B

30
C

40
D

50

Solution

Given,
$\frac{^{n + 1} C_{r + 1}}{^{n} C_{r}} = \frac{11}{6} or \frac{\frac{n + 1}{r + 1} \times^{n} C_{r}}{^{n} C_{r}} = \frac{11}{6}$
or $6 n + 6 = 11 r + 11 or 6 n - 11 r = 5$ (1)
Also,
$\frac{^{n} C_{r}}{^{n - 1} C_{r - 1}} = \frac{6}{3} or \frac{\frac{n}{r} \times^{n - 1} C_{r - 1}}{^{n - 1} C_{r - 1}} = \frac{6}{3} or n = 2 r$ (2)
From (1) and (2), r = 5 and n = 10,
$∴ nr = 50$

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