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JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Permutations and Combinations

If

^{n} C_{4},^{n} C_{5}

and

^{n} C_{6}

are in A.P., then n can be :

(A)9
(B)14✓ Correct
(C)11
(D)12

Answer: (B)

Solution

For

(4 n), (5 n), (6 n)

in A.P.,

2 (5 n) = (4 n) + (6 n)

. Using

\frac{( 4 n )}{( 5 n )} = \frac{5}{n - 4}

and

\frac{( 6 n )}{( 5 n )} = \frac{n - 5}{6}

, the condition becomes

\frac{5}{n - 4} + \frac{n - 5}{6} = 2

, which reduces to

n^{2} - 21 n + 98 = 0

, i.e.

(n - 7) (n - 14) = 0

. Taking the larger value,

n = 14

.

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option

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