Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The number of elements in the set {n ∈ {1, 2, 3,…, 100} for
(11) n > (10) n + (9) n }is ____.
Text Solution
Verified by ExpertsThe correct answer is:
96
(96)
11 n > 10 n + 9 n
⇒ 11 n − 9 n > 10 n
⇒ (10 + 1) n − (10 − 1) n > 10 n
⇒ { n C 1 ⋅ 10 n−1 + n C 3 10 n−0 + n C 5 10 n−5 + ⋯⋅⋅ } > 10 n
⇒ 2n ⋅ 10 n−1 + 2 { n C 3 10 n−3 + n C 5 10 n−5 + ⋯⋅⋅ } > 10 n …..(1)
For n=5
(True)
For n = 6, 7, 8,…. .100
For 2n10 n−1 > 10 n
For n = 5, 6, 7,……100,
For n=4 Inequality (1) is not satisfied ⇒ Inequality does not hold good for N = 1, 2, 3, 4
So, required number of elements =96
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