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JEE Main 202621 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
21 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2026 · 21 January · Morning Shift · Mathematics · Permutation and Combination

The number of strictly increasing functions f from the set \...

The number of strictly increasing functions ff from the set {1,2,3,4,5,6}\{1,2,3,4,5,6\} to the set {1,2,3,….,9}\{1,2,3, \ldots., 9\} such that f(i)≠if(i) \neq i for 1≤i≤61 \leq i \leq 6, is equal to :

Options

  1. A2727
  2. B2222
  3. C2121
  4. D2828

Correct answer

D. 2828

Step-by-step solution

For strictly increasing ff, if we choose elements a1<a2<⋯<a6a_1 < a_2 < \cdots < a_6, then f(i)=aif(i) = a_i.
Since f(i)≥if(i) \geq i always, condition f(i)≠if(i) \neq i means f(i)≥i+1f(i) \geq i + 1 for all ii.
Let h(i)=f(i)−ih(i) = f(i) - i. Then h(i)≥1h(i) \geq 1, h(6)≤3h(6) \leq 3, and hh is non-decreasing.
So h(i)∈{1,2,3}h(i) \in \{1, 2, 3\} for all ii.
Number of non-decreasing sequences of length 6 from {1,2,3}=(82)=28\{1, 2, 3\} = \binom{8}{2} = 28.
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