Question
The number of strictly increasing functions f from the set \ 1,2,3,4,5,6\ to the set \ 1,2,3, ., 9\ such that f(i) i for 1 i 6, is equal to :
JEE Main
Mathematics
Permutation Combination
2026
JEE Main 2026 (21 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 27
- B. 22
- C. 21
- D. 28
Answer
D. 28
Step-by-step solution
For strictly increasing f, if we choose elements a_1 Since f(i) i always, condition f(i) i means f(i) i + 1 for all i. Let h(i) = f(i) - i. Then h(i) 1, h(6) 3, and h is non-decreasing. So h(i) \ 1, 2, 3\ for all i. Number of non-decreasing sequences of length 6 from \ 1, 2, 3\ = 8 2 = 28.
Related: Mathematics — Permutation Combination · All PYQ Banks