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Functions: Functions Strictly Monotonic Functions

JEE Maths question with a full step-by-step solution.

Question
A={1,2,3}A = \{1,2,3\}, B={1,3,5,7,9}B = \{1,3,5,7,9\}. Then No. of one-one functionsNo. of strictly monotonic functions\dfrac{\text{No. of one-one functions}}{\text{No. of strictly monotonic functions}}.
Solution
Answer: 3
Step 1: One-one functions from AA to BB
5P3=5×4×3=60{}^5P_3 = 5 \times 4 \times 3 = 60
 Step 2: Strictly monotonic functions from AA to BB Each strictly monotonic function is determined by choosing 3 elements from BB and assigning them in order. Strictly increasing: 5C3=10{}^5C_3 = 10. Strictly decreasing: 5C3=10{}^5C_3 = 10. Total = 20. Step 3: Ratio
6020=3\frac{60}{20} = 3
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