JEE 2023 — Mathematics PYQ

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Question

JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is $7$ and the sum of the first two digits is equal to the sum of the last two digits. Then, the maximum number of trials necessary to obtain the correct code is _____.

Choose the correct answer:

Explanation

Solution :

Possible combinations $\{ (d_1, d_2), (d_3, d_4) \}$ nikalna:

Kyunki ek digit $7$ hona zaroori hai, hum aise pairs dhundenge jinka sum barabar ho aur digits repeat na hon.
- Agar $S = 7$ : Pairs hain $\{7, 0\}$ aur $\{6, 1\}, \{5, 2\}, \{4, 3\}$ . (3 combinations)
- Agar $S = 8$ : Pairs hain $\{7, 1\}$ aur $\{6, 2\}, \{5, 3\}$ . (2 combinations)
- Agar $S = 9$ : Pairs hain $\{7, 2\}$ aur $\{6, 3\}, \{5, 4\}$ . (2 combinations)
- Agar $S = 10$ : Pairs hain $\{7, 3\}$ aur $\{6, 4\}$ . (1 combination)
- Agar $S = 11$ : Pairs hain $\{7, 4\}$ aur $\{6, 5\}$ . (1 combination)
Total combinations = $3 + 2 + 2 + 1 + 1 = 9$ .
Har combination ke arrangements:

Ek set $\{ (a, b), (c, d) \}$ ke liye PIN banane ke tarike:
- Pehle do spots ke liye 2 options aur aakhri do ke liye 2 options ( $2 \times 2 = 4$ ).
- Dono pairs aapas mein jagah badal sakte hain ( $\times 2$ ).
- Total trials per combination = $4 \times 2 = 8$ .
Total number of trials:

$\text{Total trials} = 9 \times 8 = 72$

Final Answer:

Maximum number of trials 72 hain.

Choose the correct answer:

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