Hidden rule a @ b = a^2 + b^2: find it from the examples and apply

This type of question, asked 7 times: 12 Sep 2025 S2, 13 Sep 2025 S3, 16 Sep 2025 S1, 17 Sep 2025 S1, 17 Sep 2025 S3, 19 Sep 2025 S2, 26 Sep 2025 S1. All 7 questions below, oldest first.

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Question 1
12 Sep 2025 S2
20 $If 7 $ 3 = 58 and 6 $ 2 = 40, what is 5 $ 1?$
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Question 2
13 Sep 2025 S3
19 $If 3 & 4 = 25 and 5 & 2 = 29, then find the value of 6 & 3 =?$
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Question 3
16 Sep 2025 S1
17 $5 \ast 4 = 41$
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Question 4
17 Sep 2025 S1
21 $If 2 @ 3 = 13, 3 @ 4 = 25, then what is 4 @ 5?$
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Question 5
17 Sep 2025 S3
18 $If 4 & 4 = 32 and 5 & 5 = 50, what is 6 & 6?$
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Question 6
19 Sep 2025 S2
2 $If 3 + 2 = 13, 4 + 3 = 25, then 5 + 4 = ?$
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Question 7
26 Sep 2025 S1
3 $If 2 # 3 = 13, 3 # 4 = 25, then 4 # 5 = ?$
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Hidden rule a @ b = a^2 + b^2: find it from the examples and apply

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Question 7