3 $ 4 Pattern Analysis
The problem defines a mathematical operation '$' using the following examples:
3 $ 4 = 37
4 $ 5 = 61
We need to find the value of 5 $ 6 by identifying the common pattern.
Rule Derivation
Observe that each result can be obtained using:
[
a $ b = a2 + b2 + (a × b)
]
Let's verify the pattern with the given examples.
For 3 $ 4:
[
32 + 42 + (3 × 4)
]
[
= 9 + 16 + 12
]
[
= 37
]
So, the pattern correctly gives:
[
3 $ 4 = 37
]
For 4 $ 5:
[
42 + 52 + (4 × 5)
]
[
= 16 + 25 + 20
]
[
= 61
]
So, the pattern also correctly gives:
[
4 $ 5 = 61
]
Therefore, the rule is:
[
a $ b = a2 + b2 + ab
]
5 $ 6 Calculation
Now apply the same rule for (5 $ 6):
[
5 $ 6 = 52 + 62 + (5 × 6)
]
[
= 25 + 36 + 30
]
[
= 91
]
Therefore:
[
5 $ 6 = 91
]
Final Answer
Option 4: 91
Similar Questions
If POSTER is coded as 592314 and DARK is coded as 8647, then how will STROKE be coded as?
In a certain code language, "who are you" is written as "4 3 2", "they is you" is written as "4 8 5" and "they are dangerous" is written as "2 9 5". How is "dangerous" written in that code language?
In a certain code language, ‘POUND’ is coded as ‘106’ and ‘CLEAN’ is coded as ‘41’. How will ‘MAKER’ be coded as in that language?
In a code language, REGULAR is written as GERTRAL. How will BROTHER be written as in that language?
In a certain code language, "DEAF" is written as "4516" and "KILL" is written as "1191212". How will "LORD" be written in that language?
In a certain code language, if 'EAR' is written as '2037' and 'PBU' is written as '23418', how will 'DIG' be written in the same code language?
In a certain code language, ‘CROW’ is coded as ‘64’ and ‘EAGLE’ is coded as ‘125’. How will ‘PARROT’ be coded in that language?
In a certain code language, ‘MANGO’ is coded as ‘13-2-42-28-75’and ‘GRAPE’ is coded as ‘7-36-3-64-25’. How will ‘APPLE’ be coded in that language?
- If $2 \text{ \# } 3 = 13$, $3 \text{ \# } 4 = 25$, then $4 \text{ \# } 5 = ?$
If 2 @ 3 = 25 and 3 @ 4 = 49, what is 4 @ 5?
Important Questions from Coding Decoding Based on Numbers
In a certain code language, 'IT' is written as '58', 'SAD' is written as '48'. What is the code for 'FISH' in that code language?
If 31 L 31 J 5 = 186 and 47 J 2 L 43 = 137, then 52 L 64 J 3 = ?
If R is coded as 4, M is coded as 1, N is coded as 5, S is coded as 8, Q is coded as 0, L is coded as 6 and P is coded as 3, then what is the coded form of SMLRP ?
If in a certain code, 6723 is coded as 8901, how is 2435 coded in that language?
In a certain code language, 'CHOICE' is written as '53', 'CHARGE' is written as '52', how will 'CHANCE' be written in that language?
