JAMIA 2025 — Computer PYQ

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Question

JAMIA 2025 — Computer PYQ

JAMIA | Computer | 2025

If (123)₅ = (A3)_B, then the number of possible values of A is:

Choose the correct answer:

Explanation

1. Decimal Conversion

(123)_{5} = 1 \cdot 5^{2} + 2 \cdot 5^{1} + 3 \cdot 5^{0} = 38

RHS equation:

AB + 3 = 38 \implies AB = 35

2. Constraints (Shartein)

Rule ke mutabiq:

$B > A$ aur $B > 3$

3. Factor Pairs Check

$35$ ke factors:

$A = 1, B = 35 \rightarrow$ ( $1 < 35$ aur $1 < 5$ ) — Valid
$A = 5, B = 7 \rightarrow$ ( $5 < 7$ lekin $A$ base $5$ ke digits se bada hai) — Valid
$A = 7, B = 5 \rightarrow$ ( $7 > 5$ ) — Invalid

4. Final Result

Sirf do hi value ( $A = 1$ ) ( $A = 1$ )bachti hai jo conditions ko satisfy karti hai.

Total possible values of A = 2