CUET PG 2024 — Computer PYQ

Q: How do I solve CUET PG 2024 Computer questions?

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Question

CUET PG 2024 — Computer PYQ

CUET PG | Computer | 2024

Given $(224)_{r} = (13)_{r}$ , where $r$ is the radix. The value of $r$ is ___

Choose the correct answer:

Explanation

Given Equation:

\sqrt{(224)_r} = (13)_r

Step 1: Base $r$ ko Decimal (Base 10) mein convert karein

(224)_r = 2r^2 + 2r + 4

(13)_r = 1r + 3

Step 2: Equation banayein aur solve karein

\sqrt{2r^2 + 2r + 4} = r + 3

Dono sides ka Square karne par:

2r^2 + 2r + 4 = (r + 3)^2

2r^2 + 2r + 4 = r^2 + 6r + 9

Ab terms ko rearrange karke quadratic equation banayein:

2r^2 - r^2 + 2r - 6r + 4 - 9 = 0

r^2 - 4r - 5 = 0

Step 3: Quadratic Equation ke Factors nikalna

r^2 - 5r + r - 5 = 0

r(r - 5) + 1(r - 5) = 0

(r - 5)(r + 1) = 0

Yahan do values milti hain:

r = 5 \quad \text{ya} \quad r = -1

Step 4: Answer Select karna

Chunkee radix ( $r$ ) hamesha positive hota hai aur di gayi digits ( $2, 2, 4$ ) se bada hona chahiye ( $r > 4$ ):

\mathbf{r = 5}