Official PYQ · 1988Q2-viNumber Representations (Fixed and Floating Point)NAT1 mark

GATE CS 1988 Q2-vi — Number Representations (Fixed and Floating Point)

Define the value of

r

in the following:

\sqrt {(41)_{r}} = (7)_{10}

View worked solution

Answer: 12

To find the value of the base $r$ , we start with the given equation:

\sqrt{(41)_r} = (7)_{10}

Squaring both sides of the equation, we get:

(41)_r = (7)_{10}^2

(41)_r = 49_{10}

Now, we convert the number $(41)_r$ from base $r$ to base $10$ :

4 \cdot r^1 + 1 \cdot r^0 = 49

4r + 1 = 49

Solving for $r$ :

4r = 48

r = 12

Since the digits in $(41)_r$ are $4$ and $1$ , the base $r$ must be strictly greater than $4$ . Thus, $r = 12$ is a valid base.

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Published 10 Oct 2026

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