DSSSB TGT 2021
December 19, 2023Question 14297 – Theory-of-Computation
December 19, 2023GATE 2008
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Question 6
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Let r denote number system radix. The only value(s) of r that satisfy the equation 
is/are
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decimal 10
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decimal 11
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decimal 10 and 11
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any value > 2
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Question 6 Explanation:
√121r = 11r
(r2 + 2r + 1)1/2 = r + 1
(r + 1)2 * 1/2 = r + 1
r + 1 = r + 1
Any value of r will satisfy the above equation. But the radix should be greater than 2 because the 121 has 2. So r > 2 is correct.
(r2 + 2r + 1)1/2 = r + 1
(r + 1)2 * 1/2 = r + 1
r + 1 = r + 1
Any value of r will satisfy the above equation. But the radix should be greater than 2 because the 121 has 2. So r > 2 is correct.
Correct Answer: D
Question 6 Explanation:
√121r = 11r
(r2 + 2r + 1)1/2 = r + 1
(r + 1)2 * 1/2 = r + 1
r + 1 = r + 1
Any value of r will satisfy the above equation. But the radix should be greater than 2 because the 121 has 2. So r > 2 is correct.
(r2 + 2r + 1)1/2 = r + 1
(r + 1)2 * 1/2 = r + 1
r + 1 = r + 1
Any value of r will satisfy the above equation. But the radix should be greater than 2 because the 121 has 2. So r > 2 is correct.