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If (L)M represents a number L in base-M number system, then which of the following equalities are true?

A.(127.125)10 = (1111111.001)2
B.(127.125)10 = (1333.02)4
C.(127.125)10 = (177.1)8
D. (127.125)10 = (7F.2)16

1. A
2. AB
3. ABC
4. ABCD

यदि (L)M आधार-M संख्या प्रणाली में एक संख्या L का प्रतिनिधित्व करता है, तो निम्नलिखित में से कौन सी समानताएँ सत्य हैं?

A.(127.125)10 = (1111111.001)2
B.(127.125)10 = (1333.02)4
C.(127.125)10 = (177.1)8
D. (127.125)10 = (7F.2)16

1. A
2. AB
3. ABC
4. ABCD
This Question came in
UGC-NET-English-21-August-2024-Shift-1-Q43
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Detailed Explanation & Answer
A. (127.125)10 = (1111111.001)2
Conversion: The integer part 12710 = 11111112 and the fractional part 0.12510 = 0.0012. Therefore, (127.125)10 = (1111111.001)2 is true.

B. (127.125)10 = (1333.02)4
Conversion: The integer part 12710 = 13334 and the fractional part 0.12510 = 0.024. Thus, (127.125)10 = (1333.02)4 is true.

C. (127.125)10 = (177.1)8
Conversion: The integer part 12710 = 1778 and the fractional part 0.12510 = 0.18. Hence, (127.125)10 = (177.1)8 is true.

D. (127.125)10 = (7F.2)16
Conversion: The integer part 12710 = 7F16 and the fractional part 0.12510 = 0.216. Thus, (127.125)10 = (7F.2)16 is true.
A. (127.125)10 = (111111.001)2
रूपांतरण: पूर्णांक भाग 12710 = 111111112 और भिन्नात्मक भाग 0.12510 = 0.0012। इसलिए, (127.125)10 = (111111.001)2 सत्य है।

B. (127.125)10 = (1333.02)4
रूपांतरण: पूर्णांक भाग 12710 = 13334 और भिन्नात्मक भाग 0.12510 = 0.024। इस प्रकार, (127.125)10 = (1333.02)4 सत्य है।

C. (127.125)10 = (177.1)8
रूपांतरण: पूर्णांक भाग 12710 = 1778 और भिन्नात्मक भाग 0.12510 = 0.18। अतः, (127.125)10 = (177.1)8 सत्य है।

D. (127.125)10 = (7एफ.2)16
रूपांतरण: पूर्णांक भाग 12710 = 7एफ16 और भिन्नात्मक भाग 0.12510 = 0.216। इस प्रकार, (127.125)10 = (7एफ.2)16 सत्य है।
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