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If (L)M represents a number L in base- M number system, then identify the correct descending order of the following numbers A-D when converted to decimal number system.

A. (123)7
B. (1211)3
C. (212)6
D. (201)5

1. A,C.B,D
2. B,D,A,C
3. D,B.C,A
4. C,A,D,B

यदि (L)M आधार-M संख्या प्रणाली में एक संख्या L का प्रतिनिधित्व करता है, तो दशमलव संख्या प्रणाली में परिवर्तित होने पर निम्नलिखित संख्याओं A-D के सही अवरोही क्रम की पहचान करें।

A. (123)7
B. (1211)3
C. (212)6
D. (201)5

1. A,C.B,D
2. B,D,A,C
3. D,B.C,A
4. C,A,D,B
This Question came in
UGC-NET-Law-30-August-2024-Shift-2-Q35
UGC-NET Paper 1 Full Course

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Detailed Explanation & Answer
A. (123)₇:
Calculation: 1 * 7^2 + 2 * 7^1 + 3 * 7^0
= 1 * 49 + 2 * 7 + 3 * 1
= 49 + 14 + 3 = 66

B. (1211)₃:
Calculation: 1 * 3^3 + 2 * 3^2 + 1 * 3^1 + 1 * 3^0
= 1 * 27 + 2 * 9 + 1 * 3 + 1 * 1
= 27 + 18 + 3 + 1 = 49

C. (212)₆:
Calculation: 2 * 6^2 + 1 * 6^1 + 2 * 6^0
= 2 * 36 + 1 * 6 + 2 * 1
= 72 + 6 + 2 = 80

D. (201)₅:
Calculation: 2 * 5^2 + 0 * 5^1 + 1 * 5^0
= 2 * 25 + 0 * 5 + 1 * 1
= 50 + 0 + 1 = 51

Descending order of these values is:
C (80)
A (66)
D (51)
B (49)
A. (123)₇:
गणना: 1 * 7^2 + 2 * 7^1 + 3 * 7^0
= 1 * 49 + 2 * 7 + 3 * 1
= 49 + 14 + 3 = 66

B. (1211)₃:
गणना: 1 * 3^3 + 2 * 3^2 + 1 * 3^1 + 1 * 3^0
= 1 * 27 + 2 * 9 + 1 * 3 + 1 * 1
= 27 + 18 + 3 + 1 = 49

C. (212)₆:
गणना: 2 * 6^2 + 1 * 6^1 + 2 * 6^0
= 2 * 36 + 1 * 6 + 2 * 1
= 72 + 6 + 2 = 80

D. (201)₅:
गणना: 2 * 5^2 + 0 * 5^1 + 1 * 5^0
= 2 * 25 + 0 * 5 + 1 * 1
= 50 + 0 + 1 = 51

इन मानों का अवरोही क्रम है:
C (80)
A (66)
D (51)
B (49)
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