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

(A) (102)4
(B) (10001)2
(C) (103)6
(D) (201)3

1. BACD
2. ACDB
3. ABDC
4. BADC

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 आरोही क्रम की पहचान करें।

(A) (102)4
(B) (10001)2
(C) (103)6
(D) (201)3

1. BACD
2. ACDB
3. ABDC
4. BADC

This Question came in

UGC-NET-PolSci-04-September-2024-Shift-1-Q25

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Detailed Explanation & Answer

Convert (A) (102)4:
Base 4: (1 × 4^2) + (0 × 4^1) + (2 × 4^0) = 1 × 16 + 0 × 4 + 2 × 1 = 16 + 0 + 2 = 18 in decimal.

Convert (B) (10001)2:
Base 2: (1 × 2^4) + (0 × 2^3) + (0 × 2^2) + (0 × 2^1) + (1 × 2^0) = 1 × 16 + 0 + 0 + 0 + 1 = 17 in decimal.

Convert (C) (103)6:
Base 6: (1 × 6^2) + (0 × 6^1) + (3 × 6^0) = 1 × 36 + 0 + 3 = 39 in decimal.

Convert (D) (201)3:
Base 3: (2 × 3^2) + (0 × 3^1) + (1 × 3^0) = 2 × 9 + 0 + 1 = 18 + 0 + 1 = 19 in decimal.

ascending order:
(B) = 17
(A) = 18
(D) = 19
(C) = 39

कनवर्ट करें (ए) (102)4:
आधार 4: (1 × 4^2) + (0 × 4^1) + (2 × 4^0) = 1 × 16 + 0 × 4 + 2 × 1 = 16 + 0 + 2 = 18 दशमलव में।

कनवर्ट करें (बी) (10001)2:
आधार 2: (1 × 2^4) + (0 × 2^3) + (0 × 2^2) + (0 × 2^1) + (1 × 2^0) = 1 × 16 + 0 + 0 दशमलव में + 0 + 1 = 17.

कनवर्ट करें (सी) (103)6:
आधार 6: (1 × 6^2) + (0 × 6^1) + (3 × 6^0) = 1 × 36 + 0 + 3 = 39 दशमलव में।

कनवर्ट करें (डी) (201)3:
आधार 3: (2 × 3^2) + (0 × 3^1) + (1 × 3^0) = 2 × 9 + 0 + 1 = 18 + 0 + 1 = 19 दशमलव में।

आरोही क्रम:
(बी) = 17
(ए)=18
(डी)=19
(सी) = 39

The Correct Answer is 4

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