381 Advanced Mathematics • Group Theory What is the order of an element g of a cyclic group G? What is the order of an element g of a cyclic group G? सेव करें Save सेव्ड Saved A. The smallest positive integer r such that g^r is the identity. The smallest positive integer r such that g^r is the identity. B. The order axioms imposed on the group. The order axioms imposed on the group. C. The number of elements in the group. The number of elements in the group. D. The number of elements a in G such that a^2=e, the identity. The number of elements a in G such that a^2=e, the identity. उत्तर और व्याख्या देखें Show answer and explanation सही उत्तर: A Correct Answer: A By definition, the order of g is the least positive integer r for which g^r=e, provided such an integer exists. By definition, the order of g is the least positive integer r for which g^r=e, provided such an integer exists.
382 Number System • Number System Basics The binary number 10101 is equivalent to the decimal number: The binary number 10101 is equivalent to the decimal number: सेव करें Save सेव्ड Saved A. 12 12 B. 27 27 C. 19 19 D. 21 21 उत्तर और व्याख्या देखें Show answer and explanation सही उत्तर: D Correct Answer: D Binary 10101 equals 1x16+0x8+1x4+0x2+1x1=21. Binary 10101 equals 1x16+0x8+1x4+0x2+1x1=21.