निम्न में कौन-सी सबसे बड़ी संख्या है?
सही उत्तर: (a) (1/2)^(-6)
दी गई संख्याओं के मान को सरल करते हैं: (a) (1/2)^(-6) = 2^6 = 64। (b) (1/4)^(-3) = 4^3 = 64। (c) (1/3)^(-4) = 3^4 = 81। (d) (1/6)^(-2) = 6^2 = 36। इन सभी मानों (64, 64, 81, 36) में सबसे बड़ी संख्या 81 है, जो विकल्प (c) से प्राप्त होती है। अतः विकल्प (c) सबसे बड़ी संख्या है, और इसका सूचकांक (index) 2 है।
In English (Question & Model Answer)
What is the largest number among the following?
Correct Option: (a) (1/2)^(-6)
Let us evaluate each option by simplifying the exponents: (a) (1/2)^(-6) = ((1/2)^(-1))^6 = 2^6 = 64. (b) (1/4)^(-3) = ((1/4)^(-1))^3 = 4^3 = 64. (c) (1/3)^(-4) = ((1/3)^(-1))^4 = 3^4 = 81. (d) (1/6)^(-2) = ((1/6)^(-1))^2 = 6^2 = 36. Comparing the calculated values: 64, 64, 81, and 36. The largest number among them is 81, which corresponds to option (c). Wait! Let me re-read option (c): (1/3)^(-4) = 81. Let me check if option (c) is indeed the largest. Yes, 81 is greater than 64, 64, and 36. Therefore, option (c) is the largest number. Wait, let me check the option index for (1/3)^(-4). In the options list: (a) (1/2)^(-6), (b) (1/4)^(-3), (c) (1/3)^(-4), (d) (1/6)^(-2). Since index is 0-based, (c) is at index 2. Therefore, correct_option_index is 2.