जब 7n - 6n को 36 से विभाजित किया जाता है, तो n = 100 के लिए शेषफल क्या होगा?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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Answer (Detailed Solution Below)

Option 2 : 1
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व्याख्या:

मान लीजिये p(n) = 7n - 6n

= (6+1)n - 6n

= 1+6n +nC262 + nC363+.......... 6n -6n

= 1+ 62(nC2+ nC3 x 6 +....... 6n-2)

= 1+ 36(100C2 + 100C3 x 6 +........698).....(n =100)

= 1 + 36 k

जहाँ k = (100C2 + 100C3 x 6 +........698)

इस प्रकार जब 7n - 6n को 36 से विभाजित किया जाता है, तो शेषफल 1 होगा

∴ विकल्प (b) सही है

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