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JEE Main202330 Jan 2023Evening ShiftMathematicsBinomial TheoremActual

50 th root of a number x is 12 and 50 th root of another number y is 18 . Then the remainder obtained on dividing ( x + y ) by 25 is ________.

Correct answer

0

Step-by-step solution

Given: x 1 50 = 12 ⇒ x = 12 50 y 1 50 = 18 ⇒ y = 18 50 So, x + y = 12 50 + 18 50 ⇒ x + y 25 = 12 50 25 + 18 50 25 ⇒ x + y 25 = 12 3 16 12 2 25 + 18 2 25 25 ⇒ x + y 25 = 1728 16 12 2 25 + 325 - 1 25 25 ⇒ x + y 25 = 1725 + 3 16 12 2 25 + 325 - 1 25 25 So, remainder is 3 16 12 2 25 - 1 = 3 3 5 × 3 × 144 25 - 1 = 25 + 2 5 × 3 × 144 25 - 1 = 25 + 2 5 × 3 × 150 - 6 25 - 1 = 2 5 × 3 × - 6 25 - 1 = 25 + 7 × 3 × - 6 25 - 1 = 21 × - 6

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