CATAlgebra > Hard32\frac{3}{2}2352\frac{5}{2}2512\frac{1}{2}213✅ Correct Option: 3Related questions:CAT 2023 Slot 2Let aaa, bbb, mmm and nnn be natural numbers such that a>1a > 1a>1 and b>1b > 1b>1. If ambn=144145a^m b^n = 144^{145}ambn=144145, then the largest possible value of n−mn - mn−m is2025 Slot 3If 1212x×424x+12×52y=84z×2012x×2433x−612^{12x}\times4^{24x+12}\times5^{2y}=8^{4z}\times20^{12x}\times243^{3x-6}1212x×424x+12×52y=84z×2012x×2433x−6, where xxx, yyy and zzz are natural numbers, then x+y+zx+y+zx+y+z equalsCAT 2020 Slot 2The number of integers that satisfy the equality (x2−5x+7)x+1=1(x^2 - 5x + 7)^{x + 1} = 1(x2−5x+7)x+1=1 is