CAT 2025 Slot 1 QA Question & Solution

AlgebraHard

The number of distinct integers n for which $\log_{\frac{1}{4}}({n^{2}-7n+11})$

infinite

For base of log in range $$1/4\in(0,1)$$ and $$\log_{1/4}(x)>0$$ is true only if 0<x<1.

For integer n, $$x=n^2-7n+11$$ is an integer, so it cannot lie strictly between 0 and 1.

So, there is no integer value for which this inequality is satisfied.