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CMI-2021-DataScience-B: 18

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  1. Consider the function $f(x)=\frac{\ln x}{x}$. Find the critical point(s) of $f$ and say whether $f$ has a maximum or minimum at that point. 
  2. Prove that for integers $a>b \geq 3$, we must have $a^{b}<b^{a}$.
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admin asked Jul 23, 2022
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CMI-2021-DataScience-A: 18
Let $A_{11}, A_{12}, A_{21}, A_{22}, B_{11}, B_{12}, B_{21}, B_{22}$ be $n \times n$ matrices. Consider the $2n \times 2n$ matrices $A = \left[\begin{array}{cc}A_{11} & A_{12} \\ A_{21} & A_{22}\end{array}\right]$ ...
Let $A_{11}, A_{12}, A_{21}, A_{22}, B_{11}, B_{12}, B_{21}, B_{22}$ be $n \times n$ matrices. Consider the $2n \times 2n$ matrices $A = \left[\begin{array}{cc}A_{11} & A...
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