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ISI 2021 | PCB Mathematics | Question: 8

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  1. Calculate the number of different ways you can divide $2 n$ elements of the set $S=\{1,2, \ldots, 2 n\}$ to form $n$ disjoint subsets, each containing a pair of elements.
  2. Calculate the number of different ways in which the above division can be done if each subset is required to contain an even number and an odd number.
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admin asked Aug 8, 2022
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ISI 2021 | PCB Mathematics | Question: 2
Consider three real numbers $a \geq b \geq c>0$. If $\left(a^{x}-b^{x}-c^{x}\right)(x-2)>0$ for any rational number $x \neq 2$, show that $a, b$ and $c$ can be the lengths of the three sides of a triangle $A B C;$ $A B C$ is a right-angled triangle.
Consider three real numbers $a \geq b \geq c>0$. If $\left(a^{x}-b^{x}-c^{x}\right)(x-2)>0$ for any rational number $x \neq 2$, show that$a, b$ and $c$ can be the lengths...
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