Number of elements in set is

JEE MainMathematicsEasySets

Number of elements in set
$A = \left\{ p:p = \frac{\left( 2n^{5} + 3n^{4} + 4n^{3} + 5n^{2} + 6 \right)(n + 2)}{n^{2} + 2n};n,p \in Z^{+} \right\}$
is

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P = \frac{\left( 2n^{5} + 3n^{4} + 4n^{3} + 5n^{2} + 6 \right) \times (n + 2)}{n^{2} + 2n}

\Rightarrow P = 2n^{4} + 3n^{3} + 4n^{2} + 5n + \frac{6}{n}

\because P \in z^{+}

\frac{6}{n} \in z^{+} \Rightarrow n

is a factor of 6

\Rightarrow n = 1,2,3,6

Source: Grass-G / M-05 Mathematics Paper 10 October.docx

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