Question 131

If the expansion of $$(x - 3x^2)^{25}$$ is a polynomial of $$n^{th}$$ degree in x, then n =

Solution

$$(x-3x^2)^{25}=^{25}C_0x^{25}+^{25}C_1x^{24}\left(-3x^2\right)+....+^{25}C_{24}x\left(-3x^2\right)^{24}+^{25}C_{25}\left(-3x^2\right)^{25}$$

$$=^{25}C_0x^{25}+^{25}C_1\left(-3\right)x^{26}+....+^{25}C_{24}\left(-3\right)^{24}x^{49}+^{25}C_{25}\left(-3\right)^{25}x^{50}$$

The degree of the polynomial (n) = highest power of $$x$$ = 50

Hence, the correct answer is Option C

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