In the expanded form of $(- 2 x + 5 y - 3 z)^{2}$ , coefficient of $x y$ is

- 10

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10

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- 20

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20

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Solution

The correct option is C $- 20$
$(- 2 x + 5 y - 3 z)^{2}$

$= (- 2 x)^{2} + (5 y)^{2} + (- 3 z)^{2} + 2 (- 2 x) (5 y) + 2 (5 y) (- 3 z) + 2 (- 2 x) (- 3 z)$

......... Using $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 a c + 2 b c$

$= 4 x^{2} + 25 y^{2} + 9 z^{2} - 20 x y - 30 y z + 12 z x$

Hence, coefficient of $x y$ is $- 20$ .

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