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Question

The number of integral value(s) of $$x$$ satisfying the equation $$\left | x^{4}\cdot3^{\left | x-2 \right |}\cdot5^{x-1} \right |=-x^{4}\cdot3^{\left | x-2 \right |}\cdot5^{x-1}$$, is


A
2
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B
3
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C
1
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D
infinite
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Solution

The correct option is C $$1$$
The two sides of the equation are always of opposite signs.
The left hand side is under modulus and is therefore always positive.
$$x^4$$, $$3^{|x-2|}$$ and $$5^{|x-1|}$$ are always positive. 
Therefore, the right hand side is always negative.
Hence, the only possible solution is when $$x=0$$

Maths

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