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If $\;\lim_{x\to2} \large\frac{tan(x-2) \{ x^{2}+(k-2)x-2k\}}{x^{2}-4x+4}=5\;$ ,then k is equal to :

$(a)\;0\qquad(b)\;1\qquad(c)\;2\qquad(d)\;3$

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