A) \[f(x)\]is continuous at \[x=0\]
B) \[f(x)\]is discontinuous at \[x=0\], when \[a\ne \pm 1\]
C) \[\underset{x\to 1}{\mathop{\lim }}\,(1-x+[x-1]+[1-x])\] is continuous at \[x=a\]
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,f(x)=\frac{{{\sin }^{2}}ax}{{{(ax)}^{2}}}{{a}^{2}}={{a}^{2}}\] and \[f(0)=1.\] Hence \[f(x)\] is discontinuous at \[x=0\], when \[a\ne 0\].
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