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Let \left [ t \right ] denote the greatest integer \leq t and \lim_{x\rightarrow 0}x\left [ \frac{4}{x} \right ]=A. Then the function, f\left ( x \right )=\left [ x^{2} \right ]\sin \left ( \pi x \right ) is discontinuous, when x is equal to: 
Option: 1 \sqrt{A+1}
 
Option: 2 \sqrt{A}
 
Option: 3 \sqrt{A+5}
 
Option: 4 \sqrt{A+21}
 
 

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\\\lim _{x \rightarrow 0} x\left(\frac{4}{x}-\left\{\frac{4}{x}\right\}\right)=A \quad \Rightarrow \lim _{x \rightarrow 0} 4-x\left\{\frac{4}{x}\right\}=A\\\Rightarrow 4-0=A

\\\text { (1) } x=\sqrt{A+1} \Rightarrow x=\sqrt{5} \Rightarrow \text { discontinuous }\\\text { (2) } x=\sqrt{A+21} \Rightarrow x=5 \Rightarrow \text { continuous }\\\text { (3) } x=\sqrt{A} \Rightarrow x=2 \Rightarrow \text { continuous }\\\text { (4) } x=\sqrt{A+5} \Rightarrow x=3 \Rightarrow \text { continuous }

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