1) Let [X] be the greatest integer less than or equals to x. Then , at which of the following points(s) the function $f(x)=x\cos(\pi(x+[x]))$ discontinous? A) x=-1 B) x=1 C) x=0 D) x=2 Answer: Option A,B,DExplanation:$f(x)=x\cos(\pi(x+[x]))$ At x=0 $\lim_{x \rightarrow 0}f(x)=\lim_{x \rightarrow 0}x\cos(\pi(x+[x])=0$ and f(x)=0 It is continous at x=0 and clearing discontinous at other integer points
