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JEE Main & Advanced JEE Main Paper (Held On 25 April 2013)

  • question_answer
                    Consider the function                 \[f(x)=[x]+\left| 1-x \right|,-1\le x\le 3\]where\[\left[ x \right]\]is the greatest integer function.                 Statement I: \[f\]in not continuous at \[x=0,\]1,2 and 3.                 Statement II: \[f(x)\left( \begin{matrix}    -x, & -1\le x<0  \\    1-x, & 0\le x<1  \\    1+x, & 1\le x<2  \\    2+x, & 2\le x\le 3  \\ \end{matrix} \right.\]

    A)                 Statement I is true; Statement II is false.

    B)       

    C)                                        Statement I is true: Statement II is true; Statement II is a correct explanation for Statement I.

    D)                                        Statement I is false; Statement ii is true.

    Correct Answer: B

    Solution :

                    Let\[f(x)=[x]+|1-x|,-1\le x\le 3\]where [x] = greatest integer function. f is not continuous at x = 0,1,2,3 But in statement-2 f(x) is continuous at x = 3. Hence, statement-1 is true and 2 is false.                           Statement I is true; Statement II is true; Statement II in not correct explanation for Statement I.


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