The number of real roots of the equation $\log_{e} x + ex = 0$ is
- A$0$
- B$1$
- C$2$
- D$3$
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View SolutionMatch the functions in Column $I$ with their properties in Column $II$. In the following $[x]$ denotes the greatest integer less than or equal to $x$.
Column $I$ Column $II$ $A$. $x|x|$ $I$. Strictly increasing and continuous in $(-1,1)$ $B$. $\sqrt{|x|}$ $II$. Continuous but not differentiable in $(-1,1)$ $C$. $x+[x]$ $III$. Differentiable in $(-1,1)$ $D$. $|x-1|+|x+1|+|x|$ $IV$. Differentiable in $(-1,0) \cup (0,1)$ $V$. Strictly increasing and not differentiable in $(-1,1)$
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| Column $I$ | Column $II$ |
| $A$. $x|x|$ | $I$. Strictly increasing and continuous in $(-1,1)$ |
| $B$. $\sqrt{|x|}$ | $II$. Continuous but not differentiable in $(-1,1)$ |
| $C$. $x+[x]$ | $III$. Differentiable in $(-1,1)$ |
| $D$. $|x-1|+|x+1|+|x|$ | $IV$. Differentiable in $(-1,0) \cup (0,1)$ |
| $V$. Strictly increasing and not differentiable in $(-1,1)$ |
The correct match is
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