The number of real roots of the equation $\log_{e} x + ex = 0$ is
- A$0$
- B$1$
- C$2$
- D$3$
Explore More
Similar Questions
If $f(x) = \begin{cases} \int_{0}^{x} (5 + |1-t|) \, dt, & x > 2 \\ 5x + 1, & x \leq 2 \end{cases}$,then:
DifficultJEE MAIN 2021
View SolutionUsing the fact that $\sin (A+B)=\sin A \cos B+\cos A \sin B$ and the differentiation,obtain the sum formula for cosines.
Difficult
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 $(-1,1)$
The correct match is
| 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
DifficultAP EAMCET 2025
View SolutionIf $f$ is defined by $f(x) = \begin{cases} x & \text{for } 0 \leq x < 1 \\ 2-x & \text{for } x \geq 1 \end{cases}$,then at $x=1$,$f(x)$ is
Let $f(x)$ be a quadratic expression which is positive for all real $x$. If $g(x) = f(x) + f'(x) + f''(x)$,then for any real $x$,which one is correct?
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo