Let $S$ be the set of all real roots of the equation, $3^{x}\left(3^{x}-1\right)+2=\left|3^{x}-1\right|+\left|3^{x}-2\right| .$ Then $\mathrm{S}$

  • [JEE MAIN 2020]
  • A

    is an empty set.

  • B

    contains at least four elements.

  • C

    contains exactly two elements

  • D

    is a singleton

Similar Questions

If $\alpha, \beta$ are roots of the equation $x^{2}+5 \sqrt{2} x+10=0, \alpha\,>\,\beta$ and $P_{n}=\alpha^{n}-\beta^{n}$ for each positive integer $\mathrm{n}$, then the value of $\left(\frac{P_{17} P_{20}+5 \sqrt{2} P_{11} P_{19}}{P_{18} P_{19}+5 \sqrt{2} P_{18}^{2}}\right)$ is equal to $....$

  • [JEE MAIN 2021]

If $|{x^2} - x - 6| = x + 2$, then the values of $x$ are

The smallest value of ${x^2} - 3x + 3$ in the interval $( - 3,\,3/2)$ is

The sum of the solutions of the equation $\left| {\sqrt x  - 2} \right| + \sqrt x \left( {\sqrt x  - 4} \right) + 2 = 0\left( {x > 0} \right)$ is equal to

  • [JEE MAIN 2019]

If ${x^2} + 2ax + 10 - 3a > 0$ for all $x \in R$, then

  • [IIT 2004]