The complete solution of the inequation ${x^2} - 4x < 12\,{\rm{ is}}$

  • A

    $x < - \,2$ or $x > 6$

  • B

    $ - \,6 < x < 2$

  • C

    $2 < x < 6$

  • D

    $ - \,2 < x < 6$

Similar Questions

Let $\mathrm{S}=\left\{x \in R:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\right\}$. Then the number of elements in $\mathrm{S}$ is :

  • [JEE MAIN 2024]

The number of roots of the equation $\log ( - 2x)$ $ = 2\log (x + 1)$ are

Consider the following two statements

$I$. Any pair of consistent liner equations in two variables must have a unique solution.

$II$. There do not exist two consecutive integers, the sum of whose squares is $365$.Then,

  • [KVPY 2018]

Let $\alpha$ and $\beta$ be the two disinct roots of the equation $x^3 + 3x^2 -1 = 0.$ The equation which has $(\alpha \beta )$ as its root is equal to

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]