AP EAPCET 2025 - 21st May Morning Shift | Quadratic Equations Question 37 | Mathematics

All the values of $k$ such that the quadratic expression $2 k x^2-(4 k+1) x+2$ is negative for exactly three integrals values of $x$, lie in the interval

$\left[\frac{1}{12}, \frac{1}{10}\right)$

$\left(\frac{1}{6}, \frac{1}{5}\right)$

$[-1,2)$

$[2,6)$

AP EAPCET 2025 - 21st May Morning Shift

MCQ (Single Correct Answer)

-0

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3-13 x^2+k x+189=0$ such that $\beta-\gamma=2$, then $\beta+\gamma: k+\alpha=$

$4: 3$

$2: 1$

$6: 5$

$3: 4$

AP EAPCET 2024 - 23th May Morning Shift

MCQ (Single Correct Answer)

-0

The set of all real values of $x$ satisfying the inequality $\frac{7 x^2-5 x-18}{2 x^2+x-6}<2$ is

$\left(-\infty,-\frac{2}{3}\right] \cup[3, \infty)$

$\left(-2,-\frac{2}{3}\right) \cup\left(\frac{3}{2}, 3\right)$

$(-\infty,-2) \cup\left(\frac{3}{2}, \infty\right)$

$\left[-\frac{2}{3}, \frac{3}{2}\right)$

AP EAPCET 2024 - 23th May Morning Shift

MCQ (Single Correct Answer)

-0

The set of all values of $k$ for which the inequality $x^2-(3 k+1) x+4 k^2+3 k-3>0$ is true for all real values of $x$, is

$\left(-\frac{13}{7}, 1\right)$

$\left(-1, \frac{13}{7}\right)$

$\left(-\infty,-\frac{13}{7}\right) \cup(1, \infty)$

$(-\infty,-1) \cup\left(\frac{13}{7}, \infty\right)$

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