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1
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-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 $\beta+\gamma: k+\alpha=$

A

$4: 3$

B

$2: 1$

C

$6: 5$

D

$3: 4$

2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-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
A
$\left(-\infty,-\frac{2}{3}\right] \cup[3, \infty)$
B
$\left(-2,-\frac{2}{3}\right) \cup\left(\frac{3}{2}, 3\right)$
C
$(-\infty,-2) \cup\left(\frac{3}{2}, \infty\right)$
D
$\left[-\frac{2}{3}, \frac{3}{2}\right)$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-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
A
$\left(-\frac{13}{7}, 1\right)$
B
$\left(-1, \frac{13}{7}\right)$
C
$\left(-\infty,-\frac{13}{7}\right) \cup(1, \infty)$
D
$(-\infty,-1) \cup\left(\frac{13}{7}, \infty\right)$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The cubic equation whose roots are the square of the roots of the equation is

$$ 12 x^3-20 x^2+x+3=0 $$

A
$x^3+376 x^2-121 x-9=0$
B
$144 x^3-400 x^2+121 x+98=0$
C
$144 x^3-376 x^2+121 x-9=0$
D
$x^3+400 x^2-121 x-98=0$
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