1
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\alpha$ is a root of the equation $\frac{x-1}{\sqrt{2 x^2-5 x+2}}=\frac{41}{60}$. If $-\frac{1}{2}<\alpha<0$, then $\alpha$ is equal to
A
$-\frac{5}{31}$
B
$-\frac{7}{34}$
C
$-\frac{9}{37}$
D
$-\frac{11}{41}$
2
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$\alpha, \beta, \gamma, 2$ and $\varepsilon$ are the roots of the equation

$$ \begin{aligned} & \alpha, \beta, \gamma+4 x^4-13 x^3-52 x^2+36 x+144=0 . \text { If } \\ & \alpha<\beta<\gamma<2<\varepsilon \text {, then } \alpha+2 \beta+3 \gamma+5 \varepsilon= \end{aligned} $$

A
-1
B
66
C
-36
D
48
3
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the quadratic equation $3 x^2+(2 k+1) x-5 k=0$ has real and equal roots, then the value of $k$ such that

$\frac{1}{2}$ < $k$ < 0 is

A
$\frac{-16+\sqrt{255}}{2}$
B
$\frac{-16-\sqrt{255}}{2}$
C
$-\frac{2}{3}$
D
$-\frac{3}{5}$
4
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The equations $2 x^2+a x-2=0$ and $x^2+x+2 a=0$ have exactly one common root. If $a \neq 0$, then one of the roots of the equation $a x^2-4 x-2 a=0$ is
A
2
B
-2
C
$\frac{-4+\sqrt{22}}{3}$
D
$\frac{-2+\sqrt{22}}{3}$
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