1
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

With respect to the roots of the equation $3 x^{3}+b x^{2}+b x+3=0$, match the items of List I with those fo List II

List I List II
A All the roots are negative. I. $(b-3)^2=36+P^2$ for $P \in R$
B Two roots are complex. II. $-3<b<9$
C Two roots are positive. III. $b \in(-\infty,-3) \cup(9, \infty)$
D All roots are real and IV. $b=9$
V. $b=-3$
A
A - V, B - III, C - I, D- II
B
A - IV, B - I, C - II, D- III
C
A - V, B - II, C - III, D-I
D
A - IV, B - II, C - V, D- III
2
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\alpha, \beta$ are the roots of the equation $x+\frac{4}{x}=2 \sqrt{3}$, then $\frac{2}{\sqrt{3}}\left|\alpha^{2024}-\beta^{2024}\right|=$
A
$2^{2024}$
B
$2^{2025}$
C
$2^{2023}$
D
$2^{1012}$
3
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\alpha, \beta$ are the real roots of the equation $12 x^{\frac{1}{3}}-25 x^{\frac{1}{6}}+12=0$. If $\alpha>\beta$, then $6 \sqrt{\frac{\alpha}{\beta}}=$
A
$\frac{3}{2}$
B
$\frac{4}{3}$
C
$\frac{9}{8}$
D
$\frac{16}{9}$
4
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+3 x^2-10 x-24=0$. If $\alpha>\beta>\gamma$ and $\alpha^3+3 \beta^2-10 \gamma-24=11 k$, then $k=$
A
1
B
11
C
5
D
55
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