1
If $f(x)$ is a quadratic function such that $f(x) f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)$, then $\sqrt{f\left(\frac{2}{3}\right)+f\left(\frac{3}{2}\right)}=$
TG EAPCET 2024 (Online) 11th May Morning Shift
2
If $\alpha$ is a root of the equation $x^{2}-x+1=0$, then $\left(\alpha+\frac{1}{\alpha}\right)^{3}+\left(\alpha^{2}+\frac{1}{\alpha^{2}}\right)^{3}+\left(\alpha^{3}+\frac{1}{\alpha^{3}}\right)^{3}+\left(\alpha^{4}+\frac{1}{\alpha^{4}}\right)^{3}=$
TG EAPCET 2024 (Online) 11th May Morning Shift
3
$\alpha, \beta$ are the real roots of the equation $x^{2}+a x+b=0$. If $\alpha+\beta=\frac{1}{2}$ and $\alpha^{3}+\beta^{3}=\frac{37}{8}$, then $a-\frac{1}{b}=$
TG EAPCET 2024 (Online) 11th May Morning Shift
4
If $\alpha, \beta, \gamma$ are the roots of the equation $4 x^{3}-3 x^{2}+2 x-1=0$, then $\alpha^{3}+\beta^{3}+\gamma^{3}=$
TG EAPCET 2024 (Online) 11th May Morning Shift
5
The equation $16 x^{4}+16 x^{3}-4 x-1=0$ has a multiple root. If $\alpha, \beta, \gamma, \delta$ are the roots of this equation, then $\frac{1}{\alpha^{4}}+\frac{1}{\beta^{4}}+\frac{1}{\gamma^{4}}+\frac{1}{\delta^{4}}=$
TG EAPCET 2024 (Online) 11th May Morning Shift
6
The solution set of the equation $3^{x}+3^{1-x}-4 < 0$ contained in $R$ is
TG EAPCET 2024 (Online) 10th May Evening Shift
7
The common solution set of the inequations $x^{2}-4 x \leq 12$ and $x^{2}-2 x \geq 15$ taken together is
TG EAPCET 2024 (Online) 10th May Evening Shift
9
If $\alpha, \beta$ are the roots of the equation $x+\frac{4}{x}=2 \sqrt{3}$, then $\frac{2}{\sqrt{3}}\left|\alpha^{2024}-\beta^{2024}\right|=$
TG EAPCET 2024 (Online) 10th May Morning Shift
10
$\alpha, \beta$ are the real roots of the equation $12 x^{\frac{1}{3}}-25 x^{\frac{1}{6}}+12=0$. If $\alpha>\beta$, then $6 \sqrt{\frac{\alpha}{\beta}}=$
TG EAPCET 2024 (Online) 10th May Morning Shift
11
$\alpha, \beta$ 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 $k=$
TG EAPCET 2024 (Online) 10th May Morning Shift
12
$\alpha, \beta$ and $\gamma$ are the roots of the equation $8 x^3-42 x^2+63 x-27=0$. If $\beta<\gamma<\alpha$ and $\beta, \gamma$ and $\alpha$ are in geometric progression, then the extreme value of the expression $\gamma x^2+4 \beta x+\alpha$ is
TG EAPCET 2024 (Online) 10th May Morning Shift
13
If $\frac{2 x^3+1}{2 x^2-x-6}=a x+b+\frac{A}{P x-2}+\frac{B}{2 x+q}$, then 51 apB $=$
TG EAPCET 2024 (Online) 10th May Morning Shift
14
$\alpha$ 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
TG EAPCET 2024 (Online) 9th May Evening Shift
17
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
TG EAPCET 2024 (Online) 9th May Morning Shift
18
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $2 x^3-3 x^2+5 x-7=0$, then $\sum \alpha^2 \beta^2=$
TG EAPCET 2024 (Online) 9th May Morning Shift
19
The sum of two roots of the equation $x^4-x^3-16 x^2+4 x+48=0$ is zero. If $\alpha, \beta, \gamma$ and $\delta$ are the roots of this equation, then $\alpha^4+\beta^4+\gamma^4+\delta^4=$
TG EAPCET 2024 (Online) 9th May Morning Shift
21
The quadratic equations $x^2-6 x+a=0$ and $x^2-c x+6=0$ have one root in common. If the other roots of the first and second equations are integers and are in the ratio $4: 3$, then their common root is
TS EAMCET 2023 (Online) 12th May Evening Shift
24
If one root of the equation $4 x^2-2 x+k-4=0$ is the reciprocal of the other, then the value of $k$ is
TS EAMCET 2023 (Online) 12th May Morning Shift
25
Two numbers $b$ and $c$ are chosen at random in succession without replacement from the set $\{1,2,3, \ldots \ldots, 9\}$. Then, the probability that $x^2+b x+c>0, \forall x \in R$ i
TS EAMCET 2023 (Online) 12th May Morning Shift
26
If $(x-2)$ is a common factor of the expressions $x^2+a x+b$ and $x^2+c x+d$, then $\frac{b-d}{c-a}=$
TS EAMCET 2023 (Online) 12th May Morning Shift
27
The sum of the roots of the equation $e^{4 t}-10 e^{3 t}+29 e^{2 t}-20 e^t+4=0$ is
TS EAMCET 2023 (Online) 12th May Morning Shift