1
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

The number of positive real roots of the equation $$3^{x+1}+3^{-x+1}=10$$ is

A
3
B
2
C
1
D
Infinitely many
2
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

The number of real roots of the equation $$\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}=\frac{13}{6}$$ is

A
1
B
2
C
3
D
4
3
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$x^2+x+1=0$$, then the equation whose roots are $$\alpha^{2021}, \beta^{2021}$$ is given by

A
$$x^2-x+1=0$$
B
$$x^2+x-1=0$$
C
$$x^2-x-1=0$$
D
$$x^2+x+1=0$$
4
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

If $$2, 1$$ and $$1$$ are roots of the equation $$x^3-4 x^2+5 x-2=0$$, then the roots of $$\left(x+\frac{1}{3}\right)^3-4\left(x+\frac{1}{3}\right)^2+5\left(x+\frac{1}{3}\right)-2=0$$

A
$$\frac{7}{3}, \frac{4}{3}, \frac{4}{3}$$
B
$$\frac{5}{3}, \frac{2}{3}, \frac{2}{3}$$
C
$$\frac{-5}{3}, \frac{-2}{3}, \frac{-2}{3}$$
D
$$\frac{-7}{3}, \frac{-4}{3}, \frac{-4}{3}$$
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