1
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The number of solutions of the equation $\sqrt{3 x^2+x+5}=x-3$ is

A

2

B

1

C

0

D

4

2
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The set of all real values of $x$ for which $\frac{x^2-1}{(x-4)(x-3)} \geq 1$ is

A

$[-1,1] \cup(3,4)$

B

$\left[\frac{13}{7}, 3\right) \cup(4, \infty)$

C

$\left(-\infty, \frac{13}{7}\right] \cup(3,4)$

D

$R-[3,4]$

3
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $2 x^3+3 x^2-5 x-7=0$, then $\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\gamma^2}=$
A

$-\frac{17}{49}$

B

$-\frac{23}{49}$

C

$\frac{55}{49}$

D

$\frac{67}{49}$

4
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Two roots of the equation, $a x^4+b x^3+c x^2+d x+e=0$ are positive and equal. If the product of the other two real roots is 1 , then

A

$b e^2=a^2 d$

B

$3 e+\frac{2 b \sqrt{e}}{\sqrt{a}}+c=a$

C

$e+2 b \sqrt{e}+3 c=a \sqrt{a}$

D

$b^2 e=a d^2$