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1
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

$\frac{67}{49}$

2
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

$b^2 e=a d^2$

3
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
Let $(a-3) x^2+12 x+(a+6)>0, \forall x \in R$ and $a \in(\ell, \infty)$. If $a$ is the least positive integral value of $a$, then the roots of $(\alpha-3) x^2+12 x+(\ell+2)=0$ are
A

1,2

B

2,3

C

$-1,-2$

D

$-2,-3$

4
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If the roots of the equation $x^2+2 a x+b=0$ are real, distinct and differ atmost by 2 m , then $b$ lies in the interval

A

$\left(a^2, a^2+m^2\right)$

B

$\left(a^2+m^2, a^2\right)$

C

$\left[a^2, a^2+2 m^2\right]$

D

$\left[a^2-m^2, a^2\right)$

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