1
JEE Main 2024 (Online) 4th April Morning Shift
+4
-1

If 2 and 6 are the roots of the equation $$a x^2+b x+1=0$$, then the quadratic equation, whose roots are $$\frac{1}{2 a+b}$$ and $$\frac{1}{6 a+b}$$, is :

A
$$x^2+8 x+12=0$$
B
$$2 x^2+11 x+12=0$$
C
$$4 x^2+14 x+12=0$$
D
$$x^2+10 x+16=0$$
2
JEE Main 2024 (Online) 1st February Evening Shift
+4
-1
Let $\alpha$ and $\beta$ be the roots of the equation $p x^2+q x-r=0$, where $p \neq 0$. If $p, q$ and $r$ be the consecutive terms of a non constant G.P. and $\frac{1}{\alpha}+\frac{1}{\beta}=\frac{3}{4}$, then the value of $(\alpha-\beta)^2$ is :
A
8
B
9
C
$\frac{20}{3}$
D
$\frac{80}{9}$
3
JEE Main 2024 (Online) 1st February Morning Shift
+4
-1
Let $\mathbf{S}=\left\{x \in \mathbf{R}:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\right\}$. Then the number of elements in $\mathrm{S}$ is :
A
4
B
0
C
2
D
1
4
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

Let $$\mathrm{S}$$ be the set of positive integral values of $$a$$ for which $$\frac{a x^2+2(a+1) x+9 a+4}{x^2-8 x+32} < 0, \forall x \in \mathbb{R}$$. Then, the number of elements in $$\mathrm{S}$$ is :

A
0
B
$$\infty$$
C
3
D
1
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