1
JEE Main 2024 (Online) 8th April Morning Shift
+4
-1

The sum of all the solutions of the equation $$(8)^{2 x}-16 \cdot(8)^x+48=0$$ is :

A
$$1+\log _8(6)$$
B
$$1+\log _6(8)$$
C
$$\log _8(6)$$
D
$$\log _8(4)$$
2
JEE Main 2024 (Online) 6th April Morning Shift
+4
-1

Let $$\alpha, \beta$$ be the distinct roots of the equation $$x^2-\left(t^2-5 t+6\right) x+1=0, t \in \mathbb{R}$$ and $$a_n=\alpha^n+\beta^n$$. Then the minimum value of $$\frac{a_{2023}+a_{2025}}{a_{2024}}$$ is

A
$$-1 / 2$$
B
$$-1 / 4$$
C
$$1 / 4$$
D
$$1 / 2$$
3
JEE Main 2024 (Online) 5th April Evening Shift
+4
-1

The coefficients $$\mathrm{a}, \mathrm{b}, \mathrm{c}$$ in the quadratic equation $$\mathrm{a} x^2+\mathrm{bx}+\mathrm{c}=0$$ are from the set $$\{1,2,3,4,5,6\}$$. If the probability of this equation having one real root bigger than the other is p, then 216p equals :

A
38
B
76
C
57
D
19
4
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
$$x^2+10 x+16=0$$
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