1
JEE Main 2024 (Online) 9th April Evening Shift
MCQ (Single Correct Answer)
+4
-1

Let $$\alpha, \beta ; \alpha>\beta$$, be the roots of the equation $$x^2-\sqrt{2} x-\sqrt{3}=0$$. Let $$\mathrm{P}_n=\alpha^n-\beta^n, n \in \mathrm{N}$$. Then $$(11 \sqrt{3}-10 \sqrt{2}) \mathrm{P}_{10}+(11 \sqrt{2}+10) \mathrm{P}_{11}-11 \mathrm{P}_{12}$$ is equal to

A
$$10 \sqrt{3} \mathrm{P}_9$$
B
$$11 \sqrt{3} \mathrm{P}_9$$
C
$$11 \sqrt{2} \mathrm{P}_9$$
D
$$10 \sqrt{2} \mathrm{P}_9$$
2
JEE Main 2024 (Online) 9th April Morning Shift
MCQ (Single Correct Answer)
+4
-1

Let $$\alpha, \beta$$ be the roots of the equation $$x^2+2 \sqrt{2} x-1=0$$. The quadratic equation, whose roots are $$\alpha^4+\beta^4$$ and $$\frac{1}{10}(\alpha^6+\beta^6)$$, is:

A
$$x^2-180 x+9506=0$$
B
$$x^2-195 x+9506=0$$
C
$$x^2-190 x+9466=0$$
D
$$x^2-195 x+9466=0$$
3
JEE Main 2024 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+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
$$\log _8(4)$$
4
JEE Main 2024 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+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
$$1 / 2$$
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