JEE Main 2024 (Online) 1st February Morning Shift | Quadratic Equation and Inequalities Question 12 | Mathematics

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 :

$$\infty$$

JEE Main 2024 (Online) 27th January Evening Shift

MCQ (Single Correct Answer)

-1

If $$\alpha, \beta$$ are the roots of the equation, $$x^2-x-1=0$$ and $$S_n=2023 \alpha^n+2024 \beta^n$$, then :

$$2 S_{12}=S_{11}+S_{10}$$

$$S_{12}=S_{11}+S_{10}$$

$$S_{11}=S_{10}+S_{12}$$

$$2 S_{11}=S_{12}+S_{10}$$

JEE Main 2023 (Online) 15th April Morning Shift

MCQ (Single Correct Answer)

-1

The number of real roots of the equation $x|x|-5|x+2|+6=0$, is :

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