1
JEE Main 2024 (Online) 31st January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
2
JEE Main 2024 (Online) 27th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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

A
$$2 S_{12}=S_{11}+S_{10}$$
B
$$S_{12}=S_{11}+S_{10}$$
C
$$S_{11}=S_{10}+S_{12}$$
D
$$2 S_{11}=S_{12}+S_{10}$$
3
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The number of real roots of the equation $x|x|-5|x+2|+6=0$, is :
A
4
B
3
C
5
D
6
4
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\alpha, \beta$$ be the roots of the equation $$x^{2}-\sqrt{2} x+2=0$$. Then $$\alpha^{14}+\beta^{14}$$ is equal to

A
$$-64$$
B
$$-64 \sqrt{2}$$
C
$$-128 \sqrt{2}$$
D
$$-128$$
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