1
VITEEE 2025
MCQ (Single Correct Answer)
+4
-1

If $\alpha$ and $\beta$ are the roots of equation $x^2+p x+2=0$ and $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ are roots of equation $2 x^2+2 q x+1=0$, then $\left(\alpha-\frac{1}{\alpha}\right)\left(\beta-\frac{1}{\beta}\right)\left(\alpha+\frac{1}{\beta}\right)\left(\beta+\frac{1}{\alpha}\right)$ is equal to

A

$\frac{9}{4}\left(9+p^2\right)$

B

$\frac{9}{4}\left(9-q^2\right)$

C

$\frac{9}{4}\left(9-p^2\right)$

D

$\frac{9}{4}\left(9+q^2\right)$

2
VITEEE 2024
MCQ (Single Correct Answer)
+4
-1

Given, $\frac{x^2+y^2}{x^2-y^2}+\frac{x^2-y^2}{x^2+y^2}=k$, then $\frac{x^8+y^8}{x^8-y^8}$ is equal to

A
$\frac{k^2+1}{k^2-1}$
B
$\frac{k^2+4}{k^2-4}$
C
$\frac{k^2+4}{4 k}$
D
$\frac{k^2+8}{8 k}$

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