Question
If a + b + c = 0, then a × b =
- c × a
- b × c
- 0
- Both (a) and (b)
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
{where $x,y \in R^+, x^2y + x \ne 0$ }
$f(x)=\left(p^2-6 p+8\right)\left(\sin ^2 2 x-\cos ^2 2 x\right)+2(2-p) x+7$ does not have any critical point, be the interval $(a, b)$. Then $16 a b$ is equal to ..........
Match the conditions / expressions in Column $I$ with statements in Column $II$ and indicate your answers by darkening the appropriate bubbles in $4 \times 4$ matrix given in the $ORS$.
| Column $I$ | Column $II$ |
| $(A)$ If $-1 < x < 1$, then $f$ ( $x$ ) satisfies | $(p)$ $ 0 < $ f (x) $ < 1$ |
| $(B)$ If $1 < x < 2$, then $f(x)$ satisfies | $(q)$ $\mathrm{f}(\mathrm{x}) < 0$ |
| $(C)$ If $3 < x < 5$, then $f(x)$ satisfies | $(r)$ $ \mathrm{f}(\mathrm{x}) > 0$ |
| $(D)$ If $x > 5$, then $f(x)$ satisfies | $(s)$ $ f (\mathrm{x}) < 1$ |
| X: | -4 | -3 | -2 | -1 | 0 |
| P(X): | 0.1 | 0.2 | 0.3 | 0.2 | 0.2 |
The value of E(X) is: