Which graph represents the relationship between angular momentum $L$ and angular velocity $\omega$ for a rigid body rotating about a fixed axis?

The position vector of a particle of mass $m$ moving with a constant velocity $\vec{v} = v \hat{i}$ is given by $\vec{r} = x(t) \hat{i} + b \hat{j}$, where $b$ is a constant. At an instant, $\vec{r}$ makes an angle $\theta$ with the $x$-axis. The variation of the magnitude of the angular momentum $|\vec{L}|$ of the particle about the origin with $\theta$ will be:

$A$ particle with position vector $\overrightarrow{r}$ has a linear momentum $\overrightarrow{p}$. Which one of the following statements is true in respect of its angular momentum $\overrightarrow{L}$ about the origin?

$A$ particle of mass $m$ is moving with constant velocity $v$ parallel to the $x$-axis as shown in the figure. Its angular momentum about origin $O$ is ..........

$A$ particle of mass $m = 5$ is moving with a uniform speed $v = 3\sqrt{2}$ in the $XOY$ plane along the line $Y = X + 4$. The magnitude of the angular momentum of the particle about the origin is .......

$A$ particle of mass $m$ moves with a constant velocity $\vec{v}$ in the $X-Y$ plane. Its angular momentum with respect to the origin is: