In the $(x, y, z)$ coordinate system, three point-charges $Q$, $Q$, and $\alpha Q$ are located in free space at $(-1, 0, 0)$, $(1, 0, 0)$, and $(0, -1, 0)$, respectively. The value of $\alpha$ for the electric field to be zero at $(0, 0.5, 0)$ is _________________ (rounded off to 1 decimal place).

The given equation represents a magnetic field strength $\bar{H}(r, \theta, \phi)$ in the spherical coordinate system, in free space. Here, $\hat{r}$ and $\hat{\theta}$ represent the unit vectors along $r$ and $\theta$, respectively. The value of $P$ in the equation should be _________________ (rounded off to the nearest integer).

$$\bar{H}(r, \theta, \phi) = \frac{1}{r^3} ( \hat{r} P \cos \theta + \hat{\theta} P \sin \theta)$$

Which one of the following matrices has an inverse?

Let $X$ be a discrete random variable that is uniformly distributed over the set {$-10, -9, \cdots, 0, \cdots, 9, 10$}. Which of the following random variables is/are uniformly distributed?