If $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}},-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ are the position vectors of four points $A, B, C, D$ respectively, then the shortest distance between the lines $A B$ and $C D$ is

The mean and variance of the observations $x_1, x_2, x_3 \ldots x_{15}$ are respectively 2 and 4 . If the mean and variance of the observations $y_1, y_2 \ldots, y_{10}$ are respectively 2 and 5 , then the variance of the observations $x_1, x_2 \ldots, x_{15}, y_1, y_2 \ldots, y_{10}$ is

Three letters are chosen at random from the letters of the word VARIABLE and all possible three letter words (with or without meaning) are formed with them.

Then, the probability of getting a three letter word having a consonent as its middle letter is