List of top Mathematics Questions on distance between two points asked in KEAM

Let $P(2, 1, -3)$ be a given point. If the point $Q$ is such that $\vec{PQ} = 3\hat{i} - \hat{j} + 5\hat{k}$, then the distance of $Q$ from the origin $O$ is

If \( \sum_{i=1}^{9} (x_i - 5) = 9 \) and \( \sum_{i=1}^{9} (x_i - 5)^2 = 45 \), then the standard deviation of the 9 items \( x_1, x_2, \ldots, x_9 \) is:

If \( \sum_{i=1}^{9} (x_i - 5) = 9 \) and \( \sum_{i=1}^{9} (x_i - 5)^2 = 45 \), then the standard deviation of the 9 items \( x_1, x_2, \ldots, x_9 \) is:

If \( \sum_{i=1}^{9} (x_i - 5) = 9 \) and \( \sum_{i=1}^{9} (x_i - 5)^2 = 45 \), then the standard deviation of the 9 items \( x_1, x_2, \ldots, x_9 \) is: