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

Given that \( \vec{a} = 2\hat{i} - \lambda \hat{j} + 5\hat{k} \), \( \vec{b} = \mu \hat{i} + 7\hat{j} + 3\hat{k} \), and the midpoint of \( \overrightarrow{AB} = 3\hat{i} + 2\hat{j} + 4\hat{k} \), find \( \lambda + \mu \).

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: