UPSC NDA I 2015 Mathematics Paper

Concept:The diagonal of a cuboid is calculated using the 3D distance formula: for a cuboid with edges $a$, $b$, $c$, the space diagonal length is $\sqrt{a^{2}+b^{2}+c^{2}}$.Explanation:Take the cuboid with one vertex at the origin $O=(0,0,0)$ and the opposite vertex at $P=(1,2,3)$.Thus, the edge lengths along the $x$, $y$, $z$ axes are $1$, $2$, and $3$ units respectively.The diagonal $OP$ connects these two opposite corners.Apply the distance formula: $OP = \sqrt{(1-0)^{2} + (2-0)^{2} + (3-0)^{2}}$.This simplifies to $\sqrt{1^{2} + 2^{2} + 3^{2}} = \sqrt{1+4+9} = \sqrt{14}$.Therefore, the length of the diagonal is $\sqrt{14}$ units.Answer:$\sqrt{14}$ units (Option B).