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UPSC CDS I 2025 Mathematics Paper

Question Numbers: 61-62

A hall is of length l, breadth b and height h. The maximum distance between any two points (say P and Q) inside the hall is 14 m, whereas the maximum distance between two points (say P and R) on the floor is 6√5 m.

Question : 61 of 100

Marks: +1, -0

What is

h

equal to?

3·5 m
4 m
4·5 m
5 m

Validate

Solution:

Concept:

In a rectangular hall, the space diagonal connects opposite corners through the interior, while the floor diagonal lies on the floor. Both are found using the Pythagorean theorem.

Explanation:

Let length =

l

, breadth =

b

, height =

h

Space diagonal:

\sqrt{l^2 + b^2 + h^2} = 14

Floor diagonal:

\sqrt{l^2 + b^2} = 6\sqrt{5}

Square both equations:

l^2 + b^2 + h^2 = 196

and

l^2 + b^2 = 180

Subtract to get

h^2 = 196 - 180 = 16

Take square root:

h = \sqrt{16} = 4

Answer:

h = 4

m, Option B

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