PYQ Vault

Longest rod in a room = space diagonal root(l^2 + b^2 + h^2)

This type of question, asked 4 times: CDS 2 2021, CDS 2 2022, CDS 1 2025, CDS 2 2026. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2021

    66
    The length and breadth of a room are 21 m and 16 m respectively. If the length of the longest rod that can be placed in the room is 29 m, then what is the height of the room ?

    Tap an option to check your answer.

  2. Question 2

    CDS 2 2022

    70
    The length of a room is 2116\frac{21}{16} times its breadth and breadth is 43\frac{4}{3} times its height. If H is the height of the room and L is the longest rod that can be placed in the room, then which one of the following is correct ?

    Tap an option to check your answer.

  3. Question 3 (case study, 2 parts)

    CDS 1 2025

    A hall is of length ll, 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 656\sqrt{5} m.
    61
    What is h equal to ?

    Tap an option to check your answer.

    62
    If α\alpha is the angle between the line joining P and Q, and the line joining P and R, then what is cos⁡α\cos\alpha equal to ?

    Tap an option to check your answer.

  4. Question 4

    CDS 1 2025

    11
    A lamp is kept on a vertical pole. The height of the top of the lamp above the ground is 532\dfrac{5\sqrt{3}}{2} m. The perpendicular distances of the bottom of the pole from two adjacent walls meeting perpendicularly are 0.7 m and 2.4 m. What is the distance of the top of the lamp from the corner point of the walls on the ground ?

    Tap an option to check your answer.

  5. Question 5

    CDS 2 2026

    76
    A room is L m long, B m wide and H m high. Further, L > B > H and L, B and H are integers. The length of the longest pole that can be placed in the room is 17 m and the length of the longest pole that can be placed on the floor is 15 m. What is the volume of the room ?

    Tap an option to check your answer.