Question : The longest rod that can be placed in a room is 12 metres long, 9 metres broad, and 8 metres high is:

Option 1: 27 m

Option 2: 19 m

Option 3: 17 m

Option 4: 13 m

Question : If the hypotenuse of an isosceles right-angled triangle is 10 cm, then the other two sides (in cm) are __________.

Option 1: $10\sqrt{2}$ and $10\sqrt{2}$

Option 2: $8\sqrt{2}$ and $8\sqrt{2}$

Option 3: $6\sqrt{2}$ and $6\sqrt{2}$

Option 4: $5\sqrt{2}$ and $5\sqrt{2}$

Question : What is the length of the longest rod that can be placed in a room of dimensions 12 m × 9 m × 8 m?

Option 1: 15 m

Option 2: 17 m

Option 3: 16 m

Option 4: 14 m

Question : The shadow of a tower standing on a level plane is 40 metres longer when the sun's altitude is 45°, than when it is 60°. The height of the tower is:

Option 1: $30(3+\sqrt{3})$ metres

Option 2: $40(3+\sqrt{3})$ metres

Option 3: $20(3+\sqrt{3})$ metres

Option 4: $10(3+\sqrt{3})$ metres

Question : What is the length of the longest pole that can fit itself in a hall 60 feet long, 30 feet broad, and 20 feet high?

Option 1: 50 feet

Option 2: 70 feet

Option 3: 30 feet

Option 4: 20 feet