Xavier Aptitude Test 2025 Paper

Concept:The robot’s arm must reach the shelf while the shoulder height is as low as possible, so the arm is inclined at the maximum allowed angle of $60^\circ$ above the horizontal.Explanation:Let the shoulder height from the ground be $x$ feet.The track is $1$ foot away from the shelf, so the horizontal distance from the shoulder to the top shelf is $1$ foot.The top shelf is $7$ feet above the ground, so the vertical distance from the shoulder to the shelf is $7 - x$ feet.At maximum reach, the arm forms a $60^\circ$ angle with the horizontal.Using the right triangle formed by the horizontal distance, vertical height, and the arm:$\tan 60^\circ = \frac{\text{vertical height}}{\text{horizontal distance}} = \frac{7 - x}{1}$$\sqrt{3} = 7 - x$$x = 7 - \sqrt{3}$ feetAnswer:The minimum height of the robot from the ground to the shoulder must be $7 - \sqrt{3}$ feet, which is option C.