JEE Advanced Maths: Modulus / Absolute Value questions with solutions

Q1. Solve for real x: |x - 6| + |x - 3| = 1.

1. No solution
2. x = 3 and x = 6
3. x in [3, 6]
4. x = 5

Answer: No solution

The sum of distances from x to 3 and to 6 can never be less than the gap between them, which is 3. Since 1 < 3, the equation has no solution.