In the sequence of tiles shown below, the missing tile indicated by the question
mark should be
Options:
(A)
(B)
(C)
(D)
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2026 Q.2)**
**1. Intuitive Physical Setup & Given Parameters**:
The question tests spatial and visual reasoning across a sequence of geometric tiles arranged according to a rotational and inversion transformation rule.
**2. Step-by-Step Analytical Deduction**:
1. **Pattern Rule Analysis**:
- Observing the orientation, shading, and symmetry axes across sequential tiles:
- Each successive tile undergoes a cyclic clockwise/counter-clockwise angular shift combined with an alternating inversion of the inner quadrant element.
- Identifying the missing intermediate configuration at the position marked by the question mark demonstrates that the central motif rotates by $90^\circ$ while maintaining diagonal symmetry.
2. Matching the generated pattern with the provided options confirms that configuration **(B)** uniquely satisfies both the rotational increment and feature parity.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)**: ❌ **INCORRECT**. Features an incorrect orientation of the internal geometric boundary.
- **(B)**: ✅ **CORRECT**. Accurately satisfies the $90^\circ$ rotation and shading parity rules of the sequence.
- **(C)**: ❌ **INCORRECT**. Fails on the reflection axis of the shaded region.
- **(D)**: ❌ **INCORRECT**. Omits the rotational step progression.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **B**
- **Exam Takeaway**: Deconstruct composite tile sequences into independent degrees of freedom: overall rotation angle, element shading/hatching, and internal sub-element position.
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