Directions: Read the following information carefully and answer the question that follows.

Eight members — K, T, U, V, W, X, Y, and Z — hold eight distinct academic designations in a university: Chancellor, Vice-Chancellor, Dean, Department Head, Senior Professor, Associate Professor, Assistant Professor, and Lecturer. The order of seniority is from Chancellor (the senior-most) down to Lecturer (the junior-most).

K is the Lecturer of the university.
Three persons hold designations between K and T.
X holds a designation senior to Dean, but X is not the Vice-Chancellor.
The number of persons senior to V is equal to the number of persons junior to W.
Two persons hold designations between V and U.
Z is senior to Y, but junior to Vice-Chancellor.

Which of the following designation and person combinations is incorrect?

The correct option is Senior Professor - Y.

Step-by-Step Explanation:

First, let us list the eight academic designations in order of seniority from 1 (senior-most) down to 8 (junior-most):
1. Chancellor
2. Vice-Chancellor
3. Dean
4. Department Head
5. Senior Professor
6. Associate Professor
7. Assistant Professor
8. Lecturer

Now, let us determine the positions of all members step-by-step using the given clues:

1. K is the Lecturer of the university:
Lecturer is position 8, so:
Position 8 = K

2. Three persons hold designations between K and T:
Since K is at position 8, counting 3 positions above K (positions 7, 6, and 5), T must be at position 4.
Position 4 (Department Head) = T

3. X holds a designation senior to Dean, but X is not the Vice-Chancellor:
The designations senior to Dean (position 3) are Chancellor (position 1) and Vice-Chancellor (position 2). Since X is not the Vice-Chancellor, X must be the Chancellor.
Position 1 (Chancellor) = X

4. The number of persons senior to V is equal to the number of persons junior to W:
This means V and W are placed symmetrically from the top and bottom of the hierarchy (i.e., Position of V + Position of W = 9).

5. Two persons hold designations between V and U:
If V is at position 2 (Vice-Chancellor), then W must be at position 7 (Assistant Professor).
Two positions between V (position 2) and U means U must be at position 5 (Senior Professor).

6. Z is senior to Y, but junior to Vice-Chancellor:
The positions remaining to be filled are positions 3 and 6.
Since Z is junior to Vice-Chancellor (position 2) and senior to Y, Z must be at position 3 (Dean) and Y must be at position 6 (Associate Professor).

Final Arrangement:
1. Chancellor — X
2. Vice-Chancellor — V
3. Dean — Z
4. Department Head — T
5. Senior Professor — U
6. Associate Professor — Y
7. Assistant Professor — W
8. Lecturer — K

Checking the Options:
- Department Head - T: Correct
- Chancellor - X: Correct
- Senior Professor - Y: Incorrect (U is the Senior Professor, whereas Y is the Associate Professor)
- Lecturer - K: Correct
- Dean - Z: Correct

Therefore, the incorrect designation and person combination is Senior Professor - Y.