Question

Raipur University presently employs three managers - 'a', 'b' and 'c' and five faculty members - 'd', 'e', 'f', 'g', 'h' and is planning to relocate two managers and three faculty members to the new centre. Following information was available to the HR department.
(K) Manager 'a' & 'c' cannot be sent as a team to the new centre.
(L) 'c' & 'e' are excellent performers, though they do not share good rapport and hence should not be sent together.
(M) If 'd' is sent, then 'g' cannot be sent, and vice versa.
(N) 'd' & 'f' should not be together in a team.
Which of the following cannot be a possible working unit?

• A. a \(\rightarrow\) b \(\rightarrow\) d \(\rightarrow\) e \(\rightarrow\) h
• B. a \(\rightarrow\) b \(\rightarrow\) f \(\rightarrow\) g \(\rightarrow\) h
• C. a \(\rightarrow\) b \(\rightarrow\) e \(\rightarrow\) g \(\rightarrow\) h
• D. a \(\rightarrow\) b \(\rightarrow\) d \(\rightarrow\) g \(\rightarrow\) h

Hint:

To solve group-selection multiple choice questions quickly, look for the most restrictive negative constraints (like "d and g cannot be together") and scan the options to see if any of them contain that forbidden pair. Here, scanning for 'd' and 'g' instantly points to Option D.

Answer 1

The Correct Option is D

Step 1: Collect the forbidden pairings.
The rules forbid these pairs together: $(a,c)$, $(c,e)$, $(d,g)$, and $(d,f)$.
Step 2: Decide the strategy.
We only need to find the one option that breaks at least one forbidden pair. Scan each team for a banned duo.
Step 3: Test option A, a b d e h.
No $c$, so $(a,c)$ and $(c,e)$ are safe; $d$ appears without $g$ or $f$, so $(d,g)$ and $(d,f)$ are safe. Valid.
Step 4: Test options B and C.
Option B (a b f g h) has no $c$ and no $d$, so all rules hold. Option C (a b e g h) has no $c$ and no $d$, so all rules hold. Both valid.
Step 5: Test option D, a b d g h.
Here $d$ and $g$ sit together, which directly violates the rule that $d$ and $g$ cannot both be sent.
Step 6: Conclude.
Option D is the impossible working unit.
\[ \boxed{a \rightarrow b \rightarrow d \rightarrow g \rightarrow h} \]