Question

Which two candidates can belong to the same department?

• A. Prof. Pakrasi and Prof. Qureshi
• B. Prof. Qureshi and Prof. Ramaswamy
• C. Prof. Pakrasi and Prof. Samuel
• D. Prof. Ramaswamy and Prof. Samuel
• A. 7
• B. 8
• C. 6
• D. 9
• A. Only statement A
• B. Both statements A and B
• C. Neither statement A nor statement B
• D. Only statement B
• A. It was either Prof. Ramaswamy or Prof. Samuel.
• B. It was Prof. Samuel.
• C. It was either Prof. Pakrasi or Prof. Qureshi.
• D. It was Prof. Ramaswamy.
• A. Neither statement A nor statement B
• B. Both statements A and B
• C. Only statement A
• D. Only statement B

Answer 1

The Correct Option is A

As per the question, we know there is only 1 candidate from OQ, which means that the number of non-candidate voters in OQ will be 4.
We know that the non-candidates in a particular department voted as a block, and we also know that the least number of non-candidate voters in a particular department can be 1 (BH, 3-2 faculty)
R got 5 votes from non-candidates.
Then, 5 can be written as
(a) 5
(b) 4 + 1
(c) 3 + 2
Now , consider the case (b) 4 + 1,This is only possible when there is 1 candidate from OQ, and there are 2 candidates from BH, which implies that number of candidates in FA and MQ is 1.
On similar grounds, we can also eliminate Case (c) as it also implies there is only 1 candidate in FA and MQ.
Now, considering Case (a), we get that 5+0 will happen only one when there are 5 non-candidates in a single department.
This can be possible only in MS (where out of 7, there will be 2 candidates and 5 non-candidates)
So , we get the following table :

	FA	MS	OQ	BH
Total number of votes	9	7	5	3
Number of candidates	0	2	1	1
Number of non-candidates	9	5	4	2

By using the above table , we get :

	P	Q	R	S
Total Votes	3	14	6	1
Candidate Vote	1(S)	1(R)	1(P)	1(Q)
Votes from non candidates	2	13	5	0
	BH	FA+OQ	MS

Let's consider Department MS, we know that there are 2 candidates from MS and R can’t be one of them as the people in that department voted for him….. (3 rd condition)
Now , the possible combinations of candidates in MS are (P,Q), (Q,S) and (P,S).
Now , we can get that P and Q are from MS.

	FA	MS	OQ	BH
Case 1	0	P,Q	R	S
Case 2	0	P,Q	S	R

So , the correct option is (A) : Prof. Pakrasi and Prof. Qureshi.

Answer 2

Here's the extracted data from the image:

To determine the number of votes that Prof. Qureshi could have received from a single department, let’s analyze the voting distribution based on the information given:

1. Total Votes for Prof. Qureshi: Prof. Qureshi received a total of 14 votes in the election.

2. Voting Constraints: 
  - Each department, including the one Prof. Qureshi belongs to, votes as a block (i.e., all non-candidate faculty members in a department vote for the same candidate).
  - Since Prof. Qureshi cannot receive votes from his own department (as per the rules), the votes he received must have come from other departments.

3. Departmental Sizes:
  - F&A has 9 faculty members.
  - M&S has 7 faculty members.
  - O&Q has 5 faculty members.
  - B&H has 3 faculty members.

4. **Possible Voting Scenarios**:
  - For Prof. Qureshi to receive 14 votes, it is possible that he received all the votes from two of the larger departments.
  - The only department large enough to contribute 9 votes is F&A.
  - Therefore, if F&A voted as a block for Prof. Qureshi, he would have received exactly 9 votes from F&A.
Thus, the most feasible option for the number of votes Prof. Qureshi received from a single department is Option 4:(9).

Answer 3

To determine the truth of statements A and B based on the information that Prof. Samuel belongs to the B&H department, let’s examine the constraints and information provided in the comprehension:
1. Departmental Composition:- According to the setup, each department has a limited number of faculty members, and only one of the four candidates can be from O&Q.- Since Prof. Samuel is confirmed to be in the B&H department, this restriction implies that no other candidate is in B&H.
2. Analyzing Statement A:- If Prof. Pakrasi belongs to M&S, this aligns with the restriction on department sizes and the number of candidates from each department.- There is no conflict with Prof. Pakrasi being in M&S, and it satisfies the condition of department representation.
3. Analyzing Statement B:- Since Prof. Samuel is in B&H and only one candidate can belong to O&Q, Prof. Ramaswamy being in O&Q would satisfy this condition.- This assignment allows each department to have appropriate representation without exceeding the maximum allowed candidates from any department.
4. Conclusion:- Both statements A and B are consistent with the given information and constraints.- Therefore, both statements are true under the condition that Prof. Samuel belongs to B&H.
Thus, the correct answer is Option 2: Both statements A and B.

Answer 4

To deduce which candidate might belong to the O&Q department, let’s examine the information given and apply the constraints:
1.Departmental Constraint: Only one candidate can belong to the O&Q department, meaning the remaining candidates are distributed among the other departments.
2.Process of Elimination:- Prof. Pakrasi and Prof. Qureshi received a significant number of votes, suggesting they may belong to departments with more faculty members (like F&A or M&S)since O&Q only has 5 faculty members.- This makes it unlikely that either Prof. Pakrasi or Prof. Qureshi belongs to O&Q.
3.Remaining Candidates:- This leaves Prof. Ramaswamy and Prof. Samuel as the possible candidates for the O&Q department.- Based on the information given, either of these two could feasibly belong to O&Q.
4.Conclusion:- Therefore, the best conclusion we can draw is that the candidate from O&Q is either Prof. Ramaswamy or Prof. Samuel.
Thus, the correct answer is Option 1: It was either Prof. Ramaswamy or Prof. Samuel.

Answer 5

To determine the truth of each statement based on the information provided in the comprehension and constraints:
1.Voting Patterns and Departmental Rules:- All non-candidates in each department voted for a single candidate who was not from their own department.- Prof. Qureshi received a substantial number of votes (14 votes in total), suggesting that multiple departments voted for him.
2.Analysis of Statement A:- Statement A claims that non-candidates from M&S voted for Prof. Qureshi.- Given the voting restrictions, if M&S had voted for Prof. Qureshi, then all non-candidates in M&S would have aligned with him. However, based on the distribution, M&Slikely voted for another candidate to meet the voting totals, making this statement unlikely to be true.
3.Analysis of Statement B:- Statement B claims that non-candidates from F&A voted for Prof. Qureshi.- Considering that Prof. Qureshi received a large number of votes, it is plausible that the largest department, F&A (with 9 members), voted for him to account for a significant portion of his total votes. This aligns with the total vote distribution, making this statement likely to be true.
4.Conclusion:- Therefore, only Statement B is true, while Statement A is not supported by the available information.
Thus, the correct answer is Option 4: Only statement B.