Question: Which of the following statement(s) is (are) incorrect?
I. The Chemical Engineering student and the student-in-charge of Cultural activity, both stay in the same hostel.
Explanation:
From (ii), (viii) and (x), it can be observed that Ravi studies Computer Science and is the student-in-charge of the Mess activity. He is the only student to stay at Satpura.
From (ix), it can be seen that two students stay at the Aravalli hostel. Hence, two students must also stay at the Vindhya hostel.
From (i) and (ix), it can be seen that students from Nagpur and Patna stay in Aravalli hostels. The student from Nagpur must study Mechanical Engineering.
From (xiii), the student from Kochi stays at Vindhya and the student-in charge of Placement must stay at Vindhya.
From (iv) and (vi), the students who are in-charge of Sports and Cultural activities stay at the Aravalli hostels. Also, the student from Allahabad does not stay with the student-in charge of the Cultural Activity. Hence, he must stay with the student who stays in Vindhya. From (xi), it is known that there is a General Secretary of the Student Body. The General Secretary must stay in the Vindhya hostel. From (xiii), it can be seen that the General Secretary is from Kochi.
The following table summarizes the above points,
Consider the student from Nagpur.
From (i), (iii) and (xi), Abhishek, Hemant and Hardeep do not stay at Nagpur.
It is known that Abhishek does not stay at Aravalli (From (i)). From (xi), Hemant studies Chemical Engineering. Hence, it cannot be Hemant. From (iii), Hardeep does not study Mechanical Engineering. Hence, it cannot be Hardeep as well.
Hence, only Sanjoy is from Nagpur.
From (vii), Sanjoy is not the in-charge of Cultural activity. Hence, he must be in charge of the Sports activity. From (v), Sanjoy stays with the student who studies Metallurgy. Hence, the student from Patna studies Metallurgy.
From (xi), Hemant is not from Kochi and studies Chemical Engineering. Hence, Hemant is the in-charge of the Placements. From (i), Abhishek is from Kochi and studies Civil Engineering.
The final arrangement can be shown as follows,
From the above arrangement, it can be seen that statements I, II, III are incorrect.
Hence, option (b).