CAT 2025 Slot 2 Question Paper DILR: Download Question Paper PDF with Answer Key and Solutions

CAT Questions

• 1.

  There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4.
  Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a ”ping”. Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping.
  The following additional information is known:
  1. B1 and B6 each made a ping on H4, but B5 did not.
  2. B4 made a ping on H3, but B1 did not.
  3. All balls, except B3, made pings on H1.
  4. None of the balls, except B2, made a ping on H2.

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• 2.

  A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam (A), Bashir (B), Chhavi (C), and Davies (D), sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs they are sitting on.
  The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction they choose to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).
  The following information is known: 1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6. 2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.

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• 3.

  Four companies C1, C2, C3, C4 must interview candidates P, Q, R, S over four time slots (T1--T4).
  Each candidate gets one unique slot and each company interviews exactly one candidate per slot.
  Constraints:
  1. P cannot be interviewed by C1 or C3.
  2. Q must be interviewed in either T1 or T4.
  3. R must be interviewed before S.
  4. C4 only interviews in T2 or T3.
  5. No company interviews the same candidate as last year:
  (C1--P), (C2--Q), (C3--R), (C4--S).
  How many valid interview schedules are possible?
  

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• 4.

  Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different exchange values. Crown’s currency exchange rate with Zentars = 0.5, i.e., 1 Crown is worth 0.5 Zentars.
  Three travelers, Jano, Kira, and Lian set out from Zerathania visiting exactly two of the countries. Each country is visited by exactly two travelers. Each traveler has a unique Flight Cost, which represents the total cost of airfare in traveling to both the countries and back to Zerathania. The Flight Cost of Jano was 4000 Zentars, while that of the other two travelers were 5000 and 6000 Zentars, not necessarily in that order. When visiting a country, a traveler spent either 1000, 2000 or 3000 in the country’s local currency. Each traveler had different spends (in the country’s local currency) in the two countries he/she visited. Across all the visits, there were exactly two spends of 1000 and exactly one spend of 3000 (in the country’s local currency).
  The total “Travel Cost” for a traveler is the sum of his/her Flight Cost and the money spent in the countries visited.
  The citizens of the four countries with knowledge of these travels made a few observations, with spends measured in their respective local currencies:
  • Aurevia citizen: Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively.
  • Brelosia citizen: Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira’s Travel Cost was 4000.
  • Cyrenia citizen: Lian visited our country and her Travel Cost was 36000.

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• 5.

  At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu. At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3. & nbsp;
  The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher.
  1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4.
  2. Dolly and Falguni were the only employees who got the same rating across all the quarters.
  3. The following is known about ratings given by Lalu (Novice manager):
  – Bunty received a rating of 1 in Quarter 2. & nbsp;
  – Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.

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• 6.

  Five lectures L1, L2, L3, L4, L5 must be scheduled from Monday to Friday (one each day).
  Five professors A, B, C, D, E will take one lecture each. Constraints:
  1. A takes L3.
  2. L2 must be scheduled after L5.
  3. C does not teach on Wednesday or Friday.
  4. D teaches before E.
  5. B does not teach L4.
  How many valid schedules are possible?
  

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