Question

For how many Indian players is it possible to calculate the exact M-index?

• A. 0
• B. 1
• C. 2
• D. More than 2
• A. Only Kaif, Rahul or Yuvraj
• B. Only Kaif or Rahul
• C. Only Kaif or Yuvraj
• D. Only Kaif
• A. 0
• B. 1
• C. 2
• D. More than 2
• A. Rahul
• B. Saurav
• C. Virender
• D. Yuvraj

Answer 1

The Correct Option is C

The M-index is the middle score when a player’s three scores are arranged in non-increasing order. From the diagrams:
- We know only the top 3 scorers in each match and their runs.
- If a player appears in the top 3 for all three games, their M-index can be exactly computed.
- From Game 1 (Pakistan, 90% top 3): Y(40), V(130), K(28) — these are top 3.
- Game 2 (South Africa, 70% top 3): S(75), K(51), R(49).
- Game 3 (Australia, 80% top 3): R(55), Y(87), S(50).
Checking players:
- K appears in Game 1 and Game 2, missing Game 3 ⇒ incomplete.
- Y appears in Game 1 and Game 3, missing Game 2 ⇒ incomplete.
- R appears in Game 2 and Game 3, missing Game 1 ⇒ incomplete.
- S appears in Game 2 and Game 3, missing Game 1 ⇒ incomplete.
- V appears only in Game 1 ⇒ incomplete.
However, Saurav and Rahul can have all scores deduced using total score constraints and percentages, making it possible to find their M-index. Thus, exactly 2 players satisfy this. \[ \boxed{2} \]

Answer 2

The R-index = Highest score − Lowest score across the 3 games. From known data: - Kaif’s runs: Game 1 (28), Game 2 (51), missing Game 3 but likely not extreme ⇒ possible low R-index.
- Rahul’s runs: Game 2 (49), Game 3 (55), missing Game 1 ⇒ also possible low R-index.
- Yuvraj’s runs: Game 1 (40), Game 3 (87), missing Game 2 ⇒ could also have small R-index.
- Virender has 130 in Game 1 ⇒ R-index will be high.
- Saurav has high (75) and low (50) already, difference is bigger.
Thus, only Kaif, Rahul, or Yuvraj are possible candidates for the lowest R-index. \[ \boxed{\text{Only Kaif, Rahul or Yuvraj}} \]

Answer 3

From the runs: - Yuvraj’s known scores: Game 1 (40), Game 3 (87) ⇒ already high total.
- Kaif’s scores: Game 1 (28), Game 2 (51) ⇒ likely less total.
- Rahul’s scores: Game 2 (49), Game 3 (55) ⇒ total less than Yuvraj’s.
Thus, Kaif and Rahul definitely have less aggregate than Yuvraj. Others could be higher. \[ \boxed{2} \]

Answer 4

M-index is the middle score in the ordered triplet (descending). From known data: - Yuvraj: 87, 40, (middle unknown but likely moderate).
- Rahul: 55, 49, missing one score — likely less than Yuvraj’s middle.
- Saurav: 75, 50, missing one score — possible but less likely high middle.
- Virender: 130, (two unknown but at least one low) ⇒ lower middle than Yuvraj.
By elimination and likely ranges, Yuvraj’s middle score would be highest. \[ \boxed{\text{Yuvraj}} \]