Kerala KEAM 5 June 2024 Solved Paper

To form a number greater than 7000, we need to consider the four-digit numbers that can be formed with the given digits 2, 4, 5, 7, 8.The first digit must be one of the digits greater than or equal to 7 (since the number should be greater than 7000). The digits greater than or equal to 7 are 7 and 8, so we have 2 choices for the first digit.Now, we need to form a three-digit number from the remaining 4 digits (after choosing the first digit). Since repetition is not allowed, we choose 3 digits from the remaining 4, and the number of ways to arrange 3 digits from 4 is: $$P(4, 3) = 4 \times 3 \times 2 = 24$$Thus, the total number of four-digit integers greater than 7000 is: $$2 \times 24 = 48$$Now, we can form a three-digit number greater than 7000 by placing one of the digits in the thousand's place. The remaining three places can be filled in the same way as before. Hence, the total number of integers greater than 7000 is $\boxed{168}$.Thus, the correct answer is option (B), 168. Quick Tip: When forming numbers greater than a specified value, start by determining the range for the first digit (greater than the specified number), and then count the permutations of the remaining digits.