This question was previously asked in

JEE Mains Previous Paper 1 (Held On: 08 Apr 2019 Shift 2)

Option 4 : 310

JEE Mains Previous Paper 1 (Held On: 12 Apr 2019 Shift 2)

8346

90 Questions
360 Marks
180 Mins

Given digits are 0, 1, 2, 3, 4, 5

Case 1: Number of four-digit number starting with 5 is,

First digit is 5 (1 way).

Second digit can be any of the 6 digits.

Third digit can be any of the 6 digits.

Fourth digit can be any of the 6 digits.

∴ 6 × 6 × 6 = 216

Case 2: Number of four-digit numbers starting with 4, 5 is,

Third digit can be any of the 6 digits.

Fourth digit can be any of the 6 digits.

∴ 6 × 6 = 36

Case 3: Number of four-digit numbers starting with 4, 4 is,

Third digit can be any of the 6 digits.

Fourth digit can be any of the 6 digits.

∴ 6 × 6 = 36

Case 4: Number of four-digit numbers starting with 4, 3 and greater than 4321 is,

Third digit can be any of the 3 digits except 0, 1 and 2

Fourth digit can be any of the 6 digits.

∴ 3 × 6 = 18

Case 5: Number of four-digit numbers starting with 4, 3, 2 and greater than 4321 is,

Fourth digit can be any of the 4 digits except 0 and 1

Hence, the required numbers

= 216 + 36 + 36 + 18 + 4 = 310.