1
JEE Main 2022 (Online) 28th July Morning Shift
Numerical
+4
-1

Let $$S$$ be the set of all passwords which are six to eight characters long, where each character is either an alphabet from $$\{A, B, C, D, E\}$$ or a number from $$\{1,2,3,4,5\}$$ with the repetition of characters allowed. If the number of passwords in $$S$$ whose at least one character is a number from $$\{1,2,3,4,5\}$$ is $$\alpha \times 5^{6}$$, then $$\alpha$$ is equal to ___________.

2
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1

Numbers are to be formed between 1000 and 3000 , which are divisible by 4 , using the digits $$1,2,3,4,5$$ and 6 without repetition of digits. Then the total number of such numbers is ____________.

3
JEE Main 2022 (Online) 26th July Morning Shift
Numerical
+4
-1

The number of 5-digit natural numbers, such that the product of their digits is 36 , is __________.

4
JEE Main 2022 (Online) 25th July Morning Shift
Numerical
+4
-1

The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is _____________.