1
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

Let $$\alpha=\frac{(4 !) !}{(4 !)^{3 !}}$$ and $$\beta=\frac{(5 !) !}{(5 !)^{4 !}}$$. Then :

A
$$\alpha \in \mathbf{N}$$ and $$\beta \in \mathbf{N}$$
B
$$\alpha \in \mathbf{N}$$ and $$\beta \notin \mathbf{N}$$
C
$$\alpha \notin \mathbf{N}$$ and $$\beta \in \mathbf{N}$$
D
$$\alpha \notin \mathbf{N}$$ and $$\beta \notin \mathbf{N}$$
2
JEE Main 2023 (Online) 15th April Morning Shift
+4
-1
The total number of three-digit numbers, divisible by 3, which can be formed using the digits $1,3,5,8$, if repetition of digits is allowed, is :
A
21
B
22
C
18
D
20
3
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is :

A
324
B
328
C
326
D
327
4
JEE Main 2023 (Online) 12th April Morning Shift
+4
-1

The number of five digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits $$0,1,3,5,7$$ and 9 without repetition, is equal to :

A
132
B
72
C
120
D
96
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