1
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to

A
18
B
16
C
12
D
15
2
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 $$\beta \notin \mathbf{N}$$
3
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
4
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
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