1
JEE Main 2024 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If for some $$m, n ;{ }^6 C_m+2\left({ }^6 C_{m+1}\right)+{ }^6 C_{m+2}>{ }^8 C_3$$ and $${ }^{n-1} P_3:{ }^n P_4=1: 8$$, then $${ }^n P_{m+1}+{ }^{\mathrm{n}+1} C_m$$ is equal to

A
380
B
376
C
372
D
384
2
JEE Main 2024 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
3
JEE Main 2024 (Online) 27th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 $$\beta \notin \mathbf{N}$$
4
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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
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