1
JEE Main 2023 (Online) 6th April Evening Shift
+4
-1

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is :

A
578
B
576
C
580
D
582
2
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

The value of $$\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots .+\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$$ is :

A
$$\frac{2^{51}}{50 !}$$
B
$$\frac{2^{51}}{51 !}$$
C
$$\frac{2^{50}}{50 !}$$
D
$$\frac{2^{50}}{51 !}$$
3
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
The number of ways of selecting two numbers $a$ and $b, a \in\{2,4,6, \ldots ., 100\}$ and $b \in\{1,3,5, \ldots . ., 99\}$ such that 2 is the remainder when $a+b$ is divided by 23 is :
A
186
B
54
C
108
D
268
4
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is :

A
79
B
84
C
89
D
86
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