JEE Main 2023 (Online) 1st February Morning Shift | Permutations and Combinations Question 45 | Mathematics | JEE Main - ExamSIDE.com

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1

JEE Main 2023 (Online) 1st February Morning Shift

MCQ (Single Correct Answer)

+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

$$\frac{2^{50}}{51 !}$$

2

JEE Main 2023 (Online) 30th January Evening Shift

MCQ (Single Correct Answer)

+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

3

JEE Main 2023 (Online) 29th January Evening Shift

MCQ (Single Correct Answer)

+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

4

JEE Main 2023 (Online) 29th January Evening Shift

MCQ (Single Correct Answer)

+4

-1

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is :

A

400

B

472

C

507

D

432

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