Probability

JEE Main 2025 (Online) 28th January Evening ShiftMCQEasy📈 Topic in 37% papers+4−1

Ques. 1JEE Main 2025, 28 January (Evening Shift)

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:

Answer

(2) 12

Solution

GARDEN has 6 distinct letters n(S) = 6! = 720

Vowels: A, E. In every arrangement either A comes before E or E comes before A, and the two cases are equally many (swap A and E).

Words with vowels in alphabetical order (A before E) = 7202 = 360

Words NOT having vowels in alphabetical order = 720 - 360 = 360

P = 360720 = 12

Answer: (2)

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Ques. 2JEE Main 2025, 23 January (Morning Shift)

One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two faces marked 2 , two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are thrown together, is

Ques. 3JEE Main 2025, 23 January (Evening Shift)

A board has 16 squares as shown in the figure : [figure] Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

35
45
2330
710

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