1
JEE Main 2024 (Online) 9th April Evening Shift
+4
-1

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $$i^{\text {th }}$$ roll than the number obtained in the $$(i-1)^{\text {th }}$$ roll, $$i=2,3$$, is equal to

A
5/54
B
2/54
C
1/54
D
3/54
2
JEE Main 2024 (Online) 8th April Evening Shift
+4
-1

There are three bags $$X, Y$$ and $$Z$$. Bag $$X$$ contains 5 one-rupee coins and 4 five-rupee coins; Bag $$Y$$ contains 4 one-rupee coins and 5 five-rupee coins and Bag $$Z$$ contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag $$\mathrm{Y}$$, is :

A
$$\frac{1}{2}$$
B
$$\frac{1}{3}$$
C
$$\frac{5}{12}$$
D
$$\frac{1}{4}$$
3
JEE Main 2024 (Online) 8th April Morning Shift
+4
-1

Let the sum of two positive integers be 24 . If the probability, that their product is not less than $$\frac{3}{4}$$ times their greatest possible product, is $$\frac{m}{n}$$, where $$\operatorname{gcd}(m, n)=1$$, then $$n$$-$$m$$ equals

A
10
B
11
C
9
D
8
4
JEE Main 2024 (Online) 6th April Evening Shift
+4
-1

If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is :

A
$$\frac{18}{25}$$
B
$$\frac{12}{25}$$
C
$$\frac{6}{25}$$
D
$$\frac{4}{25}$$
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