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

Three dice are rolled. If the probability of getting different numbers on the three dice is $$\frac{p}{q}$$, where $$p$$ and $$q$$ are co-prime, then $$q-p$$ is equal to :

A
3
B
4
C
1
D
2
2
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1
Out of Syllabus

A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is $$\frac{k}{3^{11}}$$, then $$k$$ is equal to :

A
82
B
164
C
123
D
75
3
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1

Two dice are thrown independently. Let $$\mathrm{A}$$ be the event that the number appeared on the $$1^{\text {st }}$$ die is less than the number appeared on the $$2^{\text {nd }}$$ die, $$\mathrm{B}$$ be the event that the number appeared on the $$1^{\text {st }}$$ die is even and that on the second die is odd, and $$\mathrm{C}$$ be the event that the number appeared on the $$1^{\text {st }}$$ die is odd and that on the $$2^{\text {nd }}$$ is even. Then :

A
A and B are mutually exclusive
B
the number of favourable cases of the events A, B and C are 15, 6 and 6 respectively
C
B and C are independent
D
the number of favourable cases of the event $$(\mathrm{A\cup B)\cap C}$$ is 6
4
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1
Out of Syllabus

In a binomial distribution $$B(n,p)$$, the sum and the product of the mean and the variance are 5 and 6 respectively, then $$6(n+p-q)$$ is equal to :

A
52
B
50
C
51
D
53
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