1
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
2
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
3
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
4
JEE Main 2023 (Online) 31st January Morning Shift
+4
-1

A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is :

A
$$\frac{3}{7}$$
B
$$\frac{5}{6}$$
C
$$\frac{5}{7}$$
D
$$\frac{2}{7}$$
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