1
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
2
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
3
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
$$\frac{2}{7}$$
4
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1

If an unbiased die, marked with $$-2,-1,0,1,2,3$$ on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is :

A
$$\frac{27}{288}$$
B
$$\frac{521}{2592}$$
C
$$\frac{440}{2592}$$
D
$$\frac{881}{2592}$$
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