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) 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
$$\frac{2}{7}$$
3
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
$$\frac{881}{2592}$$
4
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1 Let $$\mathrm{S} = \{ {w_1},{w_2},......\}$$ be the sample space associated to a random experiment. Let $$P({w_n}) = {{P({w_{n - 1}})} \over 2},n \ge 2$$. Let $$A = \{ 2k + 3l:k,l \in N\}$$ and $$B = \{ {w_n}:n \in A\}$$. Then P(B) is equal to

A
$$\frac{3}{32}$$
B
$$\frac{1}{32}$$
C
$$\frac{1}{16}$$
D
$$\frac{3}{64}$$
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