1
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
$$\frac{2}{7}$$
2
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
$$\frac{881}{2592}$$
3
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
$$\frac{3}{64}$$
4
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is :

A
$$\frac{1}{6}$$
B
$$\frac{2}{15}$$
C
$$\frac{5}{24}$$
D
0.08
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