1
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
2
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1 Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that $$N-2,\sqrt{3N},N+2$$ are in geometric progression be $$\frac{k}{48}$$. Then the value of k is

A
8
B
16
C
2
D
4
3
JEE Main 2023 (Online) 25th January Morning Shift
+4
-1 Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $$S = \left\{ {x \in \mathbb{Z}:x(66 - x) \ge {5 \over 9}M} \right\}$$ and the event $$\mathrm{A = \{ x \in S:x\,is\,a\,multiple\,of\,3\}}$$. Then P(A) is equal to

A
$$\frac{1}{3}$$
B
$$\frac{1}{5}$$
C
$$\frac{7}{22}$$
D
$$\frac{15}{44}$$
4
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1 Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations

$$x + y + z = 1$$

$$2x + \mathrm{N}y + 2z = 2$$

$$3x + 3y + \mathrm{N}z = 3$$

has unique solution is $${k \over 6}$$, then the sum of value of k and all possible values of N is

A
18
B
21
C
20
D
19
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