1
JEE Main 2023 (Online) 11th April Morning Shift
+4
-1

Let $$S=\left\{M=\left[a_{i j}\right], a_{i j} \in\{0,1,2\}, 1 \leq i, j \leq 2\right\}$$ be a sample space and $$A=\{M \in S: M$$ is invertible $$\}$$ be an event. Then $$P(A)$$ is equal to :

A
$$\frac{47}{81}$$
B
$$\frac{49}{81}$$
C
$$\frac{50}{81}$$
D
$$\frac{16}{27}$$
2
JEE Main 2023 (Online) 10th April Evening Shift
+4
-1
Out of Syllabus

Let a die be rolled $$n$$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $$\frac{k}{2^{15}}$$, then $$\mathrm{k}$$ is equal to :

A
15
B
60
C
30
D
90
3
JEE Main 2023 (Online) 10th April Morning Shift
+4
-1

Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that $${2^N} < N!$$ is $${m \over n}$$, where m and n are coprime, then $$4m-3n$$ is equal to :

A
12
B
6
C
8
D
10
4
JEE Main 2023 (Online) 8th April Evening Shift
+4
-1

If the probability that the random variable $$\mathrm{X}$$ takes values $$x$$ is given by $$\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1) 3^{-x}, x=0,1,2,3, \ldots$$, where $$\mathrm{k}$$ is a constant, then $$\mathrm{P}(\mathrm{X} \geq 2)$$ is equal to :

A
$$\frac{7}{18}$$
B
$$\frac{20}{27}$$
C
$$\frac{7}{27}$$
D
$$\frac{11}{18}$$
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