1
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

Let $$S$$ be the sample space of all five digit numbers. It $$p$$ is the probability that a randomly selected number from $$S$$, is a multiple of 7 but not divisible by 5 , then $$9 p$$ is equal to

A
1.0146
B
1.2085
C
1.0285
D
1.1521
2
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

Let $$X$$ be a binomially distributed random variable with mean 4 and variance $$\frac{4}{3}$$. Then, $$54 \,P(X \leq 2)$$ is equal to

A
$$\frac{73}{27}$$
B
$$\frac{146}{27}$$
C
$$\frac{146}{81}$$
D
$$\frac{126}{81}$$
3
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

The mean and variance of a binomial distribution are $$\alpha$$ and $$\frac{\alpha}{3}$$ respectively. If $$\mathrm{P}(X=1)=\frac{4}{243}$$, then $$\mathrm{P}(X=4$$ or 5$$)$$ is equal to :

A
$$\frac{5}{9}$$
B
$$\frac{64}{81}$$
C
$$\frac{16}{27}$$
D
$$\frac{145}{243}$$
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

Let $$\mathrm{E}_{1}, \mathrm{E}_{2}, \mathrm{E}_{3}$$ be three mutually exclusive events such that $$\mathrm{P}\left(\mathrm{E}_{1}\right)=\frac{2+3 \mathrm{p}}{6}, \mathrm{P}\left(\mathrm{E}_{2}\right)=\frac{2-\mathrm{p}}{8}$$ and $$\mathrm{P}\left(\mathrm{E}_{3}\right)=\frac{1-\mathrm{p}}{2}$$. If the maximum and minimum values of $$\mathrm{p}$$ are $$\mathrm{p}_{1}$$ and $$\mathrm{p}_{2}$$, then $$\left(\mathrm{p}_{1}+\mathrm{p}_{2}\right)$$ is equal to :

A
$$\frac{2}{3}$$
B
$$\frac{5}{3}$$
C
$$\frac{5}{4}$$
D
1
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