1
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
$$\frac{11}{18}$$
2
JEE Main 2023 (Online) 8th April Morning Shift
+4
-1

In a bolt factory, machines $$A, B$$ and $$C$$ manufacture respectively $$20 \%, 30 \%$$ and $$50 \%$$ of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found the defective, then the probability that it is manufactured by the machine $$C$$ is :

A
$$\frac{2}{7}$$
B
$$\frac{9}{28}$$
C
$$\frac{5}{14}$$
D
$$\frac{3}{7}$$
3
JEE Main 2023 (Online) 6th April Evening Shift
+4
-1

Three dice are rolled. If the probability of getting different numbers on the three dice is $$\frac{p}{q}$$, where $$p$$ and $$q$$ are co-prime, then $$q-p$$ is equal to :

A
3
B
4
C
1
D
2
4
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1
Out of Syllabus

A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is $$\frac{k}{3^{11}}$$, then $$k$$ is equal to :

A
82
B
164
C
123
D
75
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