JEE Main 2021 (Online) 27th July Morning Shift | Probability Question 96 | Mathematics

Let X be a random variable such that the probability function of a distribution is given by $$P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty )$$. Then the mean of the distribution and P(X is positive and even) respectively are :

$${3 \over 8}$$ and $${1 \over 8}$$

$${3 \over 4}$$ and $${1 \over 8}$$

$${3 \over 4}$$ and $${1 \over 9}$$

$${3 \over 4}$$ and $${1 \over 16}$$

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

-1

Let 9 distinct balls be distributed among 4 boxes, B₁, B₂, B₃ and B₄. If the probability than B₃ contains exactly 3 balls is $$k{\left( {{3 \over 4}} \right)^9}$$ then k lies in the set :

{x $$\in$$ R : |x $$-$$ 3| < 1}

{x $$\in$$ R : |x $$-$$ 2| $$\le$$ 1}

{x $$\in$$ R : |x $$-$$ 1| < 1}

{x $$\in$$ R : |x $$-$$ 5| $$\le$$ 1}

JEE Main 2021 (Online) 22th July Evening Shift

MCQ (Single Correct Answer)

-1

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 $$\times$$ 2 matrices. The probability that such formed matrix have all different entries and are non-singular, is :

$${{45} \over {162}}$$

$${{21} \over {81}}$$

$${{22} \over {81}}$$

$${{43} \over {162}}$$

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