1
JEE Main 2021 (Online) 25th July Morning Shift
+4
-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 :
A
{x $$\in$$ R : |x $$-$$ 3| < 1}
B
{x $$\in$$ R : |x $$-$$ 2| $$\le$$ 1}
C
{x $$\in$$ R : |x $$-$$ 1| < 1}
D
{x $$\in$$ R : |x $$-$$ 5| $$\le$$ 1}
2
JEE Main 2021 (Online) 22th July Evening Shift
+4
-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 :
A
$${{45} \over {162}}$$
B
$${{21} \over {81}}$$
C
$${{22} \over {81}}$$
D
$${{43} \over {162}}$$
3
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 $$-$$ k), the probability that exactly one of B and C occurs is (1 $$-$$ 2k), the probability that exactly one of C and A occurs is (1 $$-$$ k) and the probability of all A, B and C occur simultaneously is k2, where 0 < k < 1. Then the probability that at least one of A, B and C occur is :
A
greater than $${1 \over 8}$$ but less than $${1 \over 4}$$
B
greater than $${1 \over 2}$$
C
greater than $${1 \over 4}$$ but less than $${1 \over 2}$$
D
exactly equal to $${1 \over 2}$$
4
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :
A
$${1 \over {66}}$$
B
$${1 \over {11}}$$
C
$${1 \over {9}}$$
D
$${2 \over {11}}$$
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