1
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 $${1 \over 2}$$
2
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
$${2 \over {11}}$$
3
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
The probability of selecting integers a$$\in$$[$$-$$ 5, 30] such that x2 + 2(a + 4)x $$-$$ 5a + 64 > 0, for all x$$\in$$R, is :
A
$${7 \over {36}}$$
B
$${2 \over {9}}$$
C
$${1 \over {6}}$$
D
$${1 \over {4}}$$
4
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to :
A
$${{40} \over {243}}$$
B
$${{128} \over {625}}$$
C
$${{80} \over {243}}$$
D
$${{32} \over {625}}$$
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