1
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
$${1 \over {4}}$$
2
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Out of Syllabus
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
$${{32} \over {625}}$$
3
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be $${1 \over 2}$$ and probability of occurrence of 0 at the odd place be $${1 \over 3}$$. Then the probability that '10' is followed by '01' is equal to :
A
$${1 \over 18}$$
B
$${1 \over 3}$$
C
$${1 \over 9}$$
D
$${1 \over 6}$$
4
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is :
A
$${4 \over 9}$$
B
$${1 \over 2}$$
C
$${5 \over {12}}$$
D
$${17 \over {36}}$$
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