1
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
In a workshop, there are five machines and the probability of any one of them to be out of service on a day is $${{1 \over 4}}$$ . If the probability that at most two machines will be out of service on the same day is $${\left( {{3 \over 4}} \right)^3}k$$, then k is equal to :
A
$${{{17} \over 4}}$$
B
$${{{17} \over 2}}$$
C
$${{{17} \over 8}}$$
D
4
2
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value of k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value -1. Then the expected value of X, is:
A
$$- {3 \over {16}}$$
B
$$- {1 \over 8}$$
C
$${1 \over 8}$$
D
$${3 \over {16}}$$
3
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :
A
$${1 \over 4}$$ loss
B
$${1 \over 2}$$ gain
C
$${1 \over 2}$$ loss
D
2 gain
4
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate solve any problem is $${4 \over 5}$$ , then the probability that he is unable to solve less than two problems is :
A
$${{164} \over {25}}{\left( {{1 \over 5}} \right)^{48}}$$
B
$${{316} \over {25}}{\left( {{4 \over 5}} \right)^{48}}$$
C
$${{201} \over 5}{\left( {{1 \over 5}} \right)^{49}}$$
D
$${{54} \over 5}{\left( {{4 \over 5}} \right)^{49}}$$
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