1
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probability P(x $$\ge$$ 5 | x > 2) is :
A
$${{125} \over {216}}$$
B
$${{11} \over {36}}$$
C
$${{5} \over {6}}$$
D
$${{25} \over {36}}$$
2
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
Two fair dice are thrown. The numbers on them are taken as $$\lambda$$ and $$\mu$$, and a system of linear equations

x + y + z = 5

x + 2y + 3z = $$\mu$$

x + 3y + $$\lambda$$z = 1

is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :
A
$$p = {1 \over 6}$$ and $$q = {1 \over 36}$$
B
$$p = {5 \over 6}$$ and $$q = {5 \over 36}$$
C
$$p = {5 \over 6}$$ and $$q = {1 \over 36}$$
D
$$p = {1 \over 6}$$ and $$q = {5 \over 36}$$
3
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, B occurs) = $${5 \over 9}$$, is :
A
$${1 \over 3}$$
B
$${2 \over 9}$$
C
$${4 \over 9}$$
D
$${5 \over 12}$$
4
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability. the smallest value of n, so that the probability of guessing at least 'n' correct answers is less than $${1 \over 2}$$, is :
A
5
B
6
C
3
D
4
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