1
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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 $$q = {5 \over 36}$$
2
JEE Main 2021 (Online) 26th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$${5 \over 12}$$
3
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
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
4
JEE Main 2021 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The probability that a randomly selected 2-digit number belongs to the set {n $$\in$$ N : (2n $$-$$ 2) is a multiple of 3} is equal to :
A
$${1 \over 6}$$
B
$${2 \over 3}$$
C
$${1 \over 2}$$
D
$${1 \over 3}$$
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