1
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

If a point A(x, y) lies in the region bounded by the y-axis, straight lines 2y + x = 6 and 5x $$-$$ 6y = 30, then the probability that y < 1 is :

A
$${1 \over 6}$$
B
$${5 \over 6}$$
C
$${2 \over 3}$$
D
$${6 \over 7}$$
2
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

Five numbers $${x_1},{x_2},{x_3},{x_4},{x_5}$$ are randomly selected from the numbers 1, 2, 3, ......., 18 and are arranged in the increasing order $$({x_1} < {x_2} < {x_3} < {x_4} < {x_5})$$. The probability that $${x_2} = 7$$ and $${x_4} = 11$$ is :

A
$${1 \over {136}}$$
B
$${1 \over {72}}$$
C
$${1 \over {68}}$$
D
$${1 \over {34}}$$
3
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1
Out of Syllabus

Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(x = 4), then the sum of the mean and the variance of X is :

A
$${105 \over {16}}$$
B
$${7\over {16}}$$
C
$${77\over {36}}$$
D
$${49\over {16}}$$
4
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1
Out of Syllabus

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is :

A
$${{275} \over {{6^5}}}$$
B
$${{36} \over {{5^4}}}$$
C
$${{181} \over {{5^5}}}$$
D
$${{46} \over {{6^4}}}$$
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