1
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
$${1 \over {34}}$$
2
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1 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
$${{46} \over {{6^4}}}$$
3
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1 A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is $${1 \over n}$$. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is :

A
$${7 \over {{2^{11}}}}$$
B
$${7 \over {{2^{12}}}}$$
C
$${3 \over {{2^{10}}}}$$
D
$${{13} \over {{2^{12}}}}$$
4
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1 Let E1 and E2 be two events such that the conditional probabilities $$P({E_1}|{E_2}) = {1 \over 2}$$, $$P({E_2}|{E_1}) = {3 \over 4}$$ and $$P({E_1} \cap {E_2}) = {1 \over 8}$$. Then :

A
$$P({E_1} \cap {E_2}) = P({E_1})\,.\,P({E_2})$$
B
$$P(E{'_1} \cap E{'_2}) = P(E{'_1})\,.\,P(E{_2})$$
C
$$P({E_1} \cap E{'_2}) = P({E_1})\,.\,P({E_2})$$
D
$$P(E{'_1} \cap {E_2}) = P({E_1})\,.\,P({E_2})$$
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