1
JEE Main 2024 (Online) 30th January Morning Shift
+4
-1

Two integers $$x$$ and $$y$$ are chosen with replacement from the set $$\{0,1,2,3, \ldots, 10\}$$. Then the probability that $$|x-y|>5$$, is :

A
$$\frac{31}{121}$$
B
$$\frac{60}{121}$$
C
$$\frac{62}{121}$$
D
$$\frac{30}{121}$$
2
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

An integer is chosen at random from the integers $$1,2,3, \ldots, 50$$. The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is

A
$$\frac{8}{25}$$
B
$$\frac{9}{50}$$
C
$$\frac{14}{25}$$
D
$$\frac{21}{50}$$
3
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

A
$$\frac{5}{11}$$
B
$$\frac{5}{6}$$
C
$$\frac{1}{6}$$
D
$$\frac{6}{11}$$
4
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is :

A
$$\frac{3}{256}$$
B
$$\frac{5}{256}$$
C
$$\frac{3}{715}$$
D
$$\frac{5}{715}$$
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