1
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
$$\frac{5}{715}$$
2
JEE Main 2023 (Online) 15th April Morning Shift
+4
-1
A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is :
A
$\frac{1}{4}$
B
$\frac{9}{50}$
C
$\frac{1}{5}$
D
$\frac{11}{50}$
3
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1
Out of Syllabus

The random variable $$\mathrm{X}$$ follows binomial distribution $$\mathrm{B}(\mathrm{n}, \mathrm{p})$$, for which the difference of the mean and the variance is 1 . If $$2 \mathrm{P}(\mathrm{X}=2)=3 \mathrm{P}(\mathrm{X}=1)$$, then $$n^{2} \mathrm{P}(\mathrm{X}>1)$$ is equal to :

A
15
B
12
C
11
D
16
4
JEE Main 2023 (Online) 13th April Morning Shift
+4
-1

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $$\mathrm{X}$$ denotes the number of tosses of the coin, then the mean of $$\mathrm{X}$$ is :

A
$$\frac{81}{64}$$
B
$$\frac{37}{16}$$
C
$$\frac{21}{16}$$
D
$$\frac{15}{16}$$
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