1
JEE Main 2024 (Online) 1st February Evening Shift
+4
-1
Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :
A
$\frac{9}{35}$
B
$\frac{3}{35}$
C
$\frac{24}{35}$
D
$\frac{18}{35}$
2
JEE Main 2024 (Online) 1st February Morning Shift
+4
-1
A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is :
A
$\frac{2}{5}$
B
$\frac{2}{7}$
C
$\frac{1}{7}$
D
$\frac{1}{5}$
3
JEE Main 2024 (Online) 31st January Evening Shift
+4
-1

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is

A
$$\frac{1}{9}$$
B
$$\frac{2}{9}$$
C
$$\frac{1}{27}$$
D
$$\frac{2}{27}$$
4
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable $$x$$ to be the number of rotten apples in a draw of two apples, the variance of $$x$$ is

A
$$\frac{57}{153}$$
B
$$\frac{40}{153}$$
C
$$\frac{37}{153}$$
D
$$\frac{47}{153}$$
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