1
JEE Advanced 2024 Paper 1 Online
+3
-1

A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question, he gives the correct answer. Assume that the probability of the student giving the correct answer for a question, given that he has guessed it, is $\frac{1}{2}$. Also assume that the probability of the answer for a question being guessed, given that the student's answer is correct, is $\frac{1}{6}$. Then the probability that the student knows the answer of a randomly chosen question is :

A
$\frac{1}{12}$
B
$\frac{1}{7}$
C
$\frac{5}{7}$
D
$\frac{5}{12}$
2
JEE Advanced 2023 Paper 2 Online
+3
-1
Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is $\frac{1}{3}$, then the probability that the experiment stops with head is :
A
$\frac{1}{3}$
B
$\frac{5}{21}$
C
$\frac{4}{21}$
D
$\frac{2}{7}$
3
JEE Advanced 2023 Paper 1 Online
+3
-1
Let $X=\left\{(x, y) \in \mathbb{Z} \times \mathbb{Z}: \frac{x^2}{8}+\frac{y^2}{20}<1\right.$ and $\left.y^2<5 x\right\}$. Three distinct points $P, Q$ and $R$ are randomly chosen from $X$. Then the probability that $P, Q$ and $R$ form a triangle whose area is a positive integer, is :
A
$\frac{71}{220}$
B
$\frac{73}{220}$
C
$\frac{79}{220}$
D
$\frac{83}{220}$
4
JEE Advanced 2022 Paper 2 Online
+3
-1
Suppose that

Box-I contains 8 red, 3 blue and 5 green balls,

Box-II contains 24 red, 9 blue and 15 green balls,

Box-III contains 1 blue, 12 green and 3 yellow balls,

Box-IV contains 10 green, 16 orange and 6 white balls.

A ball is chosen randomly from Box-I; call this ball $b$. If $b$ is red then a ball is chosen randomly from Box-II, if $b$ is blue then a ball is chosen randomly from Box-III, and if $b$ is green then a ball is chosen randomly from Box-IV. The conditional probability of the event 'one of the chosen balls is white' given that the event 'at least one of the chosen balls is green' has happened, is equal to

A
$\frac{15}{256}$
B
$\frac{3}{16}$
C
$\frac{5}{52}$
D
$\frac{1}{8}$
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