Probability · JEE Advanced previous year questions

2023 5 questions

1. Q62023 · 4 Jun 2023 · Paper 1

   Let $X=\left\{(x,y)\in \mathbb{Z}\times \mathbb{Z}:\frac{x^2}{8}+\frac{y^2}{20}<1\text{ and }{y}^2<5x\right\}$. 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

   1. A.$\frac{71}{220}$
   2. B.$\frac{73}{220}$
   3. C.$\frac{79}{220}$
   4. D.$\frac{83}{220}$
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   Answer: B

2. Q22023 · 4 Jun 2023 · Paper 2

   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

   1. A.$\frac{1}{3}$
   2. B.$\frac{5}{21}$
   3. C.$\frac{4}{21}$
   4. D.$\frac{2}{7}$
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   Answer: B

3. Q102023 · 4 Jun 2023 · Paper 2· Numerical answer

   Let $X$ be the set of all five digit numbers formed using 1,2,2,2,4,4,0. For example, 22240 is in $X$ while 02244 and 44422 are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional probability that an element chosen at random is a multiple of 20 given that it is a multiple of 5. Then the value of $38p$ is equal to ____.

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   Answer: 31

4. Q162023 · 4 Jun 2023 · Paper 2· Numerical answer
   
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   Answer: 23.99 to 24.01

5. Q172023 · 4 Jun 2023 · Paper 2· Numerical answer
   
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   Answer: 0.49 to 0.51