Probability · JEE Main previous year questions

2019 15 questions

1. Q222019 · 12 Apr 2019 · Shift 1

   If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :

   1. A.$\frac{1}{10}$
   2. B.$\frac{3}{10}$
   3. C.$\frac{3}{20}$
   4. D.$\frac{1}{5}$
   Show answer

   Answer: A

2. Q72019 · 12 Apr 2019 · Shift 2

   A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :

   1. A.$\frac{1}{4}\text{ loss}$
   2. B.$\frac{1}{2}\text{ gain}$
   3. C.$\frac{1}{2}\text{ loss}$
   4. D.2 gain
   Show answer

   Answer: C

3. Q282019 · 12 Apr 2019 · Shift 2

   For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate solve any problem is $\frac{4}{5}$, then the probability that he is unable to solve less than two problems is :

   1. A.$\frac{164}{25}{\left(\frac{1}{5}\right)}^{48}$
   2. B.$\frac{316}{25}{\left(\frac{4}{5}\right)}^{48}$
   3. C.$\frac{201}{5}{\left(\frac{1}{5}\right)}^{49}$
   4. D.$\frac{54}{5}{\left(\frac{4}{5}\right)}^{49}$
   Show answer

   Answer: D

4. Q82019 · 10 Apr 2019 · Shift 1

   Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is :

   1. A.$\frac{1}{10}$
   2. B.$\frac{1}{17}$
   3. C.$\frac{1}{11}$
   4. D.$\frac{1}{12}$
   Show answer

   Answer: C

5. Q52019 · 10 Apr 2019 · Shift 2

   Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :

   1. A.6
   2. B.5
   3. C.8
   4. D.7
   Show answer

   Answer: D

6. Q172019 · 9 Apr 2019 · Shift 1

   Four persons can hit a target correctly with probabilities $\frac{1}{2},\frac{1}{3},\frac{1}{4}$ and $\frac{1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is :

   1. A.$\frac{25}{32}$
   2. B.$\frac{25}{192}$
   3. C.$\frac{1}{192}$
   4. D.$\frac{7}{32}$
   Show answer

   Answer: A

7. Q12019 · 8 Apr 2019 · Shift 2

   The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is :

   1. A.2
   2. B.3
   3. C.4
   4. D.5
   Show answer

   Answer: C

8. Q22019 · 12 Jan 2019 · Shift 1

   In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :

   1. A.$\frac{200}{6^5}$
   2. B.$\frac{225}{6^5}$
   3. C.$\frac{150}{6^5}$
   4. D.$\frac{175}{6^5}$
   Show answer

   Answer: D

9. Q22019 · 12 Jan 2019 · Shift 2

   There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is :

   1. A.12
   2. B.9
   3. C.7
   4. D.11
   Show answer

   Answer: A

10. Q32019 · 12 Jan 2019 · Shift 2

    In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :

    1. A.$\frac{400}{3}$ loss
    2. B.0
    3. C.$\frac{400}{9}$ loss
    4. D.$\frac{400}{3}$ gain
    Show answer

    Answer: B

11. Q122019 · 12 Jan 2019 · Shift 2

    In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the students selected has opted neither for NCC nor for NSS is :

    1. A.$\frac{1}{3}$
    2. B.$\frac{1}{6}$
    3. C.$\frac{2}{3}$
    4. D.$\frac{5}{6}$
    Show answer

    Answer: B

12. Q162019 · 11 Jan 2019 · Shift 2

    Let $S=\{1,2,\dots ,20\}$. A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is "nice" is :

    1. A.$\frac{5}{2^{20}}$
    2. B.$\frac{7}{2^{20}}$
    3. C.$\frac{4}{2^{20}}$
    4. D.$\frac{6}{2^{20}}$
    Show answer

    Answer: A

13. Q292019 · 11 Jan 2019 · Shift 2

    A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then $\left(\frac{\text{mean of }X}{\text{standard deviation of }X}\right)$ is equal to :

    1. A.4
    2. B.$3\sqrt{2}$
    3. C.$\frac{4\sqrt{3}}{3}$
    4. D.$4\sqrt{3}$
    Show answer

    Answer: D

14. Q32019 · 9 Jan 2019 · Shift 1

    The value of ${\int }_0^{\pi }|\cos x{|}^{3}dx$ is :

    1. A.$\frac{4}{3}$
    2. B.$-\frac{4}{3}$
    3. C.0
    4. D.$\frac{2}{3}$
    Show answer

    Answer: A

15. Q252019 · 9 Jan 2019 · Shift 1

    Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then $P(X=1)+P(X=2)$ equals :

    1. A.$\frac{25}{169}$
    2. B.$\frac{49}{169}$
    3. C.$\frac{24}{169}$
    4. D.$\frac{52}{169}$
    Show answer

    Answer: A