1

JEE Advanced 2022 Paper 1 Online

MCQ (Single Correct Answer)

+3

-1

Two players, $$P_{1}$$ and $$P_{2}$$, play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let $$x$$ and $$y$$ denote the readings on the die rolled by $$P_{1}$$ and $$P_{2}$$, respectively. If $$x>y$$, then $$P_{1}$$ scores 5 points and $$P_{2}$$ scores 0 point. If $$x=y$$, then each player scores 2 points. If $$x < y$$, then $$P_{1}$$ scores 0 point and $$P_{2}$$ scores 5 points. Let $$X_{i}$$ and $$Y_{i}$$ be the total scores of $$P_{1}$$ and $$P_{2}$$, respectively, after playing the $$i^{\text {th }}$$ round.

List-I | List-II |
---|---|

(I) Probability of $$\left(X_{2} \geq Y_{2}\right)$$ is | (P) $$\frac{3}{8}$$ |

(II) Probability of $$\left(X_{2}>Y_{2}\right)$$ is | (Q) $$\frac{11}{16}$$ |

(III) Probability of $$\left(X_{3}=Y_{3}\right)$$ is | (R) $$\frac{5}{16}$$ |

(IV) Probability of $$\left(X_{3}>Y_{3}\right)$$ is | (S) $$\frac{355}{864}$$ |

(T) $$\frac{77}{432}$$ |

The correct option is:

2

JEE Advanced 2021 Paper 1 Online

MCQ (Single Correct Answer)

+3

-1

Consider three sets E

Let G

Let E

_{1}= {1, 2, 3}, F_{1}= {1, 3, 4} and G_{1}= {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E_{1}, and let S_{1}denote the set of these chosen elements. Let E_{2}= E_{1}$$-$$ S_{1}and F_{2}= F_{1}$$\cup$$ S_{1}. Now two elements are chosen at random, without replacement, from the set F_{2}and let S_{2}denote the set of these chosen elements.Let G

_{2}= G_{1}$$\cup$$ S_{2}. Finally, two elements are chosen at random, without replacement, from the set G_{2}and let S_{3}denote the set of these chosen elements.Let E

_{3}= E_{2}$$\cup$$ S_{3}. Given that E_{1}= E_{3}, let p be the conditional probability of the event S_{1}= {1, 2}. Then the value of p is3

JEE Advanced 2020 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

Let C

_{1}and C_{2}be two biased coins such that the probabilities of getting head in a single toss are $${{2 \over 3}}$$ and $${{1 \over 3}}$$, respectively. Suppose $$\alpha $$ is the number of heads that appear when C_{1}is tossed twice, independently, and suppose $$\beta $$ is the number of heads that appear when C_{2}is tossed twice, independently. Then the probability that the roots of the quadratic polynomial x^{2}$$-$$ ax + $$\beta $$ are real and equal, is4

JEE Advanced 2018 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

There are five students S

(There are two questions based on Paragraph "A", the question given below is one of them)

The probability that, on the examination day, the student S

_{1}, S_{2}, S_{3}, S_{4}and S_{5}in a music class and for them there are five seats R_{1}, R_{2}, R_{3}, R_{4}and R_{5}arranged in a row, where initially the seat R_{i}is allotted to the student S_{i}, i = 1, 2, 3, 4, 5. But, on the examination day, the five students are randomly allotted the five seats.(There are two questions based on Paragraph "A", the question given below is one of them)

The probability that, on the examination day, the student S

_{1}gets the previously allotted seat R_{1}, and NONE of the remaining students gets the seat previously allotted to him/her isQuestions Asked from Probability (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

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