Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Probability

NDA 2022 · Mathematics · Probability

Two numbers x and y are chosen at random from a set of first 10...

Two numbers xx and yy are chosen at random from a set of first 10 natural numbers. What is the probability that (x+y)(x+y) is divisible by 4 ?

Options

  1. A15\frac{1}{5}
  2. B29\frac{2}{9}
  3. C845\frac{8}{45}
  4. D745\frac{7}{45}

Correct answer

B. 29\frac{2}{9}

Step-by-step solution

n(s)=10×9=90n(s)=10 \times 9=90 Sum of x+yx+y is divisible by 4 are (1,3),(1,7),(2,6),(2,10),(3,1),(3,5),(3,9),(4,8)(5,3),(5,7),(6,2),(6,10),(7,1),(7,5),(7,9),(84),(9,3),(9,7),(10,2),(10,6)n(E)=20∴P(E)=2090=29\begin{aligned} & (1,3),(1,7),(2,6),(2,10),(3,1),(3,5),(3,9),(4,8) \\ & (5,3),(5,7),(6,2),(6,10),(7,1),(7,5),(7,9),(8 \\ & 4),(9,3),(9,7),(10,2),(10,6) \\ & n(E)=20 \\ & \therefore P(E)=\frac{20}{90}=\frac{2}{9} \end{aligned}
Practice Probability on Quantrex Academy →

More from Probability

Passage: Four dice are rolled. Question: What is the probability that getting a total of… NDA 2026Three events A , B and C are such that A and B are disjoint, A and C are independent, B… NDA 2026Passage: Let A , B , C and D be mutually exclusive and exhaustive events and… NDA 2026Passage: Four dice are rolled. Question: What is the probability that getting a total of… NDA 2026For a Binomial distribution with mean 6 and standard deviation 2 , what is the value of… NDA 2026Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3… NDA 2026In an entrance test there are multiple choice questions. There are four options for each… NDA 2026Passage: Let A , B , C and D be mutually exclusive and exhaustive events and… NDA 2026Consider the following statements in respect of the events A , B , C : I. (A B C) ( A B C… NDA 2026Passage: Let A , B , C and D be mutually exclusive and exhaustive events and… NDA 2026The probability that a family owns a laptop is 0.68 ; that it also owns a desktop is 0.56… NDA 2025An urn contains 10 white and 5 red balls. If two balls are drawn at random, then what is… NDA 2025An urn contains 5 white, 6 red and 4 blue balls. Three balls are drawn at random. What is… NDA 2025Under which of the following conditions may binomial distribution be used? I. The number… NDA 2025Three faces of a die are black, two faces are white and one face is red. The die is… NDA 2025A person X speaks the truth 4 out of 5 times and person Y speaks the truth 5 out of 6… NDA 2025 Full Probability list Probability JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs