Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20245 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2024 · 5 April · Evening Shift · Mathematics · Probability

The coefficients a, b, c in the quadratic equation a x^2+b x+c=0...

The coefficients a,b,ca, b, c in the quadratic equation ax2+bx+c=0a x^2+b x+c=0 are from the set {1,2,3,4,5,6}\{1,2,3,4,5,6\}. If the probability of this equation having one real root bigger than the other is pp, then 216 p equals :

Options

  1. A57
  2. B76
  3. C38
  4. D19

Correct answer

C. 38

Step-by-step solution

D>0 b2>4acb=3:(a,c)=(1,1)(1,2)(2,1)b=4:(a,c)=(1,1)(1,2)(2,1)(1,3)(3,1)b=5:(a,c)=(1,1)(1,2)(2,1)(1,3)(3,1)(1,4)(4,1)(1,5)(5,1)(1,6)(6,1)(2,3)(3,2)(2,2)b=6:(a,c)=(1,1)(1,2)(2,1)(1,3)(3,1)(1,4)(4,1)(1,5)(5,1)(1,6)(6,1)(2,3)(3,2)(2,4)(4,2)(2,2)\begin{aligned} & \mathrm{D}>0 \\ & \mathrm{~b}^2>4 \mathrm{ac} \\ & \mathrm{b}=3:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1) \\ & \mathrm{b}=4:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1)(1,3)(3,1) \\ & \mathrm{b}=5:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1)(1,3)(3,1)(1,4)(4,1) \\ &(1,5)(5,1)(1,6)(6,1)(2,3)(3,2)(2,2) \\ & \mathrm{b}=6:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1)(1,3)(3,1)(1,4)(4,1) \\ &(1,5)(5,1)(1,6)(6,1)(2,3)(3,2)(2,4)(4,2)(2,2) \end{aligned} fav. cases =38=38 Prob. : 386×6×6\frac{38}{6 \times 6 \times 6}
Practice Probability on Quantrex Academy →

More from Probability

Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red… JEE Advanced 2026A candidate has to go to the examination centre to appear in an examination. The… JEE Main 2026A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement… JEE Main 2026A bag contains (N+1) coins - N fair coins, and one coin with 'Head' on both sides. A coin… JEE Main 2026The probabilities that players A and B of a team are selected for the captaincy for a… JEE Main 2026A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the… JEE Main 2026From a month of 31 days, 3 different dates are selected at random. If the probability… JEE Main 2026A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six… JEE Main 2026A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5… JEE Main 2026The probability distribution of a random variable X is given below : (array… JEE Main 2026A bag contains 10 balls out of which k are red and ( 10-k ) are black, where 0 ≤ k ≤ 10 .… JEE Main 2026Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of… JEE Main 2026From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one… JEE Main 2026Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls.… JEE Main 2026From the first 100 natural numbers, two numbers first a and then b are selected randomly… JEE Main 2026If a random variable x has the probability distribution array |c|c|c|c|c|c|c|c|c| x & 0 &… JEE Main 2026 Full Probability list Probability JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs