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

JEE Main 2024 · 5 April · Morning 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 chosen from the set {1,2,3,4,5,6,7,8}\{1,2,3,4,5,6,7,8\}. The probability of this equation having repeated roots is :

Options

  1. A1128\frac{1}{128}
  2. B164\frac{1}{64}
  3. C3256\frac{3}{256}
  4. D3128\frac{3}{128}

Correct answer

B. 164\frac{1}{64}

Step-by-step solution

ax2+bx+c=0a,b,c∈{1,2,3,4,5,6,7,8} Repeated roots D=0⇒b2−4ac=0⇒b2=4ac Prob =88×8×8=164⇒(a,b,c)(1,2,1);(2,4,2);(1,4,4);(4,4,1);(3,6,3);(2,8,8);(8,8,2);(4,8,4)8 case \begin{aligned} & a x^2+b x+c=0 \\ & a, b, c \in\{1,2,3,4,5,6,7,8\} \\ & \text{ Repeated roots } D=0 \\ & \Rightarrow b^2-4 a c=0 \Rightarrow b^2=4 a c \\ & \text{ Prob }=\frac{8}{8 \times 8 \times 8}=\frac{1}{64} \\ & \Rightarrow(a, b, c) \\ & (1,2,1) ;(2,4,2) ;(1,4,4) ;(4,4,1) ;(3,6,3) ; \\ & (2,8,8) ;(8,8,2) ;(4,8,4) \\ & 8 \text{ case }\end{aligned}
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