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Mathematics · Probability

JEE Main 2024 — 5 April, Shift 2 — Question 15

The coefficients a,b,ca, b, c in the quadratic equation ax2+bx+c=0\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{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 :

  1. Option A:

    57

  2. Option B:

    38

    Correct
  3. Option C:

    19

  4. Option D:

    76

Answer: B

Step-by-step solution

D>0\mathrm{D}>0

b2>4ac\mathrm{b}^{2}>4 \mathrm{ac}

b=3:(a,c)=(1,1)(1,2)(2,1)\mathrm{b}=3:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1)

b=4:(a,c)=(1,1)(1,2)(2,1)(1,3)(3,1)\mathrm{b}=4:(\mathrm{a}, \mathrm{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)\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)(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)\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)(1,5)(5,1)(1,6)(6,1)(2,3)(3,2)(2,4)(4,2)(2,2)

fav. cases =38=38

Prob. : 386×6×6\frac{38}{6 \times 6 \times 6}

216p=38216 p= 38

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
5 April, Shift 2
Subject
Mathematics
Chapter
Probability
Topic
Problems based on P & C

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