Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

If the numbers appeared on the two throwsof a fair six faced die are $\mathrm{\alpha \text { and } \beta}$ , then the probability that $\mathrm{x^{2}+\alpha x+\beta>0}$ , for all $\mathrm{x \in \mathbf{R}}$ is :
Option: 1
$\frac{17}{36}$

Option: 2
$\frac{4}{9}$

Option: 3
$\frac{1}{2}$

Option: 4
$\frac{19}{36}$

Answers (1)

best_answer

$\mathrm{x^{2}+\alpha x+\beta>0, \forall x \in R} \\$

$\mathrm{D=\alpha^{2}-4 \beta<0} \\$

$\mathrm{\alpha^{2}<4 \beta}$

Total Cases $\mathrm{=6\times6=36}$

$\text { fav. cases }=\beta=1, \alpha=1 \\$

$\beta=2, \alpha=1,2 \\$

$\beta=3, \alpha=1,2,3 \\$

$\beta=4, \alpha=1,2,3 \\$

$\beta=5, \alpha=1,2,3,4 \\$

$\beta=6, \alpha=1,2,3,4$

Total Favourite cases $=17$

$\mathrm{P(x)=\left(\frac{17}{36}\right)}$

Hence correct option is 1

Posted by

shivangi.shekhar

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M HCl. If pK_b of ammonia solution is 4.75, the pH of the mixture will be :
Option: 1 3.75
Option: 2 4.75

Trending Articles/News

anam-khan

JEE Main 2026: IIT Roorkee’s ECE emerges as top choice after CSE; closing rank rises

anam-khan

JEE Main 2026 application correction begins on jeemain.nta.nic.in; edit details by December 2

anam-khan

JEE Mains 2026 LIVE: NTA to conduct session 1 from January 21 to 30; exam pattern, syllabus

Latest Question