JEE Mains · Maths · STD 12 - 13. probability
If the numbers appeared on the two throws of a fair six faced die are \(\alpha\) and \(\beta\), then the probability that \(x ^{2}+\alpha x+\beta>0\), for all \(x \in R\), is.
- A \(\frac{17}{36}\)
- B \(\frac{4}{9}\)
- C \(\frac{1}{2}\)
- D \(\frac{19}{36}\)
Answer & Solution
Correct Answer
(A) \(\frac{17}{36}\)
Step-by-step Solution
Detailed explanation
\(x^{2}+\alpha x+\beta>0, \forall x \in R\) \(D=\alpha^{2}-4 \beta<0\) \(\alpha^{2}<4 \beta\) Total cases \(=6 \times 6=36\) Fav. cases \(=\beta=1, \alpha=1\) \(\beta=2, \alpha=1,2\) \(\beta=3, \alpha=1,2,3\) \(\beta=4, \alpha=1,2,3\) \(\beta=5, \alpha=1,2,3,4\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The sum to \(20\) terms of the series \(2.2^2-3^2+2.4^2-5^2+2.6^2-\ldots \ldots\) is equal to \(........\).JEE Mains 2023 Hard
- If \(\frac{{dy}}{{dx}} + y\tan x = \sin 2x\) and \(y(0)\,=1\) , then \(y(\pi)\) is equal toJEE Mains 2014 Hard
- The interval in which the function \(\mathrm{f}(\mathrm{x})=\mathrm{x}^{\mathrm{x}}, \mathrm{x}>0\), is strictly increasing isJEE Mains 2024 Medium
- A bag contains \(8\) balls, whose colours are either white or black. \(4\) balls are drawn at random without replacement and it was found that \(2\) balls are white and other \(2\) balls are black. The probability that the bag contains equal number of white and black balls is :JEE Mains 2024 Medium
- Let a circle \(C\) have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of \(C\) on the line \(x + y = 1\) is \(\sqrt{14}\), then the square of the radius of \(C\) is _______.JEE Mains 2026 Hard
- Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, \( x>y \) be 8 and 16 respectively. Two numbers are chosen from {1, 2, 3, x-4, y, 5} one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is:JEE Mains 2026 Easy
More PYQs from JEE Mains
- Let \(Q(a,b,c)\) be the image of the point \(P(3,2,1)\) in the line \(\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}.\) Then the distance of Q from the line \(\frac{x-9}{3}=\frac{y-9}{2}=\frac{z-5}{-2}\) isJEE Mains 2026 Hard
- If the mean deviation about the mean of the numbers \(1,2,3, \ldots ., n\), where \(n\) is odd, is \(\frac{5(n+1)}{n}\), then \(n\) is equal toJEE Mains 2022 Medium
- If the probability that the random variable \(X\) takes values \(x\) is given by \(P ( X = x )= k ( x +1) 3^{- x }, x =0\), \(1,2,3 \ldots\), where \(k\) is a constant, then \(P ( X \geq 2)\) is equal toJEE Mains 2023 Hard
- If the length of the perpendicular from the point \((\beta , 0, \beta )\, (\beta \neq 0)\) to the line \(\frac{x}{1} = \frac{{y - 1}}{0} = \frac{{z + 1}}{{ - 1}}\) is \(\sqrt {\frac{3}{2}} \), then \(\beta \) is equal toJEE Mains 2019 Medium
- Lets \(S=\{z \in C:|z-1|=1\) and \((\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2 \sqrt{2}\}\). Let \(\mathrm{z}_1, \mathrm{z}_2\) \(\in S\) be such that \(\left|z_1\right|=\max _{z \in S}|z|\) and \(\left|z_2\right|=\min _{z \in S}|z|\). Then \(\left|\sqrt{2} z_1-z_2\right|^2\) equals :JEE Mains 2024 Hard
- The value of \(\int_{-\pi}^\pi \frac{2 y(1+\sin y)}{1+\cos ^2 y} d y\) is :JEE Mains 2024 Hard