TS EAMCET · Maths · Probability
Two numbers \(b\) and \(c\) are chosen at random in succession without replacement from the set \(\{1,2,3, \ldots, 9\}\). Then the probability that \(\mathrm{x}^2+\mathrm{bx}+\mathrm{c}>0, \forall \mathrm{x} \in \mathbb{R}\) is
- A \(\frac{29}{72}\)
- B \(\frac{32}{81}\)
- C \(\frac{45}{143}\)
- D \(\frac{82}{125}\)
Answer & Solution
Correct Answer
(A) \(\frac{29}{72}\)
Step-by-step Solution
Detailed explanation
\(x^2+b x+c>0, \forall x \in R\) \(\begin{aligned} \Rightarrow & D < 0 \\ & b^2-4 c < 0 \\ & b^2 < 4 c \end{aligned}\) Possible outcomes : \begin{array}{|c|c|c|} \hline \boldsymbol{b} & \boldsymbol{c} & Number of pairs \\ \hline 1 & 2,3,4,5,6,7,8,9 & 8 \\ \hline 2 &…
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
- For \(x \in R\), the least value of \(\frac{x^2-6 x+5}{x^2+2 x+1}\) isTS EAMCET 2010 Medium
- \(\operatorname{Arg}\left(\sin \frac{6 \pi}{5}+i\left(1+\cos \frac{6 \pi}{5}\right)\right)=\)TS EAMCET 2023 Medium
- If \(\sqrt{\frac{y}{x}}+\sqrt{\frac{x}{y}}=2\), then \(\frac{d y}{d x}\) is equal toTS EAMCET 2013 Easy
- If \(\int \sin ^{-1}\left(\sqrt{\frac{x}{a+x}}\right) d x=A(x)+\) constant, then \(A(x)=\)TS EAMCET 2018 Medium
- If \(\sin \mathrm{A}=-\frac{60}{61}, \cot \mathrm{~B}=-\frac{40}{9}\) and neither A nor B is in \(4^{\text {th }}\) quadrant then \(6 \cot A+4 \sec B=\)TS EAMCET 2025 Medium
- If \(z_1=2-3 i\) and \(z_2=-1+i\), then the locus of a point \(P\) represented by \(z=x+i y\) in the argand plane satisfying the equation \(\arg \left(\frac{z-z_1}{z-z_2}\right)=\frac{\pi}{2}\) isTS EAMCET 2018 Medium
More PYQs from TS EAMCET
- Dehydration of an organic acid X with concentrated \(\mathrm{H}_2 \mathrm{SO}_4\) at 373 K gives \(\mathrm{H}_2 \mathrm{O}\) and gas Y. The hybridisation of the carbon in Y and nature of Y are respectivelyTS EAMCET 2025 Medium
- When same quantity of electricity is passed through aqueous \(\mathrm{AgNO}_3\) and \(\mathrm{H}_2 \mathrm{SO}_4\) solutions connected in series, \(5.04 \times 10^{-2} \mathrm{~g}\) of \(\mathrm{H}_2\) is liberated. What is the mass of silver (in grams) deposited ? (Eq. wts. of hydrogen \(=1.008\), silver \(=108)\)TS EAMCET 2008 Easy
- In an experiment on photoelectric emission from a metallic surface, wavelength of incident light is \(2 \times 10^{-7} \mathrm{~m}\) and stopping potential is \(2.5 \mathrm{~V}\). The threshold frequency of the metal (in \(\mathrm{Hz}\) ) approximately (charge of electron \(e=1.6 \times 10^{-19} \mathrm{C}\), Planck's constant \(\left.h=6.6 \times 10^{-34} \mathrm{~J}-\mathrm{s}\right)\)TS EAMCET 2007 Easy
- A polygon has 54 diagonals. Then, the number of its sides isTS EAMCET 2010 Easy
- The coefficient of \(x^5\) in the expansion of \(\left(1+x^2\right)^5(1+x)^4\), is :TS EAMCET 2003 Medium
- If \(\frac{2 x^3+3 x^2+3 x+5}{\left(x^2+1\right)\left(x^2+2\right)}\) is expanded in terms of the powers of \(x\), then the coefficient of \(x^5\) isTS EAMCET 2023 Medium