TS EAMCET · Maths · Quadratic Equation
If \(x\) is real, then the minimum value of \(y=\frac{x^2-x+1}{x^2+x+1}\) is
- A \(3\)
- B \(\frac{1}{3}\)
- C \(\frac{1}{3}\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
Let \(y=\frac{1-x+x^2}{1+x+x^2}\) On differentiating w.r.t. \(x\), we get…
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
- Numerically greatest term in the expansion of \((2 x-3 y)^{11}\) when \(x=\frac{1}{3}\) and \(y=\frac{1}{2}\) isTS EAMCET 2022 Medium
- The centre of the circle \(r^2-4 r(\cos \theta+\sin \theta)-4=0\) in cartesian coordinates isTS EAMCET 2004 Medium
- If \(\vec{a}\) is a vector such that \(\vec{a} \times \hat{i}=\hat{j}+\hat{k}\) and \(\vec{a} \cdot \hat{i}=1\), then equation of the line passing through the point \(\hat{i}+\hat{j}+\hat{k}\) and parallel to \(\vec{a}\) isTS EAMCET 2023 Medium
- \(\int_{-2}^4\left|2-x^2\right| d x=\)TS EAMCET 2025 Medium
- Let \(A(4,3,5), B(1,-2,1), C(3,2,1)\) be the vertices of a triangle \(\mathrm{ABC}\). If the internal bisector of \(\angle \mathrm{BAC}\) meet the side \(\mathrm{BC}\) at \(\mathrm{D}\), then \(\mathrm{CD}=\)TS EAMCET 2023 Medium
- If \(\frac{d y}{d x}+2 x \tan (x-y)=1\), then \(\sin (x-y)\) is equal toTS EAMCET 2012 Medium
More PYQs from TS EAMCET
- The decomposition of \(\mathrm{O}_3(g)\) follows first order kinetics and is given by \[ \mathrm{O}_3(9) \longrightarrow \mathrm{O}_2(9)+\mathrm{O}(9) \] The rate constant for this reaction is \(1.0 \times 10^{-3} \mathrm{~s}^{-1}\). The initial pressure of \(\mathrm{O}_3(g)\) is \(100 \mathrm{~atm}\). What will be the partial pressure (in atm) of \(\mathrm{O}_3, \mathrm{O}_2, \mathrm{O}\) respectively after 38.38 minutes?TS EAMCET 2019 Medium
- Match the following.
TS EAMCET 2019 Medium - If \(X\) is a Poisson variate such that \(P(X=1)=P(X=2)\), then \(P(X=4)\) is equal toTS EAMCET 2008 Easy
- An aeroplane flying with uniform speed horizontally one \(\mathrm{km}\) above the ground is observed at an elevation of \(60^{\circ}\). After \(10 \mathrm{~s}\) if the elevation is observed to be \(30^{\circ}\), then the speed of the plane (in \(\mathrm{km} / \mathrm{h}\) ) isTS EAMCET 2004 Medium
- The coefficient of \(x y^2 z^3\) in the expansion of \((x-2 y+3 z)^6\) isTS EAMCET 2024 Medium
- A pump on the ground floor of a building can pump up water to fill a tank of volume \(36 \mathrm{~m}^3\) in \(30 \mathrm{~min}\). If the tank is \(50 \mathrm{~m}\) above the ground, and the electric power consumed by the pump is \(40 \mathrm{~kW}\), the efficiency of the pump is (Use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) and density of water \(=1000 \mathrm{~kg} / \mathrm{m}^3\) )TS EAMCET 2022 Easy