AP EAMCET · Maths · Quadratic Equation
Let \(f(x)=x^2+2 x+2, g(x)=-x^2+2 x-1\) and \(a, b\) be the extreme values of \(f(x), g(x)\) respectively. If \(c\) is the extreme value of \(\frac{f}{g}(x)\) (for \(x \neq 1\) ), then \(a+2 b+5 c+4=\)
- A 2
- B 1
- C 4
- D 3
Answer & Solution
Correct Answer
(C) 4
Step-by-step Solution
Detailed explanation
Given, \[ \begin{aligned} f(x) & =x^2+2 x+2 \\ & =x^2+2 x+1+1=(x+1)^2+1 \end{aligned} \] Here, \(f(x)\) \[ \begin{aligned} & \in[1, \infty) \text { and } g(x)=-x^2+2 x-1 \\ & =-\left(x^2-2 x+1\right)=-(x-1)^2 \end{aligned} \] Here, \(g(x) \in(-\infty, 0]\) Now,…
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
- Let \(\alpha\) be a root of \(x^2+x+\mathrm{I}=0\) and suppose that a fair die is thrown 3 times. If \(a, b\) and \(c\) are the numbers shown on the die, then the probability that \(\alpha^a+\alpha^b+\alpha^c=0\), isAP EAMCET 2019 Easy
- A bag contains 4 red and 5 black balls. Another bag contains 3 red and 6 black balls. If one ball is drawn from first bag and two balls from the second bag at random, the probability that out of the three, two are black and one is red, isAP EAMCET 2024 Medium
- If \(a \pm i b\) and \(b \pm a i\) are the roots of \(x^4-10 x^3+50 x^2-130 x+169=0\), then \(\frac{a}{b}+\frac{b}{a}=\)AP EAMCET 2025 Hard
- A rational number is selected at random from the distinct rational numbers of the form \(\mathrm{p} / \mathrm{q}\) formed with p and q belonging to the set \(\{1,2,3,4,5,6\}\). The probability that the rational number selected is a proper fraction, isAP EAMCET 2025 Medium
- If \(l, m, n\) are in arithmetic progression, then the straight line \(l x+m y+n=0\) will pass through the pointAP EAMCET 2008 Medium
- The maximum value of the modulus of \(e^{z^2}\) on the set \(\{z \in C / 0 \leq \operatorname{Re}(z) \leq 1,0 \leq \operatorname{Im}(z) \leq 1\}\) isAP EAMCET 2018 Medium
More PYQs from AP EAMCET
- If some heat is given to a metal of mass 100 g, its temperature rises by \(20^{\circ} \mathrm{C}\). If the same heat is given to 20 g of water, the change in its temperature (in \({ }^{\circ} \mathrm{C}\) ) is (The ratio of specific heat capacities of metal and water is \(1: 10\) )AP EAMCET 2025 Easy
- Which of the following pair of ions have same paramagnetic moment?AP EAMCET 2004 Easy
- If \(\theta\) is any angle, then \(\sin ^2 \theta \cos ^2 \theta=\)AP EAMCET 2022 Easy
- If \(y=\operatorname{Tan}^{-1}\left(\frac{3 x-x^3}{1-3 x^2}\right)+\operatorname{Tan}^{-1}\left(\frac{7 x}{1-12 x^2}\right)\), then at \(x=0, \frac{d y}{d x}=\)AP EAMCET 2025 Medium
- A die is thrown twice. Let A be the event of getting a prime number when the die is thrown first time and \(B\) be the event of getting an even number when the die is thrown second time. Then \(\mathrm{P}(\mathrm{A} / \overline{\mathrm{B}})=\)AP EAMCET 2025 Medium
- Let \(L\) be the line joining the origin to the point of intersection of the lines represented by \(2 x^2-3 x y\) \(-2 y^2+10 x+5 y=0\). If \(L\) is perpendicular to the line \(k x+y+3=0\), then \(k\) is equal toAP EAMCET 2016 Medium