AP EAMCET · Maths · Application of Derivatives
If \(a\) and \(b\) are the maximum and minimum values of the quadratic expressions \(1-2 x-5 x^2\) and \(x^2-2 x+5\) respectively, then the set of all values of \(x\) for which the expression \(5 a x^2+b x+7\) is positive, is
- A \((a, b)\)
- B \((-\infty, 7)\)
- C \((5, \infty)\)
- D \((-\infty, \infty)\)
Answer & Solution
Correct Answer
(D) \((-\infty, \infty)\)
Step-by-step Solution
Detailed explanation
The maximum value of the expression \(\begin{aligned} & 1-2 x-5 x^2 \\ & a=-\frac{4+20}{4(-5)}=\frac{6}{5} \end{aligned}\) and minimum value of the expression \(x^2-2 x+5\), \(b=-\frac{4-20}{4}=4\) Now, the given quadratic expression \(5 a x^2+b x+7\) at \(a=\frac{6}{5}\) and…
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
- \(\int \frac{x}{\left(1-x^2\right) \sqrt{2-x^2}} d x=\)AP EAMCET 2025 Medium
- If \(\cos \alpha+\cos \beta=a, \sin \alpha+\sin \beta=b\) and \(\alpha-\beta=2 \theta\), then \(\frac{\cos 3 \theta}{\cos \theta}=\)AP EAMCET 2017 Hard
- \(\int \frac{1}{x^2\left(\sqrt{1+x^2}\right)} d x=\)AP EAMCET 2024 Easy
- The locus of the point which is equidistant from the point \((1,1)\) and the line \(\mathrm{x}+\mathrm{y}+1=0\) isAP EAMCET 2023 Easy
- The harmonic conjugate of \((2,3,4)\) with respect to the points \((3,-2,2)\) and \((6,-17,-4)\) isAP EAMCET 2020 Hard
- The value of isAP EAMCET 2022 Medium
More PYQs from AP EAMCET
- The graph between two quantities \(P\) and \(Q\) is a straight line whenAP EAMCET 2020 Easy
- For an \(L E D\) to emit light in visible region of the electromagnetic spectrum, it can have energy band gap in the range of, (Plank's constant, \(h=6.6 \times 10^{-34} \mathrm{Js}\) and speed of light, \(e=3 \times 10^8 \mathrm{~ms}^{-1}\) in vacuum)AP EAMCET 2019 Medium
- If \(\int \frac{x}{x \tan x+1} \mathrm{~d} x=\log \mathrm{f}(x)+\mathrm{k}\), then \(\mathrm{f}\left(\frac{\pi}{4}\right)=\)AP EAMCET 2025 Medium
- If \(X=x+h, Y=y+k\) transforms \(\frac{d y}{d x}=\frac{2 x+3 y-7}{3 x+2 y-8}\) to a homogeneous differential equation, then \((\mathrm{h}, \mathrm{k})=\)AP EAMCET 2023 Medium
- If the equation \(2 x^2+k x y-6 y^2+3 x+y+1=0\), \((k>0)\) represents a pair of straight lines, then their point of intersection isAP EAMCET 2021 Medium
- \(\mathrm{AU}^{235}\) nuclear reactor generates energy at a rate of \(3.70 \times 10^7 \mathrm{~J} / \mathrm{s}\). Each fission liberates \(185 \mathrm{MeV}\) useful energy. If the reactor has to operate for \(144 \times 10^4 \mathrm{~s}\), then, the mass of the fuel needed is (Assume Avogadro's number \(\left.=6 \times 10^{23} \mathrm{~mol}^{-1}, 1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}\right)\)AP EAMCET 2013 Medium