AP EAMCET · Maths · Basic of Mathematics
If \(\frac{2 x^3+x^2-5}{x^4-25}=\frac{A x+B}{x^2-5}+\frac{C x+1}{x^2+5}\), then \((A, B, C)\) equals to
- A \((1,1,1)\)
- B \((1,1,0)\)
- C \((1,0,1)\)
- D \((1,2,1)\)
Answer & Solution
Correct Answer
(C) \((1,0,1)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {Given, } \frac{2 x^3+x^2-5}{x^4-25}=\frac{A x+B}{x^2-5}+\frac{C x+1}{x^2+5} \\ & \therefore 2 x^3+x^2-5=(A x+B)\left(2 x^2+5\right) \\ & +(C x+1)\left(x^2-5\right) \\ & \Rightarrow 2 x^3+x^2-5=A x^3+5 A x+B x^2+5 B \\ & +C x^3-5 C x+x^2-5 \\ &…
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 point to which the origin is to be shifted to eliminate \(x\) and \(y\) terms of the equation \(4 x^2+9 y^2-8 x+36 y+4=0\) isAP EAMCET 2017 Medium
- The area (in sq. units) of the triangle formed by the lines \(x^2-3 x y+y^2=0\) and \(x+y+1=0\), isAP EAMCET 2014 Medium
- \(A\) and \(B\) are independent events of a random experiment if and only ifAP EAMCET 2023 Easy
- The sum of the coefficients of \(x^{32}\) and \(x^{-31}\) in \(\left(x^4-\frac{1}{x^3}\right)^{15}\) is \(\left(x^4-\frac{1}{x^3}\right)^{15}\)AP EAMCET 2018 Easy
- The value of the integral \(\int_0^4 \frac{d x}{1+x^2}\) obtained by using Trapezoidal rule with \(h=1\) isAP EAMCET 2012 Easy
- If \(f(x)=x^\alpha \log x\) and \(f(0)=0\), then the value of \(\alpha\) for which Rolle's theorem can be applied in \([0,1]\) isAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- Two long straight parallel conductors A and B carrying currents 4.5 A and 8 A respectively are separated by 25 cm in air. The resultant magnetic field at a point which is at a distance of 15 cm from conductor A and 20 cm from conductor B isAP EAMCET 2024 Easy
- The time period of revolution of a satellite ( T ) around the earth depends on the radius of the circular orbit ( R ), mass of the earth (M) and universal gravitational constant (G). The expression for T , using dimensional analysis is ( K is constant of proportionality)AP EAMCET 2024 Medium
- The interval in which the function \(f(x)=2 x^2-\log x\), for \(x>0\) decreases, isAP EAMCET 2018 Medium
- A rod of length 2l slides with its ends on two perpendicular lines, then the locus of its mid-point isAP EAMCET 2021 Medium
- Which of the following statements is not correct?
1. Reduction of alumina to give aluminium by magnesium is thermodynamically feasible.
2. The point of intersection of \(\mathrm{AlO}_3\) and \(\mathrm{MgO}\) curves in Ellingham diagram is below \(1665 \mathrm{~K}\).
3. Use of magnesium as reducing agent in metallurgy of aluminium is economical.
4. Ellingham diagram represents the graphical plot of Gibbs energy vs temperature for the formation of the oxides of common metals and reducing agents.AP EAMCET 2020 Medium - In the magnetic meridian of a certain place, the vertical component of the earth's magnetic field is \(0.3464 \mathrm{G}\) and the dip angle is \(30^{\circ}\). The horizontal component of the earth's magnetic field at this location isAP EAMCET 2018 Easy