AP EAMCET · Maths · Basic of Mathematics
If \(\frac{5 x^2+2}{x^3+x}=\frac{A_1}{x}+\frac{A_2 x+A_3}{x^2+1}\), then \(\left(A_1, A_2, A_3\right)=\)
- A (0, 2, 3)
- B (3, 0, 2)
- C (2, 3, 0)
- D (2, 0, 3)
Answer & Solution
Correct Answer
(C) (2, 3, 0)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {Given that, } \frac{5 x^2+2}{x^3+x}=\frac{A_1}{x}+\frac{A_2 x+A_3}{x^2+1} \\ & \Rightarrow \frac{5 x^2+2}{x\left(x^2+1\right)}=\frac{A_1\left(x^2+1\right)+\left(A_2 x+A_3\right) x}{x\left(x^2+1\right)} \\ & \Rightarrow 5 x^2+2=A_1\left(x^2+1\right)+A_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
- If \(y=\operatorname{Sin}^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)\) and \(\frac{-3 \pi}{2} < x < \frac{-\pi}{2}\), then \(\frac{d y}{d x}=\)AP EAMCET 2025 Medium
- Gas is being pumed into a spherical balloon at the rate of \(30 \mathrm{ft}^3 / \mathrm{min}\). The rate at which the radius increase when it reaches the value \(15 \mathrm{ft}\), is :AP EAMCET 2003 Medium
- If the projections of the line segment on and planes are respectively, then the projection of on axis isAP EAMCET 2021 Easy
- The points \((5,-4,5),(-3,-3,2)\) and \((-1,-6,8)\) form ......AP EAMCET 2020 Easy
- AP EAMCET 2021 Medium
- If \(A=\left[\begin{array}{cc}-2 & 1 \\ 3 & 4\end{array}\right]\) and \(\mathrm{A}=\mathrm{P}+\mathrm{Q}\), where \(\mathrm{P}\) is symmetric matrix and \(\mathrm{Q}\) is Skew-Symmetric matrix; then Q isAP EAMCET 2017 Easy
More PYQs from AP EAMCET
- The values of such that the matrix has no inverse, areAP EAMCET 2018 Easy
- From the given reaction
\(2 \mathrm{KMnO}_4 +3 \mathrm{H}_2 \mathrm{SO}_4+5 \mathrm{H}_2 \mathrm{O}_2 \longrightarrow \mathrm{K}_2 \mathrm{SO}_4+2 \mathrm{MnSO}_4 +8 \mathrm{H}_2 \mathrm{O}+5 \mathrm{O}_2\)
Find the normality of \(\mathrm{H}_2 \mathrm{O}_2\) solution, if \(20 \mathrm{~mL}\) of it is required to react completely with 16 \(\mathrm{mL}\) of \(0.02 \mathrm{M} \mathrm{KMnO}_4\) solution.
\(\left(\right.\) Molar mass of \(\mathrm{KMnO}_4=158 \mathrm{~g} \mathrm{~mol}^{-1}\) )AP EAMCET 2018 Medium - 2 aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly is 0.3 and 0.2 respectively. The second plane will bomb only if first misses the target. The probability that the target is hit by the 2 nd plane isAP EAMCET 2021 Easy
- In \(\triangle A B C, \frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}+\frac{1}{r^2}=\)AP EAMCET 2019 Easy
- The time period of a particle in simple harmonic motion is \(8 \mathrm{~s}\). At \(t=0\), it is at the mean position. The ratio of the distances travelled by it in the first and second seconds isAP EAMCET 2012 Medium
- The square of the distance from the origin to the point of intersection of the pair of lines \(a x^2+2 h x y-a y^2+2 g x+\) \(2 \mathrm{fy}+\mathrm{c}=0\) isAP EAMCET 2023 Medium