AP EAMCET · Maths · Basic of Mathematics

If \(\frac{1}{x^4+x^2+1}=\frac{A x+B}{x^2+x+1}+\frac{C x+D}{x^2-x+1}\), then \(C+D\) is equal to

A \(-1\)
B \(1\)
C \(2\)
D \(0\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(0\)

Step-by-step Solution

Detailed explanation

Given,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

There are three sections in a question paper, each containing 4 questions. If a candidate has to answer only 5 questions from this paper without leaving any section, then number of ways the candidate can make the choice of questions is

AP EAMCET 2018 Medium
\(\int \frac{\sin ^{-1} \sqrt{x}-\cos ^{-1} \sqrt{x}}{\sqrt{x}\left(\sin ^{-1} \sqrt{x}+\cos ^{-1} \sqrt{x}\right)} d x=\)

AP EAMCET 2023 Medium
If the mean and variance of a binomial variable \(\mathrm{X}\) are 2 and 1 respectively, then \(\mathrm{P}(\mathrm{X}>1)=\)

AP EAMCET 2023 Medium
Geometric mean of \(\tan 1^{\circ}, \tan 2^{\circ}, \ldots \ldots . . .\), \(\tan 89^{\circ}\) is

AP EAMCET 2020 Easy
\(\int \frac{x}{\sqrt{x+1}+\sqrt{x-1}} d x=A(x)(x+1)^{\frac{3}{2}}+B(x)(x-1)^{\frac{3}{2}}+C\) , then \(A(x)+B(x)=\)

AP EAMCET 2019 Hard
If \(\alpha\) is a repeated root of multiplicity 2 of the equation \(18 x^3-33 x^2+20 x-4=0\), then

AP EAMCET 2025 Medium

Explore more questions on app

From AP EAMCET

Two equally charged metal spheres \(A\) and \(B\) repel each other with a force of \(4 \times 10^{-5} \mathrm{~N}\). Another identical uncharged sphere \(C\) is touched to \(A\) and then placed at the mid- point of the line joining the spheres \(A\) and \(B\). The net electric force on the sphere \(C\) is

AP EAMCET 2018 Easy
The energy released when one nucleus of \({ }_{92} \mathrm{U}^{235}\) undergoes fission is \(188 \mathrm{MeV}\). The energy released when \(100 \mathrm{~g}\) of \({ }_{92} \mathrm{U}^{235}\) undergoes fission is

AP EAMCET 2019 Easy
The velocity (v) of a particle starting from rest increases linearly withtime \((t)\) as \(v=4 t\), where \(v\) is in \(m s^{-1}\) and \(t\) is in second. The distance covered by the particle in the first 4 seconds is

AP EAMCET 2023 Easy
Which of the following orders are correct regarding their covalent character?
i. \(\mathrm{KF} \lt \mathrm{KI}\)
ii. \(\mathrm{LiF} \lt \mathrm{KF}\)
iii. \(\mathrm{SnCl}_2 \lt \mathrm{SnCl}_4\)
iv. \(\mathrm{NaCl} \lt \mathrm{CuCl}\)
The correct option is

AP EAMCET 2024 Medium
Suppose that \(E_1\) and \(E_2\) are two events of a random experiment such that \(P\left(E_1\right)=\frac{1}{4}\), \(P\left(E_2 / E_1\right)=\frac{1}{2}\) and \(P\left(E_1 / E_2\right)=\frac{1}{4}\), observe the lists given below

The correct matching of the List I from the List II is
(A) (B) (C) (D)

AP EAMCET 2009 Medium
If a heat engine and a refrigerator are working between the same two temperatures \(T_1\) and \(T_2\left(T_1>T_2\right)\), then the ratio of efficiency of heat engine to coefficient of performance of refrigerator is

AP EAMCET 2025 Medium

Explore more questions on app