List of top Questions asked in AP EAPCET

If the equation \(3x^2 + 4y^2 - xy + k = 0\) is the transformed equation of \(3x^2 + 4y^2 - xy - 5x - 7y + 2 = 0\) after shifting the origin to \((\alpha, \beta)\), then \(\alpha + \beta = k =\)
\( \int \frac{x}{(1-x^2)\sqrt{2 - x^2} dx = \)}
If \(P\) is a variable point which is at a distance of 2 units from the line \(2x - 3y + 1 = 0\) and \(\sqrt{13}\) units from the point (5, 6), then the equation of the locus of \(P\) is
If five logic gates are connected as shown in the figure, then the values of $y_1$, $y_2$, and $y_3$ are respectively
logic gates
If $a = \ln \left( \frac{1}{z^2} \right)$ and $z$ is any non-zero complex number such that $|z| = 1$, then which of the following is the correct expression for $a$?
If \[ \left(\frac{\cos \theta + i \sin \theta}{\sin \theta + i \cos \theta}\right)^{2024} + \left(\frac{1 + \cos \theta + i \sin \theta}{1 - \cos \theta + i \sin \theta}\right)^{2025} = x + iy, \] and $x + y$ at $\theta = \frac{\pi}{2}$ is
Which of the following is the common monomer for the polymers Bakelite and Melamine?
If the variance of the first \(n\) natural numbers is 10 and the variance of the first \(m\) even natural numbers is 16, then \(n : m =\)
If \(x\) is a real number, then the number of solutions of \(\tan^{-1}\left(\sqrt{x(x+1)}\right) + \sin^{-1}\left(\sqrt{x^2 + x + 1}\right) = \dfrac{\pi}{2}\) is
Coefficient of $x^2$ in the expansion of $(x^2 + x - 2)^5$ is
If $P_n$ denotes the product of the binomial coefficients in the expansion of $(1 + x)^n$, then find \[ \frac{P_{n+1}}{P_n}. \]
A horizontal telegraph wire of length $30~\text{m}$ fell from a height of $20~\text{m}$. If resistance is $40~\Omega$ and horizontal component of Earth’s magnetic field is $2 \times 10^{-5}~\text{T}$, the induced current is
In an LCR series circuit, if the potential differences across inductor, capacitor, and resistor are $60~\text{V}$, $30~\text{V}$, and $40~\text{V}$ respectively, then the net voltage applied to the circuit is
The coefficient of \(x^3\) in the expansion of \(\frac{x^4 + 1}{(x^2 + 1)(x - 1)}\) when it is expressed in terms of positive integral powers of \(x\), is
When a wire of length $L$ clamped at one end is pulled by a force $F$ from the other end, its length increases by $L'$. If the radius and the applied force are halved, then the increase in its length is
The radii of inner and outer spheres of a spherical capacitor are $8~\text{cm$ and $9~\text{cm}$ respectively. The outer sphere is earthed and the inner sphere is charged. If the space is filled with a dielectric constant $K = 5$, the capacitance is}
The power dissipated by a uniform wire of resistance $100~\Omega$ when a potential difference of $120~\text{V$ is applied across its ends is}
The roots $\alpha, \beta$ of the equation \[ x^2 - 6(k-1)x + 4(k-2) = 0 \] are equal in magnitude but opposite in sign. If $\alpha>\beta$, then the product of the roots of the equation \[ 2x^2 - \alpha x + 6\beta (\alpha + 1) = 0 \] is
If \(A + B + C = \dfrac{\pi}{4}\), then \(\sin 4A + \sin 4B + \sin 4C =\)
The specific conductance of 0.05 M NaOH solution is 0.0115 S cm$^{-1}$. What is its molar conductance ($\Lambda_m$) in S cm$^2$ mol$^{-1}$?
For the reaction: A + 2B $\rightarrow$ 3C + 2D, if rate of disappearance of B is $x \times 10^{-2}$ mol L$^{-1}$ s$^{-1}$, the ratio of rate of reaction to rate of appearance of C is:

Match the following:

List-I (Aquated ion)List-II (Colour)
A) Ni\(^{2+}\)V) Green
B) Fe\(^{3+}\)III) Yellow
C) Mn\(^{3+}\)I) Violet
D) V\(^{4+}\)II) Blue
If the angular velocity of a planet about its axis is halved, the distance of the stationary satellite of this planet from the centre of the planet becomes $2^n$ times the initial distance. Then the value of $n$ is
Which of the following orders is not correct about the property shown against it?
Consider the following changes I and II
Change I: ${O2 → O2^{2-}}$
Change II: ${O2 → O2^{-}}$
The correct statements about these changes (I) and (II) in accordance with MO theory are