List of top Questions asked in AP EAPCET

If \( z \) is a complex number such that \( \frac{z-1}{z-i} \) is purely imaginary and the locus of \( z \) represents a circle with center \( (\alpha, \beta) \) and radius \( r \), then the value of \( \frac{\alpha}{\beta} + \frac{\beta}{\alpha} \) is:
The rank of the matrix \( \begin{bmatrix} 2 & -3 & 4 & 0 \\ 5 & -4 & 2 & 1 \\ 1 & -3 & 5 & -4 \end{bmatrix} \) is
If \( \alpha \) is a real root of the equation \( x^3 + 6x^2 + 5x - 42 = 0 \), then the determinant of the matrix \[ \begin{bmatrix} \alpha - 1 & \alpha + 1 & \alpha + 2 \\ \alpha - 2 & \alpha + 3 & \alpha - 3 \\ \alpha + 4 & \alpha - 4 & \alpha + 5 \end{bmatrix} \] is Options:
If \( P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} \) is the adjoint of a matrix \( A \) and \( \det(A) = 4 \), then the value of \( \alpha \) is:
If \( 11^{12} - 11^2 = k(5 \times 10^9 + 6 \times 10^9 + 33 \times 10^8 + 110 \times 10^7 + \ldots + 33) \), then find the value of \( k \).
If \( f(x) = (x+1)^2 - 1, x \ge -1 \), then \( \{x \mid f(x) = f^{-1}(x)\} \) is:
Let \( [t] \) denote the greatest integer function and \( [t - m] = [t] - m \) when \( m \in \mathbb{Z} \). If \( k = 2[2x - 1] - 1 \) and \( 3[2x - 2] + 1 = 2[2x - 1] - 1 \), then the range of \( f(x) = [k + 5x] \) is:
In Young's double-slit experiment, if the distance between the slits is increased to 3 times its initial distance, then the ratio of initial and final fringe widths is.
One of the two identical capacitors having the same capacitance C, is charged to a potential \(V_1\) and the other is charged to a potential \(V_2\). If they are connected with their like plates together, then the decrease in the electrostatic potential energy of the combined system is
In a Carnot engine, if the absolute temperature of the source is \( 25% \) more than the absolute temperature of the sink, then the efficiency of the engine is
If a heat engine and a refrigerator are working between the same two temperatures \(T_1\) and \(T_2\) (\(T_1>T_2\)), then the ratio of efficiency of heat engine to coefficient of performance of refrigerator is
A force \( F \) is applied on a body of mass \( m \) so that the body starts moving from rest. The power delivered by the force at time \( t \) is proportional to:
The equations for the displacements of two particles in simple harmonic motion are \( y_1 = 0.1\sin\left(100\pi t + \frac{\pi}{3}\right) \) and \( y_2 = 0.1\cos(\pi t) \) respectively. The phase difference between the velocities of the two particles at a time \( t = 0 \) is
If $ \alpha $, $ \beta $, and $ \gamma $ are the angles made by a vector with the $ x $-, $ y $-, and $ z $-axes respectively, then find the value of $ \sin^2\alpha + \sin^2\beta $.
Evaluate: \( \int_0^{400\pi} \sqrt{1 - \cos 2x} \, dx \)
If \( \int \frac{dx}{2\cos x + 3\sin x + 4} = \frac{2}{\sqrt{3}}f(x) + c \), then \( f\left(\frac{2\pi}{3}\right) = \)
Evaluate \( \int \frac{\sec^2 x}{\sin^7 x} \, dx - \int \frac{7}{\sin^7 x} \, dx \):
If \(y = \sqrt{\cosh x + \sqrt{\cosh x}}\), then \(\frac{dy}{dx} =\)
If $ A(0, 1, 2) $, $ B(2, -1, 3) $, and $ C(1, -3, 1) $ are the vertices of a triangle, then the distance between its circumcentre and orthocentre is
In a triangle ABC, if \((r_1 - r_3)(r_1 - r_2) - 2r_2r_3 = 0\), then \(a^2 - b^2 =\)
In triangle $ ABC $, if $ a = 13 $, $ b = 8 $, $ c = 7 $, then $ \cos(B+C) = $
If $ \alpha, \beta, \gamma $ are the roots of the equation $ x^3 + px^2 + qx + r = 0 $, then $ \alpha^3 + \beta^3 + \gamma^3 = $
A short bar magnet is placed in a uniform magnetic field of $2~\text{T}$ such that the axis of the magnet makes an angle of $45^\circ$ with the field. If the torque acting is $0.36~\text{Nm}$, the magnetic moment of the magnet is
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