List of top Questions asked in AP EAPCET

A ball of mass 10 g is allowed to fall down from 10 m height. After collision with the ground, if 50\% of its energy is lost, then the height reached by the ball is:
A bomb at rest explodes into three pieces of equal masses. If two pieces move perpendicular to each other, each with a speed \( v \), then the speed of the third piece is:
The mechanical energy of a damped oscillator becomes half of its initial energy in 4 seconds. In another \( t \) seconds its mechanical energy becomes 12.5\% of its initial mechanical energy. Then \( t = \):
When an external force with angular frequency \( \omega_0 \) acts on a system of natural angular frequency \( \omega \), the system oscillates with angular frequency \( \omega_d \). The condition for the amplitude of oscillations to be maximum is:
Which one of the following is a homogeneous differential equation?
The number of significant figures in 4.870 m is:
The resultant of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is perpendicular to vector \( \mathbf{A} \), and the resultant magnitude is equal to half of the magnitude of \( \mathbf{B} \). The angle between \( \mathbf{A} \) and \( \mathbf{B} \) is:
A lorry is moving on a smooth circular path of radius 50 m with a velocity of 20 m/s. Then the banking angle of the road is:
Evaluate the following integral: \[ \int (x^3 + x^2 m + x^m) (2x^{2m} + 3x^m + 6x^m) \, dx \]
If \( a \in \mathbb{Z}^+ \), \([x]\) is the greatest integer not more than \( x \) and \[ \int_0^a \left\lfloor x \right\rfloor \, dx = 127, \text{ then } a = ? \]
Evaluate the integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin x \cdot \sin^2 x \cdot \cos x \, dx \]
The positive value of \( x \) satisfying the equation \[ \int_0^x (1 - t) \, dt = \frac{1}{2} \] is:
The area (in square units) bounded by \[ x = 4, \quad y = -4, \quad \text{and} \quad y = x \quad \text{is:} \]
The particular solution of the differential equation \[ (1 + y^2) \, dx - xy \, dy = 0, \quad y(1) = 0 \quad \text{represents:} \]
If \( c \) and \( d \) are arbitrary constants, then \[ y = e^{2x} \left( \cosh \sqrt{2} x + d \sinh \sqrt{2} x \right) \] is the general solution of the differential equation:
The function \( f(x) = x^2 + \dfrac{54}{x} \)
If \( (a^2 - 1)x + ay + (3 - a) = 0 \) is a normal to the curve \( xy = 1 \), then the interval in which ‘a’ lies is:
The maximum value of \( x^4 y^4 \) when \( a^2 x^4 + b^2 y^4 = c^6 \) is:
Evaluate: \[ \int e^{\sin x} \cdot \frac{x \cos^3 x - \sin x}{\cos^2 x} \, dx \]
If \( f'(x) = a \cos x + b \sin x \), \( f'(0) = 4 \), \( f(0) = 3 \), and \( f\left( \frac{\pi}{2} \right) = 5 \), then \( f(x) = \)
If \( \int f(x)\,dx = \Psi(x) \), then \( \int x^5 f(x^3)\,dx = \):
If \[ \int \frac{\sin^2 \alpha - \sin^2 x}{\cos x - \cos \alpha} \, dx = f(x) + Ax + B, \, B \in \mathbb{R}, \text{ then} \] \[ \frac{\sin^2 \alpha - \sin^2 x}{\cos x - \cos \alpha} \, dx = f(x) + Ax + B, \, B \in \mathbb{R} \]
If \( f(x) = \begin{vmatrix} 1 & 6 + x & 36 + x^2 \\ 0 & x - 3 & 3x^2 - 27 \\ 0 & 2x - 4 & 8x^2 - 32 \end{vmatrix} \), then \( \lim\limits_{x \to 1} \frac{f(x)}{f(-x)} \) is:
Let \( f(x) \) be differentiable on \( \mathbb{R} \) and \( f'(m) \ne 0, m \in \mathbb{R} \). If \( \lim\limits_{x \to m} \frac{x f(m) - m f(x)}{x - m} + f'(m) = f(m) \), then \( m = \):
Let \( f(x) \) be a differentiable function such that \( f(1) = 2 \), \( f(2) = 6 \), and \[ f(x+y) = f(x) + kxy + \frac{4}{3} y^2, \quad \forall x, y \in \mathbb{R}. \] Then \( f(x) = \) ?