List of top Questions asked in AP EAPCET

When the mass attached to a spring is increased from 4 kg to 9 kg, the time period of oscillation increases by \(0.2\pi\) s. Then the spring constant of the spring is
For a particle executing simple harmonic motion, the ratio of kinetic and potential energies at a point where displacement is one half of the amplitude is
Two balls each of mass 250 g moving in opposite directions each with a speed 16 m/s collide and rebound with the same speeds. The impulse imparted to one ball due to the other is
A train of mass \(10^6 \, \text{kg}\) is moving at a constant speed of \(108 \, \text{km/h}\). If the frictional force acting on it is \(0.5 \, \text{N per 100 kg}\), then the power of the train is
The magnitudes of two vectors are A and B (A>B). If the maximum resultant magnitude of the two vectors is ‘n’ times their minimum resultant magnitude, then \(\frac{A}{B} =\)
The ratio of the displacements of a freely falling body during second and fifth seconds of its motion is
The dimensional formula of Planck’s constant is
The general solution of the differential equation \[ y + \cos x \left( \frac{dy}{dx} \right) - \cos^2 x = 0 \] is
If the degree of the differential equation corresponding to the family of curves
\[ y = ax + \frac{1}{a} \quad (\text{where } a \neq 0 \text{ is an arbitrary constant}) \] is \(r\) and its order is \(m\), then the solution of
\[ \frac{dy}{dx} - \frac{y}{2x}, \quad y(1) = \sqrt{r + m} \] is
Evaluate the integral: \[ \left| \int_{-\pi/4}^{\pi/3} \tan\left(x - \frac{\pi}{6}\right) dx \right| \]
Evaluate the integral: \[ \int \frac{(3x - 2)\tan\left(\sqrt{9x^2 - 12x + 1}\right)}{\sqrt{9x^2 - 12x + 1}} \, dx =\ ?\]
Evaluate the integral: \[ \int \frac{x^4 - 1}{x^2 \sqrt{x^4 + x^2 + 1}} \, dx =\ ? \]
Evaluate the integral: \[ \int \frac{1}{9\cos^2 x - 24 \sin x \cos x + 16 \sin^2 x} \, dx = \]
If the tangent drawn at the point \((\alpha, \beta)\) on the curve \[ x^{2/3} + y^{2/3} = 4 \] is parallel to the line \[ \sqrt{3}x + y = 1, \] then \( \alpha^2 + \beta^2 =\)
\[ \text{If the function } f(x) = \begin{cases} 1 + \cos x, & x \leq 0 \\ a - x, & 0 < x \leq 2 \\ x^2 - b^2, & x > 2 \end{cases} \text{ is continuous everywhere, then } a^2 + b^2 =\ ? \]
\[ \text{If } \lim_{x \to 0} \frac{\cos 2x - \cos 4x}{1 - \cos 2x} = k, \text{ then evaluate } \lim_{x \to k} \frac{x^k - 27}{x^{k+1} - 81} \]
A plane \( \pi \) is passing through the points \( A(1, -2, 3) \) and \( B(6, 4, 5) \). If the plane \( \pi \) is perpendicular to the plane \( 3x - y + z = 2 \), then the perpendicular distance from \( (0, 0, 0) \) to the plane \( \pi \) is
If \( A(0,0,0),\ B(3,4,0),\ C(0,12,5) \) are the vertices of a triangle ABC, then the x-coordinate of its incenter is:
The distance between the tangents of the hyperbola \( 2x^2 - 3y^2 = 6 \) which are perpendicular to the line \( x - 2y + 5 = 0 \) is:
If a tangent to the hyperbola \( xy = -1 \) is also a tangent to the parabola \( y^2 = 8x \), then the equation of that tangent is:
Let \( \theta \) be the angle between the circles \( S = x^2 + y^2 + 2x - 2y + c = 0 \) and \( S' = x^2 + y^2 - 6x - 8y + 9 = 0 \). If \( c \) is an integer and \( \cos\theta = \dfrac{5}{16} \), then the radius of the circle \( S = 0 \) is:
If the circle passing through the points \( (3,5), (5,5), (3,-3) \) cuts the circle \( x^2 + y^2 + 2x + 2fy = 0 \) orthogonally, then the value of \( f \) is:
One line of the pair of lines \( x^2 + xy - 2y^2 = 0 \) is perpendicular to one line of the pair of lines \( 3y^2 - 5xy - 2x^2 = 0 \). If the combined equation of the two lines other than those two perpendicular lines is \( ax^2 + 2hxy + by^2 = 0 \), then \( a + 2h + b = \)
If \( M \) is the foot of the perpendicular drawn from the origin to the line \( x - 2y + 3 = 0 \), which meets the X and Y-axes at \( A \) and \( B \) respectively, then \( AM = \)
If the lines \( x + 2ay + a = 0 \), \( x + 3by + b = 0 \), \( x + 4cy + c = 0 \) are concurrent, then \( a, b, c \) are in