List of top Questions asked in AP EAPCET

A body is projected at an angle of \(60^\circ\) with the horizontal. If the initial kinetic energy of the body is \(X\), then its kinetic energy at the highest point is
A body is moving along a straight line under the influence of a constant power source. If the relation between the displacement (s) of the body and time (t) is \(s \propto t^x\), then \(x =\)
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
A particle crossing the origin at time \(t = 0\), moves in the xy-plane with a constant acceleration ‘a’ in y-direction. If the equation of motion of the particle is \(y = bx^2\) (where \(b\) is a constant), then its velocity component in the x-direction 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
The area of the region lying between the curves \( y = \sqrt{4 - x^2} \), \( y^2 = 3x \) and the Y-axis 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: \[ \int \frac{1}{9\cos^2 x - 24 \sin x \cos x + 16 \sin^2 x} \, dx = \]
The interval in which the curve represented by \( f(x) = 2x + \log\left(\frac{x}{2 + x}\right) \) is increasing is
If the extreme value of the function \( f(x) = \frac{4}{\sin x} + \frac{1}{1 - \sin x} \) in \(\left[0, \frac{\pi}{2}\right]\) is \(m\) and it exists at \(x = k\), then \(\cos k =\)}
The displacement \(S\) of a particle measured from a fixed point \(O\) on a line is given by \[ S = t^3 - 16t^2 + 64t - 16. \] Then the time at which the displacement of the particle is maximum is
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 \( \alpha^2 + \beta^2 =\)
\[ \text{If } y = |\cos x - \sin x| + |\tan x - \cot x|, \text{ then } \left( \frac{dy}{dx} \right)_{x = \frac{\pi}{3}} + \left( \frac{dy}{dx} \right)_{x = \frac{\pi}{6}} = \]
\[ \text{Assertion (A): If } y = f(x) = (|x| - |x - 1|)^2, \text{ then } \left.\frac{dy}{dx}\right|_{x = 1} = 1 \] \[ \text{Reason (R): If } \lim_{x \to a} \frac{f(x) - f(a)}{x - a} \text{ exists, then it is called the derivative of } f(x) \text{ at } x = a. \] Then:
\[ \text{If } x = 2 \cos^3 \theta \text{ and } y = 3 \sin^2 \theta, \text{ then } \frac{dy}{dx} =\ ? \]
\[ \text{If the function } f(x) = \begin{cases} 1 + \cos x, & x \leq 0 \\ a - x, & 0 < x \leq 2 \\ x^2 - b^2, & x > 2 \end{cases} \text{ is continuous everywhere, then } a^2 + b^2 =\ ? \]
\[ \text{If } \lim_{x \to 0} \frac{\cos 2x - \cos 4x}{1 - \cos 2x} = k, \text{ then evaluate } \lim_{x \to k} \frac{x^k - 27}{x^{k+1} - 81} \]
\[ \lim_{y \to 0} \frac{\sqrt{1 + \sqrt{1 + y^4}} - \sqrt{2}}{y^4} = \ ? \]