List of top Questions asked in AP EAPCET

If a particle of mass 'm' covers half of the horizontal circle with constant speed 'v', then the change in its kinetic energy is

The bob of a simple pendulum of length $200~\text{cm}$ is released from horizontal position.
If $10%$ of its initial energy is lost to air resistance, then the speed of bob at the mean position is
(Acceleration due to gravity $= 10~\text{m/s}^2$)

A steel sphere of radius $1.2~\text{cm}$ collides with another steel sphere at rest.
If the collision is elastic and the first sphere moves with $\dfrac{7}{9}$ of its initial velocity after collision,
then the radius of the second sphere is

Ratio of angular velocity of hour hand of a watch and the angular velocity of rotation of earth is

Evaluate the integral \[ \int_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}} \frac{1}{\left(x + \sqrt{1 - x^2}\right) \cdot \left(1 - x^2\right)} \, dx = \]

The area of the region (in sq. units) enclosed between the curves \( y = |x| \), \( y = [x] \) and the ordinates \( x = -1, x = 0, x = 1 \) is

The general solution of the differential equation \((x+2y)^3\frac{dy}{dx} = y = 0, y>0\) is

The general solution of the differential equation \(\frac{dy}{dx} = \frac{x + y + 1}{x - 3y + 5}\) is

If the maximum and minimum temperatures at a place on a day are measured as $44^\circ C \pm 0.5^\circ C$ and $22^\circ C \pm 0.5^\circ C$ respectively, then the temperature difference is

If \( \int \frac{dx}{(x-1)^2(x-3)^2 = \sqrt{f(x)} + c \), then \( f(-1) - f(0) = \)}

\( \int \frac{x}{(1-x^2)\sqrt{2 - x^2} dx = \)}

Evaluate the integral $\displaystyle \int_0^{\frac{\pi{2}} \log(\tan x + \cot x)\, dx$}

Evaluate the integral \[ \int_{0}^{\pi} x \cdot \sin x \cdot \int_{x}^{5} \frac{\cos x}{x} \cdot dx = \]

If \(x^2 + y^2 = \dfrac{1}{t} \text{ and } x^4 + y^4 = t^2 + \dfrac{1}{t^2},\) then \(\dfrac{dy}{dx} =\)

If \(y = (ax + b)\cos x\), then \(y_2 + y_1 \sin 2x + y(1 + \sin^2 x) = \)

If the normal drawn at the point P on the curve \(y = x \log x\) is parallel to the line \(2x - 2y = 3\), then P =

If the curves \(y^2 = 16x \text{ and } 9x^2 + \alpha y^2 = 25\) intersect at right angles, then \(\alpha =\)

If the function \(y = \sin(x)(1 - \cos x)\) is defined in the interval \([-\pi, \pi]\), then y is strictly increasing in the interval