List of top Questions asked in AP EAPCET

If a force F = (3i - 2j) N acting on a body displaces it from point (1 m, 2 m) to point (2 m, 0 m), then work done by the force is
A body moving along a straight line collides another body of same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is 0.5, then the ratio of the velocities of the two bodies after collision is (treat the collision as one dimensional)
If a solid sphere is rolling without slipping on a horizontal plane, then the ratio of its rotational and total kinetic energies is
As shown in the figure, two thin coplanar circular discs A and B each of mass 'M' and radius 'r' are attached to form a rigid body. The moment of inertia of this system about an axis perpendicular to the plane of disc B and passing through its centre is
The time period of a simple pendulum on the surface of the earth is T. If the pendulum is taken to a height equal to half of the radius of the earth, then its time period is
A particle is executing simple harmonic motion starting from its mean position. If the time period of the particle is 1.5 s, then the minimum time at which the ratio of the kinetic and total energies of the particle becomes 3:4 is
If the error in the measurement of the surface area of a sphere is 1.2%, then the error in the determination of the volume of the sphere is
A body starts from rest with uniform acceleration and its velocity at a time of \( n \) seconds is \( v \). The total displacement of the body in the \( n \)-th and \( (n - 1) \)-th seconds of its motion is
If the range of a body projected with a velocity of 60 m/s is \( 180\sqrt{3} \) m, then the angle of projection of the body is (Acceleration due to gravity = 10 m/s\(^2\))
A disc of mass 0.2 kg is kept floating in air without falling by vertically firing bullets each of mass 0.05 kg on the disc at the rate of 10 bullets per every second. If the bullets rebound with the same speed, then the speed of each bullet is (Acceleration due to gravity = 10 m/s$^2$)
Two bodies A and B of masses 1.5 kg and 3 kg are moving with velocities 20 m/s and 15 m/s respectively. If the same retarding force is applied on the two bodies, then the ratio of the distances travelled by the bodies A and B before they come to rest is
For \( 0<x<1 \), \(\int_0^1 \left( \tan^{-1}\left( \frac{1 + x^2 - x}{x} \right) + \tan^{-1}(1 - x + x^2) \right) dx =\)
\(\int_{-2\pi}^{2\pi} \sin^2(2x) \cos^4(2x) \, dx =\)
If \( f(t) = \int_0^t \tan^{2n-1}(x) \, dx \), \( n \in \mathbb{N} \), then \( f(t + \pi) =\)
\(\int_0^2 \frac{x^{\frac{8}{3}}}{|x - 1|^{\frac{5}{2}}} \, dx =\)
The area (in sq. units) of the region bounded by the curves \( y = x^2 \) and \( y = 8 - x^2 \) is
The solution of the differential equation \( x^2 (y + 1) \frac{dy}{dx} + y^2 (x + 1) = 0 \), when \( y(1) = 2 \), is
The general solution of the differential equation \( \frac{dy}{dx} = \frac{2x + y - 3}{2y - x + 3} \) is
If the slope of the tangent drawn at any point \((x, y)\) on a curve is \(x + y\), then the equation of that curve is
\(\int (\sqrt{\tan x} + \sqrt{\cot x}) \, dx =\)
\(\int \frac{\sqrt{x - 2}}{2x + 4} \, dx =\)
If \(\int \left( \frac{x^{49} \tan^{-1}(x^{50})}{1 + x^{100}} + \frac{x^{50}}{1 + x^{100}} \right) dx = k f(x) + c\) where \(k\) is a constant, then \(f(x) - f\left( \frac{1}{x^{49}} \right) =\)
\(\int \frac{x}{\sqrt{x^2 - 2x + 5}} \, dx =\)
\(\lim_{x \to 0} \frac{x \tan 2x - 2x \tan x}{(1 - \cos 2x)^2} =\)
If \( f(x) = \begin{cases} \frac{(e^x - 1) \log(1 + x)}{x^2} & \text{if } x>0 \\ 1 & \text{if } x = 0 \\ \frac{\cos 4x - \cos bx}{\tan^2 x} & \text{if } x<0 \end{cases} \) is continuous at \( x = 0 \), then \(\sqrt{b^2 - a^2} =\)