List of top Questions asked in AP EAPCET

Two wooden blocks of mass M\(_1\) and M\(_2\) rest on a frictionless table. A bullet of mass m is fired at M\(_1\) with speed v which embedded in it and the two together finally collide with M\(_2\). Find the velocity of M\(_2\) after collision. [Ignore any energy loss and treat the problem to be one dimensional]
An object of mass 20 kg. is displayed by \(x = 5t^2\) m (here t is time) by the application of a force. Then the ratio of the work done in times 3 s and 5 s is
A uniform rod of length 60 cm is placed with one end in contact with the horizontal table and is then inclined at an angle 30\(^\circ\) to the horizontal and allowed to fall. The angular velocity of the rod when it becomes horizontal is (acceleration due to gravity = 10 ms\(^{-2}\))
A wheel undergoes a constant acceleration starting form rest at t = 0. The angular velocity of the wheel is 3.14 \(\frac{\text{rad}}{\text{sec}}\) when t = 2 s. The accelerator is abruptly ceased at t = 20 s. The number of revolutions, wheel makes in the interval t = 0 to t = 40 s is
Assertion (A): In S.H.M kinetic and potential energy become equal when the distance is $\frac{1}{\sqrt{2}}$ times its amplitude. Reason (R): The potential energy of a particle executing S.H.M is periodic with time period being maximum at the extreme displacement.
As shown in the figure, two spherical cavities are made in the uniform solid sphere of radius R. The boundaries of the cavities touch at the centre of the sphere. The centers of the cavities and the sphere lie on the x-axis. The mass of the solid sphere before the cavities were created was M. The gravitational force on a point mass m at a distance 'd' away from the center of the solid sphere is
two spherical cavities are made in the uniform solid sphere of radius R
If the general solution of \( \frac{dy}{dx} = \frac{-y^2}{xy-y^2-x^2} \) is \( \tan^{-1}\left(\frac{x}{y}\right) = f(y) + C \), then \( f(e^3) = \)
A physical quantity P is related to four observables a, b, c, and d as \( P = \frac{\sqrt{ab}.d^\alpha}{\sqrt{C}} \) (\(\alpha\) is constant). The percentage errors in a, b, c and d are 0.5% in each. If the percentage error in P is 2%, then \(\alpha\) is
A car is moving along a straight line is brought to a stop within a distance of 200 m and in time 10 s. The initial speed of the car is
A ball is thrown upward from the top of a building at an angle of 30\(^\circ\) to the horizontal and with an initial speed of 20 m s\(^{-1}\). If the ball strikes the ground after 3 s, then the height of the building is (acceleration due to gravity = 10 ms\(^{-2}\))
A particle is moving on a circular path with a constant speed v. It's change of velocity as it moves from A to B in the figure is
moving on a circular path with a constant speed
A box of mass 2 kg is placed on a inclined plane that makes 30\(^\circ\) with the horizontal. The coefficient of friction between the box and inclined plane is 0.2. A force F is applied on the box perpendicular to the incline to prevent the box from sliding down. The minimum value of F is (acceleration due to gravity = 10 m s\(^{-2}\))
box of mass 2 kg is placed on a inclined plane that makes 30◦
Which of the following is true about the coefficient of static friction (\(\mu_s\)) and the coefficient of kinetic friction (\(\mu_k\))
\( \int_{-\pi/4}^{\pi/4} \cos^8 x \ dx = \)
If \( f(x) = \sin(\tan^{-1} x) \), then \( \int_0^1 xf''(x)dx = \)
If an open cylinder of given surface area has maximum volume then its radius is
If \(x+y=k, x>0, y>0\) then \(x^2+y^2\) is minimum if
If \( \int \frac{x^8+4}{x^4-2x^2+2} dx = Ax^5+Bx^3+Cx+K \), then \(5A+3B+C = \)
\( \int \sqrt{x+\sqrt{x^2+2}} \ dx = \)
If \( f(x) = \begin{cases 4 & -\infty<x<-\sqrt{5}
x^2-1 & -\sqrt{5} \le x \le \sqrt{5}
4 & \sqrt{5}<x<\infty \end{cases} \). If k is the number of points where f(x) is not differentiable then k -- 2 =}
Assertion (A) : \( f(x)=|x| \) is differentiable at \( x=a \neq 0 \) and continuous but not differentiable at \( x=0 \) Reason (R) : If a function is differentiable at a point then it is continuous at that point. But converse is not true. .
Equation of tangent to the curve \( y = x + \frac{4}{x^2} \) which is parallel to x-axis is
The normal to the curve y = f(x) at the points (3, 4) makes an angle \( \frac{3\pi}{4} \) with positive x-axis then \(f'(3) = \)
The minimum distance of a point on the curve \( y = x^2 - 4 \) from the origin is
If the centroid of a triangle with vertices \((4, p, -3), (-1, -1, 2)\) and \((3, 5, -8)\) is given by mid point of \((1, 4, -2)\) and \((q, 2, -4)\), then \(p^2+q^2 = \)