List of top Questions asked in AP EAMCET

Two blocks of equal masses are tied with a light string passing over a massless pulley (Assuming frictionless surfaces). The acceleration of the centre of mass of the two blocks is (Given \( g = 10 \, \text{m/s}^2 \)):
Two blocks of equal masses are tied
A ring and a disc of same mass and same diameter are rolling without slipping. Their linear velocities are same, then the ratio of their kinetic energy is:
A force of \( (4\hat{i} + 2\hat{j} + \hat{k}) \) N is acting on a particle of mass \( 2 \) kg displaces the particle from a position of \( (2\hat{i} + 2\hat{j} + \hat{k}) \) m to a position of \( (4\hat{i} + 3\hat{j} + 2\hat{k}) \) m. The work done by the force on the particle in joules is:
The acceleration of a body sliding down the inclined plane, having coefficient of friction \( \mu \), is
A body of 2 kg mass slides down with an acceleration of \( 4 \, \text{ms}^{-2} \) on an inclined plane having a slope of \( 30^\circ \). The external force required to take the same body up the plane with the same acceleration will be (Acceleration due to gravity \( g = 10 \, \text{ms}^{-2} \))
A body of mass \( 30 \) kg moving with a velocity \( 20 \) ms\(^{-1}\) undergoes one-dimensional elastic collision with another ball of the same mass moving in the opposite direction with a velocity of \( 30 \) ms\(^{-1}\). After collision, the velocities of the first and second bodies respectively are:
A boy throws a ball with a velocity \(V_0\) at an angle \(\alpha\) to the ground. At the same time, he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of:
A particle starts from rest and moves in a straight line. It travels a distance \(2L\) with uniform acceleration and then moves with a constant velocity a further distance of \(L\). Finally, it comes to rest after moving a distance of \(3L\) under uniform retardation. Then the ratio of average speed to the maximum speed \( \left( \frac{V_{avg}}{V_{m}} \right) \) of the particle is:
In the equation \( \left( P + \frac{a}{V^2} \right) (V - b) = RT \), where \( P \) is pressure, \( V \) is volume, \( T \) is temperature, \( R \) is the universal gas constant, and \( a, b \) are constants. The dimensions of \( a \) are:
Evaluate the integral: \[ \int_{-2}^{2} (4 - x^2)^{\frac{5}{2}} \, dx. \]
The differential equation of the family of hyperbolas having their centers at origin and their axes along the coordinate axes is:
Evaluate the following limit: \[ \lim_{x \to \infty} \left[ \left(1 + \frac{1}{n^3} \right)^{\frac{1}{n^3}} \left(1 + \frac{8}{n^3} \right)^{\frac{8}{n^3}} \left(1 + \frac{27}{n^3} \right)^{\frac{9}{n^3}} \dots (2n)^{\frac{1}{n}} \right]. \]
Evaluate the integral: \[ I = \int_{-5\pi}^{5\pi} \left(1 - \cos 2x \right)^{\frac{5}{2}} dx. \]
Evaluate the integral: \[ \int e^{4x^2 + 8x -4} (x+1) \cos(3x^2 + 6x -4) \, dx.= \]
Evaluate the integral: \[ \int \frac{1}{(1 + x^2) \sqrt{x^2 + 2}} \, dx. \]
Evaluate the integral: \[ \int \left[ (\log_2 x)^2 + 2 \log_2 x \right] dx. \]
Evaluate the integral: \[ \int \sin^4 x \cos^4 x \, dx. \]
Evaluate the integral: \[ \int_{0}^{1} \sqrt{\frac{2 + x}{2 - x}} \, dx \]
The interval containing all the real values of \( x \) such that the real valued function \[ f(x) = \sqrt{x} + \frac{1}{\sqrt{x}} \] is strictly increasing is:
If a man of height 1.8 m is walking away from the foot of a light pole of height 6 m with a speed of 7 km per hour on a straight horizontal road opposite to the pole, then the rate of change of the length of his shadow is (in kmph):
The semi-vertical angle of a right circular cone is \( 45^\circ \). If the radius of the base of the cone is measured as 14 cm with an error of \( \left(\frac{\sqrt{2}-1}{11} \right) \) cm, then the approximate error in measuring its total surface area is (in sq. cm).
If \[ f(x) = 5 \cos^3 x - 3 \sin^3 x \quad \text{and} \quad g(x) = 4 \sin^3 x + \cos^2 x, \] then the derivative of \( f(x) \) with respect to \( g(x) \) is:
Evaluate the limit: \[ \lim\limits_{x \to 0} \frac{\cos 2x - \cos 3x}{\cos 4x - \cos 5x}.= \]
Evaluate the limit: \[ \lim\limits_{x \to \infty} \frac{[2x - 3]}{x}. \]
The foot of the perpendicular drawn from a point \( A(1,1,1) \) onto a plane \( \pi \) is \( P(-3,3,5) \). If the equation of the plane parallel to the plane \( \pi \) and passing through the midpoint of \( AP \) is \[ ax - y + cz + d = 0, \] then \( a + c - d \) is: