List of top Questions asked in AP EAMCET

The focal length of the objective lens of a telescope is 30 cm and that of its eye lens is 3 cm. It is focused on a scale at a distance 2 m from it. The distance of the objective lens from the eye lens to see the clear image is:
A solid cylinder rolls down on an inclined plane of height \( h \) and inclination \( \theta \). The speed of the cylinder at the bottom is:
A body is executing simple harmonic motion. At a displacement \( x \), its potential energy is \( E_1 \), and at a displacement \( y \), its potential energy is \( E_2 \). The potential energy \( E \) at a displacement \( (x + y) \) is:
A particle is projected from the surface of the Earth with a velocity equal to twice the escape velocity. When the particle is far from the Earth, its speed will be:
A spherical ball of radius \( 1 \times 10^{-4} \) m and density \( 10^4 \) kgm\(^{-3}\) falls freely under gravity before entering water. The distance \( h \) before velocity change in water is:
The maximum height attained by the projectile is increased by 10% by keeping the angle of projection constant. What is the percentage increase in the time of flight?
A block of metal 4 kg is in rest on a frictionless surface. It was targeted by a jet releasing water of 2 kg/s at a speed of 10 ms\(^{-1}\). The acceleration of the block is:
A person climbs up a conveyor belt with a constant acceleration. The speed of the belt is \( \sqrt{\frac{g h}{6}} \) and the coefficient of friction is \( \frac{5}{3\sqrt{3}} \). The time taken by the person to reach from A to B with maximum possible acceleration is: \includegraphics[]{87.png}
A machine with efficiency \( \frac{2}{3} \) used 12 J of energy in lifting a 2 kg block through a certain height and it is allowed to fall through the same. The velocity while it reaches the ground is:
Evaluate the integral \[ I = \int_{-1}^{1} \left( \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right) \, dx \]
The differential equation formed by eliminating arbitrary constants \( A \) and \( B \) from the equation \[ y = A \cos 3x + B \sin 3x \] is:
If \[ \cos x \frac{dy}{dx} - y \sin x = 6x, \quad (0<x<\frac{\pi}{2}) \quad {and} \quad y(\frac{\pi}{3}) = 0, \quad {then} \quad y(\frac{\pi}{6}) = \]
The solution of the differential equation \[ \frac{dy}{dx} = \frac{y + x \tan \left( \frac{y}{x} \right)}{x}. \] \[ \sin\frac{y}{x} = \]
The length of the side of a cube is \( 1.2 \times 10^{-2} \) m. Its volume up to correct significant figures is:
The velocity of a particle is given by the equation \( v(x) = 3x^2 - 4x \), where \( x \) is the distance covered by the particle. The expression for its acceleration is:
Evaluate the integral \[ \int \frac{\sin^6 x}{\cos^8 x} \, dx. \]
Evaluate the integral \[ \int \frac{x^5}{x^2 + 1} dx. \]
Evaluate the integral \[ \int \sum_{r=0}^{\infty} \frac{x^r 3^r}{2r} dx. \]
Evaluate the integral \[ \int \frac{x^4 + 1}{x^6 + 1} dx. \]
Evaluate the integral \[ \int e^x (x+1)^2 dx. \]
Evaluate the integral \[ I = \int_0^1 \frac{x}{(1 - x)^{3/4}} \, dx \]
If \[ \frac{d}{dx} \left(\frac{1 + x^2 + x^4}{1 + x + x^2}\right) = ax + b, \] then \( (a,b) \) is:
If \[ y = \sin^{-1} x, \] then \[ (1 - x^2)y_2 - xy_1 = 0. \]
If the percentage error in the radius of a circle is 3, then the percentage error in its area is:
The equation of the tangent to the curve \[ y = x^3 - 2x + 7 \] at the point \( (1,6) \) is: