List of top Questions asked in AP EAMCET

\[ f(x) = \begin{cases} \frac{x - |x|}{x}, & x \neq 0 \\[8pt] 2, & x = 0 \end{cases} \] Which of the following is true for \( f(x) \)
Evaluate \( \int (\log x)^m x^n dx \).
If \[ \int \frac{\sqrt[4]{x}}{\sqrt{x} + \sqrt[4]{x}} \, dx = \frac{2}{3} \left[ A \sqrt[4]{x^3} + B \sqrt[4]{x^2} + C \sqrt[4]{x} + D \log \left( 1 + \sqrt[4]{x} \right) \right] + K \] then \( \frac{2}{3} (A + B + C + D) = \)}
Evaluate the integral: \[ \int \sin^{-1} \left( \sqrt{\frac{x - a}{x}} \right) dx \]
Find the domain of \( f(x) \) given: \[ \int \frac{\sin x \cos x}{\sqrt{\cos^4 x - \sin^4 x}} dx = -\frac{f(x)}{2} + C. \] then domain of f{x) is
Given the equation: \[ y = (\tan^{-1} 2x)^2 + (\cot^{-1} 2x)^2, \] find the expression: \[ (1+4x^2)^2 y'' - 16. \]
If \( \int_0^{2\pi} (\sin^4 x + \cos^4 x) \, dx = K \int_0^\pi \sin^2 x \, dx + L \int_0^\frac{\pi}{2} \cos^2 x \, dx \) and \( K, L \in \mathbb{N} \), then the number of possible ordered pairs \( (K, L) \) is}
Evaluate the integral \( \int_0^{\pi} \frac{x \sin x}{4 \cos^2 x + 3 \sin^2 x} dx \):
If \( (a, b) \) is the stationary point of the curve \( y = 2x - x^2 \), then the area bounded by the curves \( y = 2x - x^2 \), \( y = x^2 - 2x \), and \( x = a \) is:
Among the options given below, from which option a differential equation of order two can be formed?
Which of the following is NOT a unit of permeability?
A diving board is at a height of \( h \) from the water surface. A swimmer standing on this board throws a stone vertically upward with a velocity 16 ms\(^{-1}\). It reaches the water surface in a time of 5 s. In the next 0.2s, the diver can hear the sound from the water surface. The speed of sound is (acceleration due to gravity \( g = 10 \) ms\(^{-2} \))
Path of projectile is given by the equation \( Y = Px - Qx^2 \), match the following accordingly (acceleration due to gravity = \( g \))
Path of projectile is given by the equation Y = Px−Qx2
A bowling machine placed at a height \( h \) above the earth surface releases different balls with different angles but with the same velocity \( 10 \sqrt{3} \, \text{ms}^{-1} \). All these balls landing velocities make angles 30° or more with horizontal. Then the height \( h \) (in meters) is:
A balloon carrying some sand of mass \( M \) is moving down with a constant acceleration \( a_0 \). The mass \( m \) of sand to be removed so that the balloon moves up with double the acceleration \( a_0 \) is:
A soccer ball of mass 250 g is moving horizontally to the left with a speed of 22 m/s. This ball is kicked towards right with a velocity 30 m/s at an angle 53° with the horizontal in upward direction. Assuming that it took 0.01 s for the collision to take place, the average force acting is:
One ring, one solid sphere, and one solid cylinder are rolling down on the same inclined plane starting from rest. The radius of all three are equal. The object that reaches down with maximum velocity is
The work done on a wire of volume \( 2 \) cm\(^3 \) is \( 16 \times 10^2 \) J. If the Young's modulus of the material of the wire is \( 4 \times 10^{12} \) Nm\(^{-2} \), then the strain produced in the wire is
Water flows from a tap of diameter 1.5 cm with velocity \( 7.5 \times 10^{-5} \, \text{m}^{3}\text{s}^{-1} \). The coefficient of viscosity of water is \( 10^{-3} \) Pas. The flow is:
A uniform metal solid sphere is rotating with angular speed \( \omega_0 \) about its diameter. If the temperature is raised by 50°C, the angular speed will be: Given \( \alpha_{\text{metal}} = 20 \times 10^{-5} \, \text{°C}^{-1} \)
When 2 moles of a monatomic gas expands adiabatically from a temperature of 80°C to 50°C, the work done is \( W \). The work done when 3 moles of a diatomic gas expands adiabatically from 50°C to 20°C is:
If the ratio of the absolute temperature of the sink and source of a Carnot engine is changed from 2:3 to 3:4, the efficiency of the engine changes by:
When a convex lens is immersed in two different liquids of refractive indices 1.25 and 1.5, the ratio of the focal lengths of the lens is 5:16. The refractive index of the material of the lens is:
The work function of a photosensitive metal surface is \(6.4 \times 10^{-19} \, {J}\). The maximum kinetic energy of the emitted photoelectrons when electromagnetic radiation of wavelength 1240 Å incidents on the metal surface is nearly:
The refractive index of medium is 1.8 and its relative permeability is 2.16. The relative permittivity of the medium is (nearly):