List of top Questions asked in AP EAPCET

If \( f(x) = \frac{x^3 + 5}{\sqrt{12 + x}} \) and } \[ \int_{-5}^{5}f(x) \, dx = \int_{0}^{5} \left( f(x) + g(x) \right) \, dx, \text{ then } g(x) = \]

The area (in square units) bounded by the curves \( x^2 = 9y \), \( (x - 6)^2 = 9y \), and the X-axis is:

The substitution \( x = vy \) converts which one of the following differential equations to an equation solvable by the variable separable method?

If \( \frac{dy}{dx} = f(x,y) \) is a homogeneous differential equation, then the general form of \( f(x,y) \) is:

The order and degree of the differential equation \[ \frac{d^3 y}{dx^3} + 2 \left( \frac{d^2 y}{dx^2} \right) + xy = 0 \] are respectively:

Among the following the least unit for length is

The time of flight of a vertically projected stone is 8 s. The position of the stone after 6 s from the ground is

A stone thrown with velocity \( u \) at angles \( \theta \) and \( (90^\circ - \theta) \) with the horizontal reaches maximum heights \( H_1 \) and \( H_2 \) respectively. Its horizontal range is

Two vectors of same magnitude act at a point. Twice the product of the magnitudes of two vectors is equal to the square of the magnitude of their resultant. The angle between the two vectors is:

A car of mass 1500 kg is moving with 20 ms\(^{-1}\) velocity. If the breaks are applied it comes to rest in 5 seconds, then the retarding force is

A body is made to move up along an inclined plane of inclination \(30^\circ\) and the coefficient of friction is 0.5, then its retardation is:

A machine gun fires 300 bullets per minute each with a velocity of 500 ms\(^{-1}\). If the mass of each bullet is 4 g, the power of the machine gun is:

A body falls freely from a height of 100 m on to the ground and rebounds to a maximum height of 36 m after collision. The coefficient of restitution between the ground and the body is:

A force of \( (2\hat{i} + 3\hat{j} + 4\hat{k}) \, \text{N} \) acts on a particle whose position vector with respect to the origin of the coordinate system is \( (6\hat{i} + b\hat{j} + 12\hat{k}) \, \text{m} \). If the angular momentum of the body is constant, the value of \( b \) is:

The range of a projectile of weight \( W \) is \( R \). The average torque on the projectile between the initial and final positions \( P \) and \( Q \) about the point of projection is:

Two springs A and B fixed at the top and are stretched by 8 cm and 16 cm respectively, when loads of 20 N and 10 N are suspended at the lower ends. The ratio of the spring constants of the springs A and B is:

The amplitudes of a damped harmonic oscillator after 2 and 4 seconds are \( A_1 \) and \( A_2 \) respectively. If the initial amplitude of the oscillator is \( A_0 \), then

The value of acceleration due to gravity at a height of \( 4R_E \) from surface of earth is \[ R_E \text{ is radius of earth and acceleration due to gravity on the surface of the earth = 10 ms}^{-2} \]

The maximum possible height of a mountain on Earth is approximately.

The specific heat capacity of a copper block of mass \( M \) is \( s \). If the mass of the copper block is doubled, the specific heat capacity will be:

2 moles of a monatomic gas requires heat energy \( Q \) to be heated from 30°C to 40°C at constant volume. The heat energy required to raise the temperature of 4 moles of a diatomic gas from 28°C to 33°C at constant volume is:

A block of steel of mass 2 kg slides down a rough inclined plane of inclination of \( \sin^{-1} \left( \frac{3}{5} \right) \) at a constant speed. The temperature of the block as it slides through 80 cm, assuming that the mechanical energy lost is used to increase the temperature of the block is nearly:

Isothermal bulk modulus of a gas at a pressure \( P \) is:

A vessel of volume 10 liters is filled with \( H_2 \) gas. The total average translational kinetic energy of its molecules is \( 4.5 \times 10^5 \, \text{J} \). The pressure of hydrogen in the vessel is: