List of top Questions asked in AP EAPCET

If a constant force of \((2i + 3j + 4k) \, \text{N}\) acting on a body of mass \(5 \, \text{kg}\) displaces it from \((3i - 4k)\, \text{m}\) to \((2i + 2j + 3k)\, \text{m}\), then the work done by the force on the body is:

A motor can pump 7560 kg of water per hour from a well of depth 100 m. If the efficiency of the pump is 70%, then the power of the pump is:

A circular disc of diameter 0.8 m and mass 4 kg is rolling on a smooth horizontal plane. If 2.56 N torque is acting on the disc, then its angular acceleration is:

A solid sphere and a solid cylinder have same mass and same radius. The ratio of the moment of inertia of the solid sphere about its diameter and the moment of inertia of the solid cylinder about its axis is:

A particle is executing simple harmonic motion with amplitude \( A \). The ratio of the kinetic energies of the particle when it is at displacements of \( \frac{A}{4} \) and \( \frac{A}{2} \) from the mean position is:

If the potential energy of a particle of mass \(0.1 \, \text{kg}\) moving along the x-axis is \(5x(x - 4)\), then the speed of the particle is maximum at a position of:

The general solution of the differential equation \((1 + \sin^2 x) \, \frac{dy}{dx} + \sin 2x = 0\) is?

The displacement (\(x\)) and time (\(t\)) graph of a particle moving along a straight line is shown in the figure. The average velocity of the particle in the time of 10s is:

If the horizontal range of a body projected with a velocity \(u\) is 3 times the maximum height reached by it, then the range of the body is:

If the velocity at the maximum height of a projectile projected at an angle of \(45^\circ\) is \(20 \, \text{m/s}\), then the maximum height reached by the projectile is:

A body of mass \(m\) moving along a straight line collides with a stationary body of mass \(2m\). After collision if the two bodies move together with the same velocity, then the fraction of kinetic energy lost in the process is:

If a body of mass \(2 \, \text{kg}\) moving with initial velocity of \(4 \, \text{m/s}\) is subjected to a force of \(3 \, \text{N}\) for a time of 2 seconds normal to the direction of its initial velocity, then the resultant velocity of the body is:

Evaluate \[ \int \sin^3 x \cos^2 x \, dx = ? \]

Evaluate \[ \lim_{n \to \infty} \frac{1}{2n} \left( \sin \frac{\pi}{2n} + \sin \frac{\pi}{n} + \sin \frac{2\pi}{2n} + \dots \right) = ? \]

Evaluate \[ \int_0^\pi \left( \sin^3 x \cos^3 x + \sin^4 x \cos^4 x + \sin^3 x \cos^3 x \right) dx = ? \]

Evaluate \[ \int \frac{1}{x^4 + 1} \, dx = ? \]

The area of the region (in sq.units) bounded by the curves \(x^2 + y^2 = 16\) and \(x^2 + y^2 = 6x\) is?

If \(a\) and \(b\) are arbitrary constants, then the differential equation corresponding to the family of curves \(y = \tan (ax + b)\) is?

The general solution of the differential equation \(xy(y + 2y') + (y^2 - y) \, dx = 0\) is?

If the function \(f(x) = x^3 + b x^2 + c x - 6\) satisfies all conditions of Rolle's theorem in \([1,3]\) and \[ f'\left(\frac{2\sqrt{3} + 1}{\sqrt{3}}\right) = 0, \] then find \(bc\).

If \(P(\alpha, \beta)\) is a point on the curve \(9x^2 + 4 y^2 = 144\) in the first quadrant and the minimum area of the triangle formed by the tangent of the curve at \(P\) with the coordinate axes is \(S\), then find \(S\).

Evaluate \[ \int (\log 2x)^3 \, dx = ? \]

Evaluate \[ \int \frac{x + 1}{(x - 2) \sqrt{1 - x}} \, dx = ? \]

Evaluate \[ \int \frac{1}{1 + x^2} \, dx = ? \]

If \[ \int \frac{dx}{(x \tan x + 1)^2} = f(x) + c, \] then \(\lim_{x \to \frac{\pi}{2}} f(x)\) is?