List of top Questions asked in AP EAPCET- 2022

A body of volume \(V\) floats on water with \(\frac{1}{3}\) of its volume above the surface. Find the volume of the object above the surface when floating on a liquid of specific gravity 1.5.

A block of 10 kg mass is connected to the top of a frictionless inclined plane of inclination \(45^\circ\) by a spring of negligible mass, unstretched length 0.8 m, and spring constant \(100\sqrt{2} \, \text{N/m}\). Find the distance of the block from the top along the incline in the equilibrium position. (Acceleration due to gravity \(g = 10 \, \text{m/s}^2\))

A body is located at \((1, 1, 1) \, \text{m}\) and experiences a force of 2 N in the direction \(\hat{i} + \hat{j}\). Find the torque acting on the body in N·m.

The escape speed of an object on the surface of the Earth is \(V\). If the object is thrown out with speed \(4V\) from the surface of the Earth, find the speed of the object far away from the Earth.

The moment of inertia of a thin uniform rectangular plate of mass \(m\), having length \(a\) and width \(b\), about an axis perpendicular to the plane of the plate and passing through one of its vertices is:

A solid sphere of mass \(M\) and radius \(R\) is attached to a spring of negligible mass kept on a horizontal plane such that it can roll without slipping. The sphere is made to execute SHM by stretching through a distance and released. Find the time period of such oscillation. (K = spring constant)

The work done in stretching a spring of natural length 25 cm and spring constant 50 N/m from 50 cm to 60 cm is:

A block of mass 2 kg is pulled at a constant speed with a taut rope along a frictionless plane that is inclined at \(30^\circ\). Find the work done by the tension in the rope in pulling it a distance 4 m along the inclined plane. (Acceleration due to gravity \(g = 10 \, \text{m/s}^2\))

A particle moving in the x–y plane starts from the origin at \(t = 0\) with an initial velocity \((-\hat{i} + \hat{j}) \, \text{m/s}\) and undergoes an acceleration \((6\hat{i} + 4\hat{j}) \, \text{m/s}^2\). Its displacement after 2 s is:

A 1 kg box placed at the origin starts sliding along x-axis under the action of a force \(\vec{F} = m \vec{a}\). Its acceleration as a function of x is given by \(a(x) = \beta x\) where \(\beta = 5 \, \text{s}^{-2}\). Find the work done by \(\vec{F}\) in moving the box from \(x = 2 \, \text{cm}\) to \(x = 5 \, \text{cm}\).

A block of mass 8 kg is suspended by a rope of length 3 m from the ceiling. A horizontal force of 40 N is applied to the block. Determine the angle that the rope makes with the vertical in equilibrium. (Acceleration due to gravity \(g = 10 \, \text{m/s}^2\), neglect the mass of the rope)

An object requires 500 N force to be pulled up on a \(30^\circ\) frictionless smooth inclined plane at a constant speed. Determine the weight of the object.

The general solution of \(\frac{d^2 y}{dx^2} = 0\) is

The equation of the family of curves for which the length of the subnormal at any point \((x,y)\) is always a constant \(k\) is

The dimensional formula \[ [ML^2T^{-2}K^{-1}] \] corresponds to which physical quantity?

The correct position (x) - time (t) graph for a particle moving with negative acceleration is:

A ball is thrown upward from the top of a building at an angle of \(30^\circ\) to the horizontal with an initial speed of 15 m/s. If the ball hits the ground after 3 s, find the height of the building. (Acceleration due to gravity \(g = 10 \, \text{m/s}^2\))

If the differential equation obtained by eliminating \(A, B\) from \(y = (\sin^{-1}x)^2 + A \cos^{-1} x + B\) is \((a-x^2)y'' - xy' = b\), then \(\frac{b+a}{b-a} =\)

Evaluate \[ \int_2^5 \sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\,dx \]

If \[ \int (1+x)\log(1+x^2)\,dx= \left(x+\frac{x^2}{2}+\frac{1}{2}\right)\log(1+x^2)+g(x)+C, \] then \(g(x)=\)

Evaluate \[ \int_{\frac{\pi}{11}}^{\frac{9\pi}{22}} \frac{dx}{1+\sqrt{\tan x}} \]

Evaluate \(\lim_{n \to \infty} \frac{1}{\sqrt{n}} \left[ 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \cdots + \frac{1}{\sqrt{n}} \right]\)

If \(m,n\in \mathbb{Z}\), then \[ \int_0^{2\pi}\cos mx\cos nx\,dx+\int_{-\pi}^{\pi}\sin mx\cos nx\,dx= \]

If \(0 \lt x \lt 1, \int \frac{dx}{\sqrt{x^2 - x^5}} = \frac{1}{3} \log |f(x)| + C\), then \(f(1/2) =\)

Evaluate \[ \int \frac{dx}{\sin\left(x-\frac{\pi}{3}\right)\cos x} \]