List of top Questions asked in AP EAPCET- 2022

A solid sphere of radius \(R\) has its outer half removed, so that its radius becomes \(\left(\dfrac{R}{2}\right)\). Then its moment of inertia about the diameter is

Two balls \(A\) and \(B\), of masses \(M\) and \(2M\) respectively collide each other. If the ball \(A\) moves with a speed of \(150\;\text{m s}^{-1}\) and collides with ball \(B\), moving with speed \(v\) in the opposite direction. After collision if ball \(A\) comes to rest and the coefficient of restitution is \(1\), then the speed of ball \(B\) before it collides with ball \(A\) is

A body is executing S.H.M. At a displacement \(x\), its potential energy is \(9\;J\) and at a displacement \(y\), its potential energy is \(16\;J\). The potential energy at displacement \((x+y)\) is

As shown in the figure, an iron block \(A\) of volume \(0.25\;m^3\) is attached to a spring \(S\) of unstretched length \(1.0\;m\) and hanging to the ceiling of a roof. The spring gets stretched by \(0.2\;m\). This block is removed and another block \(B\) of iron of volume \(0.75\;m^3\) is now attached to the same spring and kept on a frictionless inclined plane of \(30^\circ\) inclination. The distance of the block from the top along the incline at equilibrium is

\(y=(Pt^2-Qt^3)\;m\) is the vertical displacement of a ball which is moving in vertical plane. Then the maximum height that the ball can reach is

A force \(\vec{F_1}\) of magnitude \(4\;N\) acts on an object of mass \(1\;kg\), at origin in a direction \(30^\circ\) above the positive \(x\)-axis. A second force \(\vec{F_2}\) of magnitude \(4\;N\) acts on the same object in the direction of the positive \(y\)-axis. The magnitude of the acceleration of the object is nearly

A cricket ball of mass \(50\;g\) having velocity \(50\;\text{cm s}^{-1}\) is stopped in \(0.5\;s\). The force applied to stop the ball is

Two masses \(M_1\) and \(M_2\) are arranged as shown in the figure. Let \(a\) be the magnitude of the acceleration of the mass \(M_1\). If the mass of \(M_1\) is doubled and that of \(M_2\) is halved, then the acceleration of the system is

An object moving along \(x\)-axis with a uniform acceleration has velocity \[ \vec{V}=(12\;\text{cm s}^{-1})\hat{i} \] at \(x=3\;\text{cm}\). After \(2\;\text{s}\), if it is at \(x=-5\;\text{cm}\), then its acceleration is

In SI units, \(kg\;m^2\;s^{-2}\) is equivalent to which of the following?

If \[ 2x-y+c\log|x-2y-4|=k \] is the general solution of \[ \frac{dy}{dx}=\frac{2x-4y-5}{x-2y+2}, \] then \(c=\)

If \(l\) and \(m\) are order and degree of a differential equation of all the straight lines at constant distance of \(P\) units from the origin, then \(lm^2+l^2m=\)

By eliminating the arbitrary constants from \[ y=(a+b)\sin(x-c)-de^{x+e+f}, \] the differential equation obtained is of order

If \[ f(x)=\max\{\sin x,\cos x\} \] and \[ g(x)=\min\{\sin x,\cos x\}, \] then \[ \int_0^{\pi} f(x)\,dx+\int_0^{\pi} g(x)\,dx= \]

Evaluate \[ \int_{0}^{\pi/4} e^{\tan^2\theta}\sin^2\theta\tan\theta\,d\theta \]

Evaluate \[ \int \frac{1+\tan x\tan(x+a)}{\tan x\tan(x+a)}\,dx \]

If \[ I_n=\int_{0}^{\pi/4}\tan^n x\,dx, \] then \[ \frac{1}{I_2+I_4}+\frac{1}{I_3+I_5}+\frac{1}{I_4+I_6} \] is equal to

Evaluate \[ \int_{\pi/4}^{5\pi/4}\left(|\cos t|\sin t+|\sin t|\cos t\right)\,dt \]

If \[ \int \frac{1+\tan x}{\sin 2x}\,dx=A\log \tan x+B\tan x+C, \] then \(4A-2B=\)

If \[ \int \frac{e^{\sqrt{x}}}{\sqrt{x}}(x+\sqrt{x})\,dx = e^{\sqrt{x}}\left[Ax+B\sqrt{x}+C\right]+K, \] then \(A+B+C=\)

The number of those tangents to the curve \[ y^2-2x^3-4y+8=0 \] which pass through the point \((1,2)\) is

A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is

If the straight line \[ x\cos\alpha+y\sin\alpha=p \] touches the curve \[ \left(\frac{x}{a}\right)^n+\left(\frac{y}{b}\right)^n=2 \] at the point \((a,b)\) on it and \[ \frac{1}{a^2}+\frac{1}{b^2}=\frac{k}{p^2}, \] then \(k=\)

If \[ f(x)=\int x^2\cos^2x\left(2x\tan^2x-2x-6\tan x\right)\,dx \] and \(f(0)=\pi\), then \(f(x)=\)

Two particles \(P\) and \(Q\) located at the points \[ P(t,t^3-16t-3),\qquad Q(t+1,t^3-6t-6) \] are moving in a plane. The minimum distance between the points in their motion is