List of top Questions asked in AP EAPCET- 2022

If the earth suddenly shrinks to \(\dfrac{1}{64}\) of its original volume, while keeping the same mass, then the duration of the day will be:
[Assume earth is a perfect sphere]
A lift raises 50 passengers each having average weight \(600\ \text{N}\) to a height of \(100\ \text{m}\) at a constant speed in time \(T\). If the average power of \(15\ \text{kW}\) is required by the lift, then the value of \(T\) in seconds is
A wheel is rotating freely at some angular speed. A second wheel initially at rest and with thrice the rotational inertia of the first, is suddenly coupled to the first wheel. The fraction of the original rotational kinetic energy lost is
A bar of mass \(m\) resting on a smooth horizontal plane starts moving due to a constant force \(F\). In the process of its rectilinear motion, the angle \(\theta\) between the direction of this force and the horizontal varies as \(\theta = kx\), where \(k\) is a constant and \(x\) is the distance traversed by the bar from its initial position. The velocity \(v\) of the bar as a function of the angle \(\theta\) is
A block of mass \(5 \, \text{kg}\) starts up a \(45^\circ\) incline plane with initial kinetic energy of \(100 \, \text{J}\). If the coefficient of friction between block and plane is \(0.5\), then the distance covered by the block before it stops is \((g=10\,\text{m s}^{-2})\):
There is a planet which is \(8\) times massive and \(27\) times denser than the earth. If \(g'\) and \(g\) are the accelerations due to gravity on the surfaces of the planet and the earth respectively, then:
A ball is projected from ground into the air. At the height of \(5 \, \text{m}\), its velocity is \(\vec{V}=(5\hat{i}+5\hat{j})\,\text{m s}^{-1}\). The maximum height reached by the ball is \((g=10\,\text{m s}^{-2})\):
A particle is moving along x-axis with velocity \(v=e^{-\beta x}\). At time \(t=0\), the particle is located at \(x=0\). The displacement of the particle as a function of time is:
The number of significant figures in quantity \(0.00005041\ \text{J}\) is
Consider three masses \(M_1\), \(M_2\) and \(M_3\), where \(M_1 \gt M_2 \gt M_3\), are at rest on a horizontal plane as shown in the figure. Now the angle of inclination \(\theta\) of the plane is gradually increased until the masses just begin to slide. Assume the coefficient of static friction between the masses and the surface is constant. Then the correct statement is
A biker travels \(\frac{1}{3}\) of the distance \(L\) with speed \(v_1\) and \(\frac{2}{3}\) of the distance with speed \(v_2\). Then the average speed is
The differential equation of the family of circles passing through \((0,0)\) and having centre on \(x\)-axis is
Evaluate \[ \int_{-\pi}^{\pi}\frac{\cos^{2022}x}{1+(2022)^x}\,dx \] =
If \[ \frac{a}{a_1}=\frac{b}{b_1}, \] then the substitution to be used to solve the differential equation \[ \frac{dy}{dx}=\frac{ax+by+c}{a_1x+b_1y+c_1} \] by using separation of variables is
Find the value of \[ \lim_{n\to\infty}\left(\frac{1^2}{n^3+1^3}+\frac{2^2}{n^3+2^3}+\cdots+\frac{1}{2n}\right) \] =
If \[ \int f(x)\,dx=F(x)+C, \] then \[ \frac{d}{dt}\int_{g(t)}^{h(t)}f(x)\,dx= \]
If \[ \int_{0}^{\pi/2}\sin^m x\cos^4 x\,dx=\frac{7\pi}{2048}, \] then \(m=\)
For the differential equation \[ \frac{d^3y}{dx^3}=0, \] \(y=ax^2+bx+c\) is
The function \(f(x)=2x^3-9ax^2+12a^2x+1\), where \(a\gt 0\), attains its maximum and minimum at \(p\) and \(q\) respectively and \(p^2=q\). Then \(a=\)
If \[ \int \frac{\cosec^2x-2022}{\cos^{2022}x}\,dx=f(x)+C \Rightarrow f\left(\frac{\pi}{4}\right)= \]
If \(f(x)\) is anti-derivative of \(g(x)\) and \[ \int f(x)g(x)(1+f^2(x))\,dx=F(x), \] then \(F(x)=\)
The set of all \(x\) for which \[ \sin x\leq x \] is
If \(k\in \mathbb{N}\), then \[ \int \frac{1-k\cos^2 x}{\sin^k x\cos^2 x}\,dx= \]
If \[ \int \cos^{-1}\left(\sqrt{\frac{x}{a+x}}\right)\,dx=f(x)+C \Rightarrow f'(a)= \]
The perimeter of a sector is constant. If its area is to be maximum, the sectorial angle should be