List of top Questions asked in AP EAPCET- 2022

A cricket ball hits the ground with a speed of \(5\,\text{m s}^{-1}\) making an angle \(30^\circ\) with the horizontal. If the coefficient of restitution is \(0.2\), then the speed of the reflected ball in \(\text{m s}^{-1}\) is

A circular portion of radius \(R_2\) has been removed from one edge of a circular disc of radius \(R_1\). The correct expression for the centre of mass for the remaining portion of the disc is

Three forces of magnitudes \(F_1\), \(F_2\) and \(F_3\) act on a body located at the origin as shown in the figure. The condition that gives zero net force is

A system consists of two springs connected in series and each having the spring constant \(10\,\text{N m}^{-1}\). The minimum work required to stretch this system by \(1\,\text{cm}\) in erg is

A cannon ball is fired from the top of a \(55\,\text{m}\) high cliff with an initial speed of \(50\,\text{m s}^{-1}\). The speed of the cannon ball while hitting the ground in \(\text{m s}^{-1}\) is \((\text{acceleration due to gravity}=10\,\text{m s}^{-2})\)

A block is lying at rest inside a bus. The maximum acceleration of the bus such that the block remain stationary is \((\text{the static friction coefficient}=0.2,\ \text{acceleration due to gravity}=10\,\text{m s}^{-2})\)

The two principal thrusts in physics are

A ball is dropped from a tower of height \(80\,\text{m}\). The time it takes to cover the last \(50\%\) of its fall is (acceleration due to gravity \(=10\,\text{m s}^{-2}\))

A vector \(\vec{P}\) directed along the \(x\)-axis is added to vector \(\vec{Q}\) which has a magnitude of \(10\,\text{m}\). The resultant vector is directed along the \(y\)-axis, with a magnitude that is \(2\) times that of \(\vec{P}\). The magnitude of \(\vec{P}\) is

In the projectile motion of an object, the object reaches its maximum height where its speed is half of initial speed. Then the ratio between range and maximum height of projectile is

If \(\displaystyle \int_{9}^{x}\frac{f(y)}{y^2}\,dy=2\sqrt{x}-6\), then \(f(x)=\)

Suppose that \(f(x,y)\) and \(g(x,y)\) are homogeneous functions of same order. If \(x=Vy\) reduces the equation \(\dfrac{dy}{dx}=\dfrac{f(x,y)}{g(x,y)}\) to the form \(\dfrac{dV}{dy}=\dfrac{1}{y}(F(V))\), then \(F(V)=\)

The general solution of \(xdy-ydx=xy\,dy\) is

If the solution of \(\dfrac{dy}{dx}=\dfrac{y^3\cos\sqrt{x}}{\sqrt{x}e^{1/y^2}}\), \(y(0)=1\), is \(\dfrac{1}{y^2}=\log_e(f(x))\), then \(f(x)=\)

\(\displaystyle \int_{-1}^{2}\left[\tan^{-1}\left(\frac{x}{x^2+1}\right)+\tan^{-1}\left(\frac{x^2+1}{x}\right)\right]dx=\)

\(\displaystyle \int_{-\pi/2}^{2\pi}\sin^{-1}(\sin x)\,dx=\)

\(\displaystyle \int_{0}^{\infty}\left(x^{12}+x^{-12}\right)\frac{\log x}{x}\,dx=\)

\(\displaystyle \int (\log x)^2 x^3\,dx=\dfrac{x^4}{32}f(x)+C \Rightarrow f(x)=\)

\(\displaystyle \int \left(\sqrt{x+\sqrt{12x-36}}+\sqrt{x-\sqrt{12x-36}}\right)\,dx=\)

If \(\displaystyle \int \frac{x\,dx}{\sqrt[15]{(1+x^2)^{12}(2+x^2)^{18}}}=\alpha\left(\frac{1+x^2}{2+x^2}\right)^{1/n}+C\), then \(\dfrac{n}{\alpha}=\)

If \(0<x<\dfrac{\pi}{2}\), then

If \(f(x)=\sqrt{3\sin x-\cos x-2ax+b}\) decreases for all values of \(x\), then

If the angle between the curves \(y^2=4x\) and \(y=e^{-x/2}\) is \(\theta\), then \(\cosec^2\left(\dfrac{\theta}{2}\right)\) is

The least intercept made by a tangent to the ellipse \(\dfrac{x^2}{64}+\dfrac{y^2}{49}=1\) with coordinate axes is

If \(\displaystyle \int \frac{3e^x-7e^{-x}}{7e^x+3e^{-x}}\,dx=Kx+L\log\left(e^{-2x}+\frac{7}{3}\right)+C\), then \(K+L=\)