List of top Questions asked in AP EAPCET- 2022

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

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

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 \(=10\,\text{m s}^{-2}\))

The two principal thrusts in physics are

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

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 \(F(V)=\)

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

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

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

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 \(f(x)=\)

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

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

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 \(\dfrac{n}{\alpha}=\)

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

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

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

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

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 \(K+L=\)

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

If \[ y=\frac{\log x}{x}, \] then \[ \frac{d^2y}{dx^2} at x=1 = \]

If \[ f(x)=|x^2-3x+2|, \] then \[ \frac{df}{dx}= \]

If \[ y=\sin\left(2\tan^{-1}\sqrt{\frac{1-x}{1+x}}\right), \quad x=\cos 2\theta, \] then \[ \frac{dy}{dx}= \]

The angle made by the tangent at \(\theta=\dfrac{\pi}{3}\) on the curve \(x=a(\theta+\sin\theta)\), \(y=a(1-\cos\theta)\) with \(x\)-axis is

Let \[ f(x)=\lim_{y\to\infty} y\left(x^{1/y}-1\right), \] and \[ 2022\,f\left(\frac{1}{x}\right)+P\,f(x)=f(x^2), \] then \(P=\)