List of top Questions asked in AP EAPCET- 2022

The coefficient of static friction between the road and tyres of a car is \(0.4\). The maximum permissible speed of the car is \(10\text{ ms}^{-1}\) on a curved unbanked road. Then the maximum radius of curvature of the road is
\[ \text{(acceleration due to gravity }=10\text{ ms}^{-2}\text{)} \]

Which of the following is the fundamental force in nature?

A particle moves along a straight line along the \(x\)-axis. Its position \((x)\) versus time \((t)\) graph is shown in the figure \([x \text{ in meters and } t \text{ in seconds}]\). Its average speed during the motion is:

\(p\) and \(q\) are positive integers and \(n\lt r\lt m\). If the order and degree of the differential equation \[ \left( \frac{d^my}{dx^m}+\frac{d^ny}{dx^n} \right)^{p/q} = 5\frac{d^ry}{dx^r} \] are respectively \(4\) and \(3\), then

The equation for the trajectory of a projectile is \[ y=\left(\frac{x}{\sqrt{3}}-\frac{x^2}{60}\right)\text{ m} \] The velocity of projection of the projectile is
\[ (\text{Acceleration due to gravity }=10\ \text{ms}^{-2}) \]

The solution of \[ (1+y^2)\,dx-xy\,dy=0,\quad y(1)=0 \] represents a conic. Its eccentricity is

In a sports competition, a javelin is thrown at an angle \(45^\circ\), which recorded a range of \(90\text{ m}\). The maximum height reached by the javelin is
\[ \text{(Neglect air resistance and acceleration due to gravity }=10\text{ ms}^{-2}\text{)} \]

Evaluate \[ \int_{0}^{\pi} \left( \cos^2\left(\frac{3\pi}{8}-\frac{x}{4}\right) - \cos^2\left(\frac{11\pi}{8}+\frac{x}{4}\right) \right)\,dx \] is equal to:

If \[ \int \frac{dx}{x^{2022}(1+x^{2022})^{\frac{1}{2022}}} = -\frac{(1+x^m)^{\frac{n}{m}}}{nx^n}+C, \] then \(m-n=\)

Evaluate \[ \int_{0}^{\pi}\frac{x}{\sin x}\left(3\cos^2x+2\sin x+\sin^3x-3\right)\,dx \] is equal to:

The substitution \[ \frac{dy}{dx}=z, \] reduces the differential equation \[ \frac{d^2y}{dx^2}-\frac{dy}{dx}=0 \] to a differential equation whose solution is \(z=\)

Evaluate \[ \int_{-a}^{a} f(x)\,dx-\int_{0}^{a} f(-x)\,dx \]

If \([\,\cdot\,]\) represents greatest integer function, then \[ \int_{\frac{3\pi}{4}}^{\pi} \left[\sin x+\left[\frac{4x}{\pi}\right]\right]\,dx = \] is equal to:

If \[ \int e^x\{f(x)-f'(x)\}=g(x)+C, \] then \[ \int e^x f'(x)\,dx= \]

The value of \(a\) for which the function \[ f(x)=a\sin x+\frac{1}{3}\sin 3x \] has an extremum value at \(x=\dfrac{\pi}{3}\) is:

The maximum area of a right angled triangle with hypotenuse \(h\) is:

If \[ \int \frac{\sin^3x\left(\tan^{-1}(\sec x+\cos x)\right)^{-1}}{\cos^4x+3\cos^2x+1}\,dx=f(x)+C, \] then \[ e^{f(x)}= \]

Evaluate \[ \int \frac{1}{\left(\sin x+\cos x+\sqrt{2\sin 2x}\right)^2}\,dx= \]

If \(m\) is the slope of a tangent to the curve \(e^y=1+x^2\) at \(x=1\), then \(m=\)

If \[ \frac{y}{x}\cos^4\alpha+\frac{x}{y}\sin^4\alpha = 2\sin^2\alpha\cos^2\alpha, \] then \[ \frac{dy}{dx}= \]

If \[ \frac{d}{dx} \left[ A\log\left(\frac{\sqrt{1-x^3}+B}{\sqrt{1-x^3}+1}\right) \right] = \frac{1}{x\sqrt{1-x^3}}, \] then \(AB=\)

\(V\) is the set of points on the curve \(y^3-3xy+2=0\) where the tangent is vertical, then \(V=\)

The equation of tangent of the curve \[ y=\sqrt{9-2x^2} \] at the point where the ordinate and abscissa are equal is

If \(a\gt 0,\ b\gt 0\), then \[ \lim_{n\to\infty} \left( \frac{a+b^{1/n}-1}{a} \right)^n = \] is equal to:

If \(a,b,c\) are the direction ratios of a line \(L\) and \(\ell,m,n\) are its direction cosines, then \[ \frac{a^2}{b^2+c^2}= \] is equal to: