List of top Questions asked in AP ECET Agricultural Engg

If we choose velocity \(V\), length \(L\) and force \(F\) as fundamental physical quantities, then how would you express power in terms of \(V\), \(L\) and \(F\)?

The particular integral of \[ \frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=e^{-2x} \] is

The solution of the differential equation \[ \frac{d^3y}{dx^3}+3\frac{d^2y}{dx^2}+2\frac{dy}{dx}=0 \] is

The solution of the differential equation \[ \frac{dy}{dx}+\frac{y}{x}=x^2 \] under the condition \(y(1)=1\) is

The solution of the differential equation \[ \frac{dy}{dx}=1+y^2 \] is

The differential equation \[ \frac{dy}{dx}=-\left(\frac{x+y}{1+x^2}\right) \] is

The order of the differential equation whose general solution is \[ y=a\sin x+b\cos x \] where \(a\) and \(b\) are arbitrary constants, is

The degree of the differential equation \[ y'+y=\frac{5}{y'} \] is

The RMS value of \(x^2\) in \([0,1]\) is

The area bounded by the curve \(y=4x^2\), the \(x\)-axis, the line \(x=0\) and the line \(x=1\) is

\[ \int_0^{\pi/2}\frac{\cos2x}{\sin x+\cos x}\,dx= \]

The value of \[ \int_0^1 x(1-x)^9\,dx \] is

\[ \int \frac{dx}{25-x^2}= \]

\[ \int \sin^2x\,dx= \]

The value of \[ \int (\log\sec x)\tan x\,dx \] is

If \(u=e^{xy}\), then the value of \[ \frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2} \] at \((1,1)\) is

If \(z=x^2-y^2\), then \[ \frac{1}{x}\frac{\partial z}{\partial x}+ \frac{1}{y}\frac{\partial z}{\partial y} = \]

For what value of \(x\), the function \[ 2x^3+3x^2-36x+10 \] has minimum?

The equation of the tangent to the curve \(y=x^3\) at \((1,1)\) is

Slope of the normal to the curve \[ x^{2/3}+y^{2/3}=2 \] at the point \((1,1)\) is

If \[ y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots}}}, \] then \(\frac{dy}{dx}=\)

\[ \frac{d}{dx}\left(\tan^{-1}\frac{x}{a}\right)= \]

The derivative of \(x^x\) with respect to \(x\) is

The value of \[ \lim_{x\to 1}\left(\frac{x^3-1}{x-1}\right) \] is

The value of \[ \lim_{x\to\infty}\frac{4x^3-x+1}{x^2-4x(1-x^2)} \] is