List of top Questions asked in AP ECET Agricultural Engg- 2025

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

The eccentricity of the ellipse \[ 16x^2+7y^2=112 \] is