List of top Questions asked in AP ECET- 2025

A block of mass \(m\) is lying on an inclined plane. The coefficient of friction between the plane and the block is \(\mu\). The force required to move the block up the inclined plane will be

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 \(\displaystyle \frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=e^{-2x}\) is

If \(A+B=C\) and \(A^2+B^2=C^2\), then the angle between vectors \(A\) and \(B\) is

Which pair of physical quantities have same dimensional formula?

The area of rectangle with sides as \(\vec A=3\hat i+4\hat j\) and \(\vec B=\hat i+3\hat j\) is

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

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

The solution of the differential equation \(\displaystyle \frac{dy}{dx}=1+y^2\) is

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

The differential equation \(\displaystyle \frac{dy}{dx}=-\left(\frac{x+y}{1+x^2}\right)\) 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 RMS value of \(x^2\) in \([0,1]\) is

\(\displaystyle \int_{-a}^{a}|x|\,dx=\)

\(\displaystyle \int \frac{dx}{25-x^2}=\)

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

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

\(\displaystyle \int_{0}^{\pi/2}\frac{\cos 2x}{\sin x+\cos x}\,dx=\)

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

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

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

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

\(\displaystyle \int \sin^2x\,dx=\)

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

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