List of top Mathematics Questions asked in AP ECET

The degree of the differential equation \(y' + y = \frac{5}{y'}\) 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 differential equation \(\displaystyle \frac{dy}{dx}=-\left(\frac{x+y}{1+x^2}\right)\) is

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The equation of the parabola with focus \((2,0)\) and vertex \((1,0)\) is

If \((2,0)\) is the vertex and \(y\)-axis is the directrix of a parabola, then its focus is

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