List of top Mathematics Questions asked in AP ECET CSE, AP ECET CE

If \(\sin 5x + \sin 3x + \sin x = 0\) then the value of x other than zero lying between \(0 \le x \le \frac{\pi}{2}\) is

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 that 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 \(y = a \sin x + b \cos x\) is (where a and b are arbitrary constants)

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

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

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

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

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

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

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

If \(u = e^{xy}\), then the value of \(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}\) 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 \(f(x) = 2x^3 + 3x^2 - 36x + 10\) 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 \(y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \dots \infty}}}\) then \( \frac{dy}{dx} = \)

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

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

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