List of top Mathematics Questions asked in AP ECET EIE

Particular integral of $f(D)y = \cos ax$ is

Complementary function of the differential equation $(D^3 - 8)y = x$ is

The Order of the differential equation $\left[ \frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 \right]^{6/5} = 6y$ is

Transform $dx + xdy = e^{-y} \sec^2 y \, dy$ into linear form

The integrating factor of $\frac{dy}{dx} + 3x = 2y$ is

Bernoulli's equation is of the form

The necessary and sufficient condition for the differential equation $Mdx + Ndy = 0$ to be exact is

$\int \frac{dx}{\sqrt{x}} =$

$\int \sin \frac{y}{2} \, dy =$

$\int_0^\pi dx =$

If $f(x)$ is an even function, then $\int_{-a}^{a} f(x)dx=$

The area under the curve $f(x) = \sin x$ in $[0, 2\pi]$ is

When $a=b$ then $\int_{a}^{b} f(x)dx =$

$\int \frac{1}{\sqrt{a^2 - x^2}} \, dx =$

$\int e^x \cos x \, dx =$

If $S = 12t - 3t^2$ then $\frac{dS}{dt} =$

$\int \cot^2 x \, dx =$

If $u = e^x \sin y$ then first partial derivative of $u$ with respect to $y$ is

$\frac{d}{dx} \left( e^{3 \log x} \right) =$

If $u(x, y) = \sin^{-1} \frac{x}{y} + \tan^{-1} \frac{y}{x}$ then $xu_x + yu_y =$

$\frac{d}{dx} [e^x(x^2 + 1)] =$

When $a \gt 0$, $\lim_{x \to 0} \frac{a^x - 1}{x} =$

If $4x - 7y + 15 = 0$ then derivative of $y$ with respect to $x$ is

If $y = \cos x$ then $\frac{d^2y}{dx^2} =$

$\frac{d}{dx} [\tan^{-1} x] =$