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

If $a$ and $b$ are arbitrary constants, then the differential equation representing the family of curves $y = a \sin(x + b)$ is

The differential equation is $\frac{dy}{dx} + \frac{y}{x} = 0$ and $y(1) = 2$. Then the value of $y(3) =$

The general solution of the differential equation $\frac{dy}{dx} = e^{x-y} + x^{2}e^{-y}$ is

The differential equation is $\frac{dy}{dx} + y\tan x = \sec x$ and $y(0) = 1$. Then the value of $y(\frac{\pi}{4}) =$

$\int \frac{dx}{\sqrt{16-25x^{2}}} =$

The solution of the differential equation $x\frac{dy}{dx} + y = 0$ passing through the point (1,1) is $y =$

Degree of the differential equation $y = x\frac{dy}{dx} + a\sqrt{1 + (\frac{dy}{dx})^2}$ is

$\int_{0}^{\pi/2} \frac{\sin^{100}x}{\sin^{100}x + \cos^{100}x} dx =$

$\int_{0}^{1} x\sqrt{x^{2}+4} dx =$

$\int_{-\pi/6}^{\pi/6} \frac{\sin^{5}x \cos^{3}x}{x^{4}} dx =$

If $z = x^{2}y^{3} + e^{y}\sin x$, then $\frac{\partial^{2}z}{\partial x\partial y} =$

$\int \frac{dx}{\sin^{2}x \cos^{2}x} =$

$\int \frac{dx}{\sqrt{x+1} + \sqrt{x}} =$

If $\int \frac{\sin^{3}x + \cos^{3}x}{\sin^{2}x \cos^{2}x} dx = A\sec x + B\csc x + c$ then $(A, B)$ are}

The integral of $f(x) = 1 + x^{2} + x^{4}$ with respect to $x^{2}$ is

If $y(x) = x^{x}, x > 0$ then $y''(2) - 2y'(2) =$

If $y + \sin^{-1}(1 - x^{2}) = e^{x}$, then $\frac{dy}{dx} =$

If $y = \frac{(a \cos x + b \sin x + c)}{\sin x}$ then $\frac{dy}{dx} = $

If $y = \sqrt{x + \sqrt{x + \sqrt{x + ... \infty}$ then $\frac{dy}{dx} = $

Slope of the tangent to the curve $y = 9x^{2} + 7x^{4} + 5$ at the point $x = 1$ is

If $f(x) = \begin{cases} 4(5^{x}) & x < 0 \\ 8k + x & x \ge 0 \end{cases}$ then $f'(-1) =$

If $2^{x} + 2^{y} = 2^{x+y}$ then $\frac{dy}{dx} =$

If the parabola $y^{2} = 4ax$ passes through the point (3, 2) then the length of its latus rectum is:}

The line $y = mx + 2$ is a tangent to the parabola $y^{2} = 8x$ if}

The length of the latus rectum and eccentricity of the Hyperbola $9x^{2} - 16y^{2} = 144$ are}