List of top Questions asked in AP ECET Metallurgical Eng- 2026

The length of a vector $(3\hat{i} + \hat{j} + 2\hat{k})$ in XY plane is

Among the following, unit less quantity is

$\frac{dy}{dx} = xy + x + y + 1$ has the solution}

The general solution of $\frac{ydx - xdy}{y^2} = 0$ represents a family of}

Which of the following is an integrating factor for the differential equation $x \cos x \frac{dy}{dx} + (x \sin x + \cos x) y = 1$?

The equation of the curve passing through the origin and satisfying the differential equation $\frac{dy}{dx} = (x-y)^2;$

If the solution $y(x)$ of the given differential equation $(e^y+1) \cos x dx + e^y \sin x dy = 0$ passes through the point $(\pi/2, 0)$ then the value of $y(\pi/6)$ is

If F is the force, S is the displacement and V is the velocity of the particle, the dimensions of the ratio $FS/V^{2}$ will be}

If the order and degree of a differential equation $(\frac{d^4y}{dt^4} + \frac{d^2y}{dt^2})^{5/2} = 10 \frac{d^3y}{dt^3}$ are $p$ and $q$, respectively, then $p+q =$

The differential equation of the family of concentric circles with Centre at the origin is

If $k \int_{0}^{1} x f(3x) dx = \int_{0}^{3} t f(t) dt$ then $k =$

$\int_{a}^{b} (|x-a| + |x-b|) dx = , (0 < a < b)$

$\int_{0}^{2} \frac{dx}{\sqrt{2+x} + \sqrt{2-x}} =$

If $I_{n} = \int \frac{t^{n}}{1+t^{2}} dt$ then $I_{6} + I_{4} =$

$\int (x+1)^{2} e^{x} dx =$

If $\int \frac{2x^{2}+a^{2}}{x^{2}(x^{2}+a^{2})} dx = \frac{k}{x} + \frac{1}{a} \tan^{-1} \frac{x}{a} + c$ then $k =$

If $\int \frac{1}{(x+100)\sqrt{x+99}} dx = f(x) + c$ then $f(x) =$

$\int \frac{1+\cos 4x}{\cot x - \tan x} dx =$

The set of all points of differentiability of the function $f(x)=e^{-|x|}$ is

If there is an error of 3% in the volume of a sphere then the percentage error in its radius is

The interval in which $f(x) = 2x^{2} - \log x$ increases is

The function $y = xe^{x}$ has}

The value of p such that the line joining (0,3), (5, -2) is a tangent to the curve $y = \frac{p}{x+1}$ is

$Lt_{x \to 0}\frac{e^{x^2}-cos x}{sin^2x}=$

Which of the following functions have finite number of points of discontinuity?