List of top Questions asked in AP ECET Metallurgical Eng

If the resultant of two vectors is equal to either of vectors, the angle between them is

Among the following, unit less quantity is

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

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

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

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

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

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

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

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 $p+q =$

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

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

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 $k =$

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?