List of top Questions asked in AP ECET CE- 2025

If a body released from the top of a tower of height H meter takes T seconds to reach the ground, where is the body at time T/2 seconds from the ground?

If a pebble is thrown vertically upwards from the top of a tower with velocity 5 m/s. It strikes the ground after 3 seconds. With what velocity the pebble strikes the ground? (take g = 10 ms\(^{-2}\))

The area of rectangle with sides as \(\vec{A} = 3\hat{i} + 4\hat{j}\) and \(\vec{B} = \hat{i} + 3\hat{j}\) is

If \(\vec{A} + \vec{B} = \vec{C}\) and \(A^2 + B^2 = C^2\) then the angle between vectors \(\vec{A}\) and \(\vec{B}\) is

Which pair of physical quantities have same dimensional formula

If we choose velocity V, length L and force F as fundamental physical quantities then how would you express power in terms of V, L and F?

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