List of top Questions asked in AP ECET

A body falling from height \(H\) takes time \(T\) seconds to reach the ground. The time taken to cover the second half of height is

With what speed should a body be thrown upwards so that the distances covered in the \(5^{th}\) second and \(6^{th}\) second are equal?

If \(P=Fv\sin\beta t\), where \(F\) is force and \(v\) is velocity, then the dimensions of \(P\) and \(\beta\) are

If velocity \(V\), energy \(E\), and time \(T\) are chosen as fundamental quantities, then dimensional representation of surface tension in this system will be

If \(|\vec A+\vec B|=|\vec A-\vec B|\), then the angle between the two vectors \(\vec A\) and \(\vec B\) is

An aeroplane is moving in a circular path with a speed of \(450\ \text{kmph}\). What is the change in velocity in half revolution?

The ratio between maximum and minimum values of two vectors \(\vec A\) and \(\vec B\), where \(A>B\), is \(4:1\). Then the ratio between the magnitudes of two vectors is

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

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

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 \[ y=x\frac{dy}{dx}+a\sqrt{1+\left(\frac{dy}{dx}\right)^2} \] is

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

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

The order of the differential equation of all circles passing through the origin and having their centres on the \(x\)-axis is

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

\[ \int_0^1 x\sqrt{x^2+4}\,dx= \]

\[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{6}} \frac{\sin^5x\cos^3x}{x^4}\,dx= \]

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

\[ \int_0^{\frac{\pi}{2}} \frac{\sin^{100}x}{\sin^{100}x+\cos^{100}x}\,dx = \]

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

\[ \int \frac{dx}{\sqrt{x+1}+\sqrt{x}}= \]

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

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

If \[ f(x)= \begin{cases} 4(5^x), & x 8k+x, & x\geq 0 \end{cases} \] then \(f'(-1)=\)

If \(y(x)=x^x,\ x>0\), then \[ y''(2)-2y'(2)= \]