List of top Mathematics Questions asked in AP EAPCET

Among the following differential equations, the equation having order 2 and degree 3 is:

Solve $(1+y^2)+(x-e^{-\tan^{-1}y})\frac{dy}{dx}=0$

The differential equation among the following, whose general solution is \( y=A e^{5x}+B e^{-4x} \) is

Eliminate constants from $y=A(x+B)^2$

Given that \[ \frac{dy}{dx}=ye^x \] and when \[ x=0,\quad y=e, \] then the value of \(y\) (\(y>0\)) when \(x=1\) is

The general solution of the differential equation \[ (x+y-1)\,dy=(x-y+1)\,dx \] is

If the differential equation of the family of curves given by \[ y=ae^x+b\cos x, \] where \(a\) and \(b\) are arbitrary constants, is \[ y_2(\cos x+\sin x)+y(\cos x-\sin x)=2y_1f(x), \] then \(f(x)=\)

The general solution of the differential equation \[ (4xy^2-2xy+2x^2y^2-x^2y)\,dx=dy \] is

The general solution of the differential equation $\frac{dy}{dx} + y \cot x = 2 \cos x$ is:

Consider the differential equations \(\frac{dy}{dx}(x+y+1)=1\) and \(\frac{dx}{dy}=3y+2x^2\).
Which of the following is correct regarding these two differential equations?

If the degree of the differential equation $\left(\frac{d^{2}y}{dx^{2}}\right)^{3/2}+5\left(\frac{d^{2}y}{dx^{2}}\right)^{5/2}=7y$ is $m$ and its order is $n$, then $y=Ae^{mx}+Be^{nx}$ is solution of the differential equation

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

If $y=f(x)$ is a solution of $\frac{dy}{dx}=(y-kx)^{2}+K$ when $x=0$ and $y=1$, then $f(2)=$

Solve $\cos(x+y)dy=dx$

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

The general solution of the differential equation \( \frac{dy}{dx}=x^{2}y(x+y+xy+1) \) is \( y = \)

If \(a\) and \(b\) are arbitrary constants, then the differential equation corresponding to the family of curves \[ ax^2+2hxy=1 \] is

The general solution of the differential equation \( \frac{dy}{dx} + y \tan x = - \tan x \log(\cos x) \) (\(0 < x < \pi/2\)) is:

The integrating factor of the differential equation $(1 + x^2) \frac{dy}{dx} + 2xy = \cos x$ is:

One of the values of the square root of \[ \left(\frac{1}{2}+\frac{\sqrt{3}}{2}i\right) \] is

If the conjugate of a complex number $z$ is $\frac{1}{z - i}$, then $z$ can be:

If \[ \frac{3}{2+\cos\theta+i\sin\theta}=x+iy, \] then \[ (x-1)(x-3)= \]

If \( z=(1+\sqrt{3}i)^{4/3} \), then the product of all the values of \( z \) is

Let a point \(P\) in the Argand plane represent the complex number \(z\). If \[ \operatorname{Arg}\left(\frac{2z-i}{z-2}\right)=\frac{\pi}{4}, \] then the locus of \(P\) is

Given that \[ \sum_{k=1}^{n} k(k-1)=\frac{n(n-1)(n+1)}{3} \] and $\omega$ and $\omega^2$ are complex cube roots of unity. If \[ \sum_{k=1}^{2026} \left( k+\frac{1}{\omega} \right) \left( k+\frac{1}{\omega^2} \right) = \frac{2026}{3}(N+3), \] then $N=$