List of top Mathematics Questions asked in AP EAPCET

If \(a\) and \(b\) are arbitrary constants, then the differential equation corresponding to the family of curves \(y = \tan (ax + b)\) is?
If the order and degree of the differential equation \(x \frac{d^2 y}{dx^2} = \left(1 + \left(\frac{d^2 y}{dx^2}\right)^2\right)^{-1/2}\) are \(k\) and \(l\) respectively, then \(k, l\) are the roots of
If \( y = \log(\sec(\tan^{-1}x)) \) for \( x>0 \), then \( \frac{dy}{dx} \) at \( x = 1 \) is:
If \( y = \tanh^{-1} \left( \dfrac{1 - x}{1 + x} \right) \), then \( \dfrac{dy}{dx} = \)
If g is the inverse of the function f(x) and \( g(x) = x + \tan x \) then, \( f'(x) = \)
The general solution of the differential equation \( \frac{dy}{dx} + \frac{\sec x}{\cos x + \sin x}y = \frac{\cos x}{1+\tan x} \) is
The equation of the curve passing through the point \( (0, \pi) \) and satisfying the differential equation \( ydx = (x + y^3 \cos y)dy \) is
The general solution of the differential equation \( \left(x - (x + y)\log(x + y)\right) dx + x\,dy = 0 \) is:
If $ a $ and $ b $ are the roots of the equation $ 4x^2 - 12x + 11 = 0 $, find the value of $ a^2 + b^2 $.
The general solution of the differential equation \( \frac{dy}{dx} = \frac{2x + y - 3}{2y - x + 3} \) is
\[ \text{If } x = 2 \cos^3 \theta \text{ and } y = 3 \sin^2 \theta, \text{ then } \frac{dy}{dx} =\ ? \]
The physical quantity having the dimensions of the square root of the ratio of the kinetic energy and surface tension is
If \( Ax^3 + Bxy = 4 \) (A and B are arbitrary constants) is the general solution of the differential equation \[ F(x)\frac{d^2y}{dx^2} + G(x)\frac{dy}{dx} - 2y = 0, \] then \( F(1) + G(1) = \)
The differential equation for which \( y^2 = 4a(x + a) \) (where \( a \) is a parameter) is the general solution is:
If $$ y = A t^2 + \frac{B}{t} \quad (A, B \text{ constants}) $$ is a general solution of the differential equation $$ f(t) y'' + g(t) y' + h(t) y = 0, $$ then find the relation between $ g(t), f(t), h(t) $.
The general solution of the differential equation \( \sec(x - y + 1) dy = dx \) is:
The solution of the differential equation \( x^2 (y + 1) \frac{dy}{dx} + y^2 (x + 1) = 0 \), when \( y(1) = 2 \), is
The differential equation of the family of circles passing through the origin and having centre on X-axis is
If $a$ and $b$ are the roots of the equation $2x^2 + 5x + 30 = 0$, find the value of $a^2 + b^2$.
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2xy-4x+y-2}{2xy+x-4y-2} \] is:
If g is the inverse of the function f(x) and \( g(x) = x + \tan x \) then, \( f'(x) = \)
If the slope of the tangent drawn at any point \((x, y)\) on a curve is \(x + y\), then the equation of that curve is
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2x^2 - xy - y^2}{x^2 - y^2} \]
The general solution of the differential equation \(\frac{dy}{dx} + xy = 4x - 2y + 8\) is
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2xy-4x+y-2}{2xy+x-4y-2} \] is: