List of top Mathematics Questions asked in AP EAPCET

The area of the region (in sq. units) enclosed between the curves \( y = |x| \), \( y = [x] \) and the ordinates \( x = -1, x = 0, x = 1 \) is

The general solution of the differential equation \(\frac{dy}{dx} = \frac{x + y + 1}{x - 3y + 5}\) is

Evaluate the integral \[ \int_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}} \frac{1}{\left(x + \sqrt{1 - x^2}\right) \cdot \left(1 - x^2\right)} \, dx = \]

The general solution of the differential equation \((x+2y)^3\frac{dy}{dx} = y = 0, y>0\) is

If \( \int \frac{dx}{(x-1)^2(x-3)^2 = \sqrt{f(x)} + c \), then \( f(-1) - f(0) = \)}

\( \int \frac{x}{(1-x^2)\sqrt{2 - x^2} dx = \)}

Evaluate the integral $\displaystyle \int_0^{\frac{\pi{2}} \log(\tan x + \cot x)\, dx$}

Evaluate the integral \[ \int_{0}^{\pi} x \cdot \sin x \cdot \int_{x}^{5} \frac{\cos x}{x} \cdot dx = \]

If the curves \(y^2 = 16x \text{ and } 9x^2 + \alpha y^2 = 25\) intersect at right angles, then \(\alpha =\)

If the normal drawn at the point P on the curve \(y = x \log x\) is parallel to the line \(2x - 2y = 3\), then P =

If \(x^2 + y^2 = \dfrac{1}{t} \text{ and } x^4 + y^4 = t^2 + \dfrac{1}{t^2},\) then \(\dfrac{dy}{dx} =\)

If the function \(y = \sin(x)(1 - \cos x)\) is defined in the interval \([-\pi, \pi]\), then y is strictly increasing in the interval

If \(y = (ax + b)\cos x\), then \(y_2 + y_1 \sin 2x + y(1 + \sin^2 x) = \)

If \( y = \tanh^{-1} \left( \dfrac{1 - x}{1 + x} \right) \), then \( \dfrac{dy}{dx} = \)

If a function defined by \[ f(x) = \begin{cases} \dfrac{1 - \cos 4x}{x^2}, & x<0
a, & x = 0
\dfrac{\sqrt{x}}{\sqrt{16 + \sqrt{x} - 4}}, & x>0 \end{cases} \] is continuous at \(x = 0\), then \(a =\)