List of top Mathematics Questions asked in AP EAPCET

For any complex number \(z\), the minimum value of \[ |z|+|z-1| \] is

If the vertices \(A\), \(B\) and \(C\) of an isosceles triangle \(ABC\) are respectively \(z_1\), \(z_2\) and \(z_3\), and if \(\angle C=90^\circ\), then

If \(\alpha_1,\alpha_2,\ldots,\alpha_{23}\) are the \(23^{rd}\) roots of unity, then \[ \alpha_1^{47}+\alpha_2^{47}+\cdots+\alpha_{23}^{47}= \]

The sum of squares of roots of the equation \[ x^{\frac{2}{3}}+x^{\frac{1}{3}}-2=0 \] is

If the system of simultaneous linear equations \[ 3x-4y+kz+13=0,\quad x+2y-z-9=0 \] \[ kx-y+3z+7=0 \] has a unique solution \(x=\alpha,\ y=\beta,\ z=\gamma\) for \(k\neq m\) and \(2\beta-\gamma=8\), then \(\alpha+m=\)

If \[ A= \begin{bmatrix} \sin\alpha & -\cos\alpha\\ \cos\alpha & \sin\alpha \end{bmatrix} \] and \(A+A^{-1}=I\), then \(\alpha=\)

If \[ A= \begin{bmatrix} x & 1 & 2\\ 2 & 4 & x\\ -3 & 3 & 2 \end{bmatrix} \] is a singular matrix and the distinct values of \(x\) are \(x_1\) and \(x_2\), then \(x_1+x_2+x_1x_2=\)

Let \[ A= \begin{bmatrix} 1 & 0 & -1 & -3\\ 0 & 1 & 1 & k-1\\ 0 & 0 & k-1 & 1 \end{bmatrix} \] and \(k\in \mathbb{R}\). Then the value of \(k\), if exists, for which the rank of \(A\) is \(2\), is

The domain of the real valued function \[ f(x)=\frac{\log_2(x+3)}{\sqrt{x^2+3x+2}} \] is

The domain of the real valued function \[ f(x)=\frac{\sqrt{2-x}+\sqrt{1+x}}{\sqrt{x+3}} \] is

The solution of \[ (1+y^2)\,dx-xy\,dy=0,\quad y(1)=0 \] represents a conic. Its eccentricity is

\(p\) and \(q\) are positive integers and \(n\lt r\lt m\). If the order and degree of the differential equation \[ \left( \frac{d^my}{dx^m}+\frac{d^ny}{dx^n} \right)^{p/q} = 5\frac{d^ry}{dx^r} \] are respectively \(4\) and \(3\), then

Evaluate \[ \int_{-a}^{a} f(x)\,dx-\int_{0}^{a} f(-x)\,dx \]

The substitution \[ \frac{dy}{dx}=z, \] reduces the differential equation \[ \frac{d^2y}{dx^2}-\frac{dy}{dx}=0 \] to a differential equation whose solution is \(z=\)

If \[ \int \frac{dx}{x^{2022}(1+x^{2022})^{\frac{1}{2022}}} = -\frac{(1+x^m)^{\frac{n}{m}}}{nx^n}+C, \] then \(m-n=\)

Evaluate \[ \int_{0}^{\pi}\frac{x}{\sin x}\left(3\cos^2x+2\sin x+\sin^3x-3\right)\,dx \] is equal to:

If \([\,\cdot\,]\) represents greatest integer function, then \[ \int_{\frac{3\pi}{4}}^{\pi} \left[\sin x+\left[\frac{4x}{\pi}\right]\right]\,dx = \] is equal to:

Evaluate \[ \int_{0}^{\pi} \left( \cos^2\left(\frac{3\pi}{8}-\frac{x}{4}\right) - \cos^2\left(\frac{11\pi}{8}+\frac{x}{4}\right) \right)\,dx \] is equal to:

If \[ \int \frac{\sin^3x\left(\tan^{-1}(\sec x+\cos x)\right)^{-1}}{\cos^4x+3\cos^2x+1}\,dx=f(x)+C, \] then \[ e^{f(x)}= \]

Evaluate \[ \int \frac{1}{\left(\sin x+\cos x+\sqrt{2\sin 2x}\right)^2}\,dx= \]

If \[ \int e^x\{f(x)-f'(x)\}=g(x)+C, \] then \[ \int e^x f'(x)\,dx= \]

The maximum area of a right angled triangle with hypotenuse \(h\) is:

The value of \(a\) for which the function \[ f(x)=a\sin x+\frac{1}{3}\sin 3x \] has an extremum value at \(x=\dfrac{\pi}{3}\) is:

If \(m\) is the slope of a tangent to the curve \(e^y=1+x^2\) at \(x=1\), then \(m=\)

\(V\) is the set of points on the curve \(y^3-3xy+2=0\) where the tangent is vertical, then \(V=\)