List of top Mathematics Questions asked in AP EAPCET

If \(\theta\) is any angle, then \[ \sin^2\theta \cos^2\theta= \]

Evaluate: \[ (4\cos^2 9^\circ-3)(4\cos^2 27^\circ-3)= \]

If the equivalent partial fraction of \[ \frac{x^3}{(2x-1)(x+2)(x-3)} \] is given by \[ A+\frac{B}{2x-1}+\frac{C}{x+2}+\frac{D}{x-3}, \] then the value of \(C\) is

Let \(T_n\) be the number of all possible triangles formed by joining vertices of an \(n\)-sided regular polygon. If \[ T_{n+1}-T_n=10, \] then the value of \(n\) is

How many numbers between \(10\) and \(10,000\) can be formed by using the digits \(1,2,3,4,5\), if no digit is repeated in any number?

If \(a\), \(b\), \(c\), \(d\) are real numbers such that \[ a\lt b\lt c\lt d, \] then the roots of the equation \[ (x-a)(x-c)+2(x-b)(x-d)=0 \] are

If one root of the quadratic equation \[ ax^2+bx+c=0 \] is equal to the \(n^{th}\) power of the other, then \[ (ac^n)^{\frac{1}{n+1}}+(a^nc)^{\frac{1}{n+1}}= \]

In how many ways can the letters of the word ``ASSASSINATION'' be arranged so that all \(S\)'s are together?

If \(a\), \(b\), \(c\) are distinct positive real numbers and \[ a^2+b^2+c^2=1, \] then the value of \(ab+bc+ca\) is

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

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

Evaluate: \[ (-1+\sqrt{3})^{60}= \]

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

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

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

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 \(x_1+x_2+x_1x_2=\)

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

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 \(\alpha+m=\)

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

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

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

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

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

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 \(z=\)