List of top Mathematics Questions asked in AP EAPCET

If \[ 1-\cot 23^\circ=\frac{x}{1-\cot 22^\circ}, \] then \(x=\)
The number of ways of dividing \(200\) dissimilar things into \(10\) groups each containing \(20\) elements is:
In how many different ways can three persons \(A\), \(B\), \(C\) having \(6\), \(7\) and \(8\) one-rupee coins respectively, donate Rs.\(10\) collectively?
A student is to answer \(10\) out of \(13\) questions in an examination such that he must choose at least \(4\) from the first \(5\) questions. The number of choices available to him is:
If \[ \frac{x^2+1}{x^4+4} = \frac{Ax+B}{x^2-2x+2} + \frac{Cx+D}{x^2+2x+2}, \] then \(3A+2B+3C=\)
If \[ y^2+z^2=ayz,\quad z^2+x^2=bxz,\quad x^2+y^2=cxy, \] then the value of \[ \frac{xz}{y^2}+\frac{y^2}{zx} \] is:
The range of the function \[ f(x)=\frac{x}{x^2-5x+9} \] is:
If \[ {}^{n-3}C_r+B\,{}^{n-3}C_{r-1}+B^1\,{}^{n-3}C_{r-2}+{}^{n-3}C_{r-3}={}^nC_r \] holds for all \(n\geq r\geq 3\), then \((B,B^1)=\)
If \(\alpha,\beta\) are the roots of the equation \[ 2x^2+6x+k=0, \] then the maximum value of \[ \frac{\alpha}{\beta}+\frac{\beta}{\alpha} \] when \(k<0\) is:
The number of pairs of consecutive positive even integers such that the sum of their squares is \(290\) is:
If \[ |z-3i|+|z+5i|=4, \] then the locus of \(z\) is:
If \[ A= \begin{bmatrix} 1 & 1 & a+1 1 & a+1 & 1 a+1 & 1 & 1 \end{bmatrix} \] is not an invertible matrix, then the sum of all the values of \(a\) is:
If \[ (x-iy)^{\frac{1}{3}}=2-i\sqrt{3} \] and the point \(z=(x,y)\) lies on the line \[ \frac{x}{2}+\frac{y}{\sqrt{3}}=k, \] then \(k=\)
If \[ \left|z+\frac{2}{z}\right|=2, \] then the maximum value of \(|z|\) is:
A complex number \(z\) among the following which does not satisfy \[ z^3+27i=0 \] is:
If \[ \begin{pmatrix} 5 & a & -7 \\ b & -7 & c \\ -7 & d & -1 \end{pmatrix} \] is the adjoint of the matrix \[ \begin{pmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 \end{pmatrix}, \] then \(a+b+c+d=\)
The domain of the real valued function \[ f(x)=\sqrt{\frac{2-|x|}{3-|x|}} \] is:
If \(A\) and \(B\) are \(n\times n\) square matrices such that \[ (2A+B)^2+(A-3B)^2=5A^2-2AB+10B^2, \] then \(ABAB=\)
The rank of the matrix \[ A= \begin{bmatrix} 1 & -1 & 0 & -2 -4 & 4 & 0 & 8 -2 & 1 & 2 & 4 \end{bmatrix} \] is:
If the function \(f:\mathbb{R}\to\mathbb{R}\) is defined by \(f(x)=x|x|\), then \(f\) is:
A circle passes through \( (0, a) \) and \( (b, h) \), and its center is at \( (c, 0) \). Find \( c \).
\( \int \frac{e^{2x}}{\sin^2 x} \left( 2 \log \csc x + \sin 2x \right) dx = \)
The curve \( y = ax^3 + bx^2 + cx + 5 \) touches the x-axis at point \( P(-2, 0) \). Then the value of \( c \) is:
If \( f(x) \) is the antiderivative of \( g(x) \) and \[ \int f(x) g(x)(1 + f^2(x)) dx = F(x) \], then \( F(x) = \)
If $x \neq 0$ and $f(x)$ satisfies $8f(x) + 6f\left(\dfrac{1}{x}\right) = x + 5$, then $\dfrac{d}{dx} \left(x^2 f(x)\right)$ at $x = 1$ is