List of top Mathematics Questions asked in AP EAPCET

The coefficient of $x^{12}$ in the expansion of \[ (3+2x)^{-5} \] is

All the letters of the word REMAIN are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in the dictionary order. The rank of the word REMAIN, when counted from the rank of the word MARINE beginning with $1$ itself, is

If \[ \frac{f(x)}{(x-1)(x-2)} = \frac{2}{x-2} - \frac{1}{x-1} \] and \[ f(x)+\frac{xf(x)}{(x-1)(x-2)} = g(x)+\frac{A}{x-2}+\frac{B}{x-1}, \] then $g(A+B)=$

In each of its move, a pawn in a chess board can move one step either horizontally or vertically to its adjacent cell from its current position. If a pawn is initially located at the South-West corner cell of the chess board, then the number of ways it can reach the North-East corner cell with minimum number of moves, is

If $\alpha,\beta$ $(\alpha<\beta)$ are the roots of \[ 2x^2-x-6=0 \] and \[ \alpha x^2+kx-\beta\leq0 \quad \forall x\in\mathbb{R}, \] then the number of integral values $k$ takes is

If the equation \[ x^4-10x^3+37x^2-60x+36=0 \] has two distinct real roots, where each one of them is a repeated root, then the sum of squares of all the roots of the given equation is

Let $P$ and $Q$ are two sets such that \[ n(P)=27,\quad n(Q)=17,\quad n(P\cap Q)=5. \] If $x$ is the number of ways of selecting $7$ elements from $P$ such that all the elements of $P\cap Q$ are in each selection and $y$ is the number of ways of selecting $10$ elements from $Q$ such that no element of $P\cap Q$ is present in any selection, then $x+y+1=$

If all the roots of the equation \[ x^5-3x^4-5x^3+27x^2-32x+12=0 \] are diminished by $h$ to get a transformed equation in which the constant term is missing, then the sum of the squares of all possible values of $h$ is

If \[ \int \frac{dx}{x^4+1} = \frac{1}{4\sqrt{2}} \log \left( \frac{x^2+\sqrt{2}x+1}{x^2-\sqrt{2}x+1} \right) + \frac{1}{2\sqrt{2}} \tan^{-1} \left( \frac{\sqrt{2}x}{1-x^2} \right) +c, \] then \[ \int_{0}^{1}\frac{x^2+1}{x^4+1}\,dx = \]

For the real values of $x$, the set of values of $k$ for which the function \[ f(x)=\frac{x^2+x+1}{x^2+kx+1} \] takes all real values is

Among the roots of \[ 3\sqrt{3}\,z^3-i=0, \] the sum of the squares of the two roots having non-zero real part is

Given that \[ \sum_{k=1}^{n} k(k-1)=\frac{n(n-1)(n+1)}{3} \] and $\omega$ and $\omega^2$ are complex cube roots of unity. If \[ \sum_{k=1}^{2026} \left( k+\frac{1}{\omega} \right) \left( k+\frac{1}{\omega^2} \right) = \frac{2026}{3}(N+3), \] then $N=$

If $x=\alpha$, $y=\beta$, $z=\gamma$ satisfy the equations \[ 3x+y+2z+2=0, \] \[ 2x-3y+z-7=0, \] \[ x-4y+3z-1=0, \] then \[ \alpha^3-\beta^3= \]

For \(n\in\mathbb{N}\), \[ 1^2+2^2+3^2+\cdots+n^2 > \]

If \[ A= \begin{bmatrix} b+c & a & a\\ b & c+a & b\\ c & c & a+b \end{bmatrix} \] is a matrix such that trace of $A=18$ and \[ \det(A)=96, \] if $a,b,c\in \mathbb{N}$ and $ab=6$, then $ab+bc+ca=$

If \(f:(-\infty,0)\to \mathbb{R}\) is defined by \[ f(x)=\frac{[x]}{|x|} \] then \(f(x):x\in(-\infty,0)\) is:

Let \(S\) be a symmetric matrix obtained from \[ A= \begin{bmatrix} 1 & 2 & -3\\ 2 & -2 & 1\\ 3 & 1 & -1 \end{bmatrix} \] and \(T\) be a skew-symmetric matrix obtained from \[ B= \begin{bmatrix} 4 & 2 & 0\\ 1 & -1 & 3\\ 0 & 2 & -3 \end{bmatrix} \] If trace of \(S=-4\) and the non-zero elements of \(T\) are \(-1,1\), then \(S+T=\)

If a real valued function \(f : A \to B\) defined by \(f(x)=|x|-[x]\) is a bijection, then \(A\) and \(B\) are respectively:

Evaluate $\int_0^{\pi/2} \sin^6 x \cos^4 x dx$

Evaluate $\int_{-\pi}^{\pi} \frac{\cos^2 x}{1+a^x} dx$

Solve $(1+y^2)+(x-e^{-\tan^{-1}y})\frac{dy}{dx}=0$

Solve $\cos(x+y)dy=dx$

Eliminate constants from $y=A(x+B)^2$

Evaluate $\int \frac{x-1}{(x+1)^3}e^x dx$:

Area between $y^2=x$ and $y=|x|$ is: