List of top Mathematics Questions asked in AP EAPCET

For what values of \(a \in \mathbb{Z}\), the quadratic expression \[ (x+a)(x+1991)+1 \] can be factorised as \[ (x+b)(x+c), \] where \(b,c \in \mathbb{Z}\)?

If a set \(A\) has \(m\)-elements and the set \(B\) has \(n\)-elements, then the number of injections from \(A\) to \(B\) is

In how many ways can the letters of the word “MULTIPLE” be arranged keeping the position of the vowels fixed?

A true statement among the following identities is

If \[ e^{i\theta}=\operatorname{cis}\theta, \] then \[ \sum_{n=0}^{\infty}\frac{\cos(n\theta)}{2^n} = \]

If \[ f(f(0))=0, \] where \[ f(x)=x^2+ax+b,\qquad b\neq0, \] then \(a+b=\)

The sum of the real roots of the equation \[ |x-2|^2+|x-2|-2=0 \] is

If \[ A= \begin{bmatrix} 1 & 0 & 0\\ a & -1 & 0\\ b & c & 1 \end{bmatrix} \] is such that \[ A^2=I, \] then

If \[ \sum_{k=0}^{440} i^k=x+iy, \] then \[ x^{100}+x^{99}y+x^{242}y^2+x^{97}y^3= \]

Multiplicative inverse of the complex number \[ (\sin\theta,\cos\theta) \] is

If \(a,b,c\) are respectively the \(5^{th}, 8^{th}, 13^{th}\) terms of an arithmetic progression, then \[ \begin{vmatrix} a & 5 & 1\\ b & 8 & 1\\ c & 13 & 1 \end{vmatrix} = \]

Let \[ A= \begin{bmatrix} -2 & x & 1\\ x & 1 & 1\\ 2 & 3 & -1 \end{bmatrix} \] If the roots of the equation \[ \det(A)=0 \] are \(l,m\), then \[ l^3-m^3= \]

If \[ A=\begin{bmatrix} 2 & -3\\ -4 & 1 \end{bmatrix}, \] then \[ (A^T)^2+(12A)^T= \]

The set \[ \left\{x \in \mathbb{R} \,/\, \frac{\sqrt{|x|^2-2|x|-8}} {\log(2-x-x^2)} \text{ is a real number} \right\} \] is equal to:

The domain of the real valued function \[ f(x)=\sin\left(\log\left(\frac{\sqrt{4-x^2}}{1-x}\right)\right) \] is:

If the solution of \(\dfrac{dy}{dx}=\dfrac{y^3\cos\sqrt{x}}{\sqrt{x}e^{1/y^2}}\), \(y(0)=1\), is \(\dfrac{1}{y^2}=\log_e(f(x))\), then \(f(x)=\)

Suppose that \(f(x,y)\) and \(g(x,y)\) are homogeneous functions of same order. If \(x=Vy\) reduces the equation \(\dfrac{dy}{dx}=\dfrac{f(x,y)}{g(x,y)}\) to the form \(\dfrac{dV}{dy}=\dfrac{1}{y}(F(V))\), then \(F(V)=\)

The general solution of \(xdy-ydx=xy\,dy\) is

\(\displaystyle \int_{-1}^{2}\left[\tan^{-1}\left(\frac{x}{x^2+1}\right)+\tan^{-1}\left(\frac{x^2+1}{x}\right)\right]dx=\)

\(\displaystyle \int_{-\pi/2}^{2\pi}\sin^{-1}(\sin x)\,dx=\)

If \(\displaystyle \int_{9}^{x}\frac{f(y)}{y^2}\,dy=2\sqrt{x}-6\), then \(f(x)=\)

\(\displaystyle \int \left(\sqrt{x+\sqrt{12x-36}}+\sqrt{x-\sqrt{12x-36}}\right)\,dx=\)

If \(\displaystyle \int \frac{x\,dx}{\sqrt[15]{(1+x^2)^{12}(2+x^2)^{18}}}=\alpha\left(\frac{1+x^2}{2+x^2}\right)^{1/n}+C\), then \(\dfrac{n}{\alpha}=\)

\(\displaystyle \int (\log x)^2 x^3\,dx=\dfrac{x^4}{32}f(x)+C \Rightarrow f(x)=\)

\(\displaystyle \int_{0}^{\infty}\left(x^{12}+x^{-12}\right)\frac{\log x}{x}\,dx=\)