List of top Mathematics Questions asked in AP EAPCET

If \[ 2\cosh2x+10\sinh2x=5, \] then \(x=\)

If \[ {}^{10}C_2=3\cdot {}^{n+1}C_3, \] then the value of \(n\) is

There are \(10\) points in a plane, out of these \(6\) are collinear. If \(N\) is the total number of triangles formed by joining these points, then \[ N= \]

In an examination, the maximum marks for each of three subjects is \(n\) and that for the fourth subject is \(2n\). The number of ways in which candidates can get \(3n\) marks is

If one root of the cubic equation \[ x^3+36=7x^2 \] is double of another, then the number of negative roots is

If \[ \frac{2x^2+1}{x^3-1} = \frac{A}{x-1} + \frac{Bx+C}{x^2+x+1}, \] then \[ 7A+2B+C= \]

205 students take an examination of whom \(105\) pass in English, \(70\) students pass in mathematics and \(30\) students fail in both. How many students pass in both subjects?

If \[ \sin^4\theta \cos^2\theta=\sum_{n=0}^{\infty} a_{2n}\cos 2n\theta, \] then the least \(n\) for which \[ a_{2n}=0 \] is

The sum of the real roots of the equation \[ x^4-2x^3+x-380=0 \] is

If \[ S=\{m\in \mathbb{R}:x^2-2(1+3m)x+7(3+2m)=0 \text{ has distinct roots}\}, \] then the number of elements in \(S\) is

If \[ 4^x-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1}, \] then \[ x= \]

Let \[ G(x)= \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}. \] If \(x+y=0\), then \(G(x)G(y)=\)

If \[ A= \begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix}, \quad B= \begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix}, \] then \[ \det(A^4+B^6)= \]

By simplifying \[ i^{18}-3i^7+i^2(1+i^4)(i)^{22} \] we get

The values of \(x\) for which \[ \sin x+i\cos 2x \] and \[ \cos x-i\sin 2x \] are conjugate to each other are

The locus of a point \(z\) satisfying \[ |z|^2=\operatorname{Re}(z) \] is a circle with centre

If \(AX=D\) represents the system of simultaneous linear equations \[ x+y+z=6, \] \[ 5x-y+2z=3, \] \[ 2x+y-z=5, \] then \((Adj\,A)D=\)

If \[ A= \begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix}, \] then \(AA^T\) is a

Let \(f:\mathbb{R}-\left\{-\frac{1}{2}\right\}\to \mathbb{R}\) be defined by \[ f(x)=\frac{x-2}{2x+1} \] If \(\alpha,\beta\) satisfy the equation \[ f(f(x))=-x, \] then \[ 4(\alpha^2+\beta^2)= \]

If \[ f(x)=\log \left(\frac{2x^2-3}{x}+\sqrt{\frac{4x^4-11x^2+9}{|x|}}\right) \] then \(f(x)\) is

\[ \frac{d}{dx}\left[ \lim_{y\to 2} \frac{1}{y-2} \left( \frac{1}{x} - \frac{1}{x+y-2} \right) \right] \]

If \[ 2x-y+c\log|x-2y-4|=k \] is the general solution of \[ \frac{dy}{dx}=\frac{2x-4y-5}{x-2y+2}, \] then \(c=\)

If \(l\) and \(m\) are order and degree of a differential equation of all the straight lines at constant distance of \(P\) units from the origin, then \(lm^2+l^2m=\)

If \[ f(x)=\max\{\sin x,\cos x\} \] and \[ g(x)=\min\{\sin x,\cos x\}, \] then \[ \int_0^{\pi} f(x)\,dx+\int_0^{\pi} g(x)\,dx= \]

By eliminating the arbitrary constants from \[ y=(a+b)\sin(x-c)-de^{x+e+f}, \] the differential equation obtained is of order