List of top Mathematics Questions asked in AP EAPCET

If \[ \sin\theta=-\frac{3}{4}, \] then \[ \sin2\theta= \]

If \[ \frac{1}{\sin1^\circ\sin2^\circ} + \frac{1}{\sin2^\circ\sin3^\circ} +\cdots+ \frac{1}{\sin89^\circ\sin90^\circ} = \] then its value is

Which of the following trigonometric values are negative?
\[ \text{I) } \sin(-292^\circ) \] \[ \text{II) } \tan(-193^\circ) \] \[ \text{III) } \cos(-207^\circ) \] \[ \text{IV) } \cot(-222^\circ) \]

Find the value of \[ \sin^2\frac{2\pi}{3}+\cos^2\frac{5\pi}{6}-\tan^2\frac{3\pi}{4} \]

If \[ \sin\theta+\cosec\theta=4, \] then \[ \sin^2\theta+\cosec^2\theta= \]

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

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

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

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

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

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 \(G(x)G(y)=\)

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

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

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