List of top Mathematics Questions asked in TS EAMCET

If \[ \sqrt{-4x+2i\sqrt{x^{4}+2x^{2}+9}} = \pm(a+ib) \] then \[ a^2+b^2-6= \]
Product of all the five values of \[ (1-i)^{4/5} \] is
If \[ A= \begin{bmatrix} 1&1\\ 0&1 \end{bmatrix} \] and \[ S=A+A^{2}+A^{3}+...+A^{12} \] then sum of all elements of matrix S is
If \[ A= \begin{bmatrix} 0&\alpha&\beta\\ \beta&\alpha&0\\ \alpha&0&\beta \end{bmatrix} \] where \(\beta>\alpha>0\) and \[ AA^T= \begin{bmatrix} 25&a&b\\ a&25&12\\ b&a&25 \end{bmatrix} \] then \[ a+b+\alpha-\beta= \]
Consider the following Assertion and Reason Assertion: \[ \frac{1}{5\cdot9}+\frac{1}{9\cdot13}+\frac{1}{13\cdot17}+... \text{ to 10 terms }=\frac{9}{41} \] Reason: \[ \text{For all }n\in N, \quad \frac{1}{5\cdot9}+\frac{1}{9\cdot13}+... =\frac{n}{5(4n+5)} \]
If the system of equations \[ ax+y-2z=3,\qquad 2x-y+3z=b,\qquad x+2y-z=3 \] has infinitely many solutions, then \(3a-2b=\)
Let \[ A= \begin{bmatrix} x&2&-1\\ -2&1&2x\\ 3x&2&1 \end{bmatrix} \] and \[ det(A)=f(x) \] If \(f(x)\) attains minimum value \(m\) at \(x=n\), then \[ \left|\frac{m}{n}\right|= \]
If the domain and the range of the real valued function \[ f(x)=\frac{1}{\sqrt{|x|-[x]}} \] are A and B, then \(A\cap B=\) (\(R^{+}\) is set of positive real numbers and \(Z^{+}\) is set of positive integers)
A real valued function \(f\) defined by \[ f(x)=|x|-x \] is

If the domain and the range of the real-valued function \[ f(x)=\frac{1}{\sqrt{|x|-[x]}} \] are \(A\) and \(B\), respectively, then \[ A\cap B = \ ? \] (Here, \(R^{+}\) denotes the set of positive real numbers and \(Z^{+}\) denotes the set of positive integers.) 

The set of all values of x satisfying \[ \sqrt{x^2-2x+1}>x+2 \] is

If \[ \sqrt[3]{i} = \operatorname{cis}\alpha,\qquad \alpha \text{ belongs to the second quadrant} \] and \[ \sqrt[3]{-i} = \operatorname{cis}\beta,\qquad \beta \text{ belongs to the third quadrant} \] then find \[ \operatorname{cis}\alpha + \operatorname{cis}\beta = \, ? \] 

If \[ \int(e^{2x}+2e^x)\sqrt{e^{2x}-4e^x+5}\,dx = \frac13[f(x)]^{3/2} + 4\left[ \frac{e^x-2}{2}\sqrt{f(x)} + \frac12g(x) \right]+c \] then \(f(0)=\)
Evaluate \[ \int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \frac{x\sin x}{1+\cos2x}\,dx \]
Evaluate \[ \int\frac1{2\cot x-3\tan x}\,dx \]
Evaluate \[ \int \frac{\cos x+\sin2x}{1-\sin x-2\sin^2x}\,dx \]
Evaluate \[ \int\frac{\cos x}{\sqrt{16\cos^2x+9}}dx \]
If the real valued function \[ f(x)=\log(2x-3)-2x^2+6x-4 \] then the interval in which \(f(x)\) is increasing is
If \(\theta\) is angle between parabolas \[ y^2=108x \] and \[ x^2=32y \] then \[ \cos2\theta= \]
If \(m\) and \(M\) are respectively the absolute minimum and absolute maximum values of the function \[ f(x)=|2x^2-x-6|+2x-3 \] in the interval \([-2,4]\), then \(2M+8m=\)
If \[ f(x)=(1+x^3)(1+x^6)(1+x^{12})(1+x^{24}) \] then \(f'(-1)=\)
By application of derivatives, approximate value of \[ \sqrt[5]{242} \] is
If displacement of particle moving in straight line is \[ S=t^3-3t^2+3t-4 \] then time interval in which \(S\) is increasing is
If \[ x=\sin2\theta+\sin3\theta,\qquad y=\cos2\theta-\cos3\theta \] then \[ \frac{d^2y}{dx^2} = \]
If \[ f(x)=\pi-\cos^{-1}\left(\frac{x^2+4x+3}{x^2+4x+5}\right) \] then \(f'(1)=\)