List of top Mathematics Questions asked in TS EAMCET

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 \[ \operatorname{cis}\alpha + \operatorname{cis}\beta = \, ? \] 

Evaluate \[ \int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \frac{x\sin x}{1+\cos2x}\,dx \]
Evaluate \[ \int\frac1{2\cot x-3\tan x}\,dx \]
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 \[ \int\frac{\cos x}{\sqrt{16\cos^2x+9}}dx \]
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 \(2M+8m=\)
Evaluate \[ \int \frac{\cos x+\sin2x}{1-\sin x-2\sin^2x}\,dx \]
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 displacement of particle moving in straight line is \[ S=t^3-3t^2+3t-4 \] then time interval in which \(S\) is increasing is
By application of derivatives, approximate value of \[ \sqrt[5]{242} \] is
If \[ f(x)=\pi-\cos^{-1}\left(\frac{x^2+4x+3}{x^2+4x+5}\right) \] then \(f'(1)=\)
If \[ x=\sin2\theta+\sin3\theta,\qquad y=\cos2\theta-\cos3\theta \] then \[ \frac{d^2y}{dx^2} = \]
If \[ f(x)=(1+x^3)(1+x^6)(1+x^{12})(1+x^{24}) \] then \(f'(-1)=\)
If the function \[ f(x)= \begin{cases} \dfrac{p(1+\sin3x)}{(\pi+6x)^2}, & -\frac{\pi}{2}[4mm]\\ z, & x=-\frac{\pi}{6}[4mm]\\ \dfrac{q(\sin12x+2\sin6x)}{\cos^3\left(\frac{\pi+12x}{2}\right)}, & -\frac{\pi}{6}& lt;x& lt;0 \end{cases} \] is continuous at \[ x=-\frac{\pi}{6} \] then \(p+2q=\)
If the image of point \((1,-1,1)\) in the plane \[ x-2y+3z=4 \] is \((x_1,y_1,z_1)\), then \(x_1-y_1-z_1=\)
If \((1,-2,2)\) and \((2,6,-3)\) are the direction ratios of two straight lines, then the direction cosines of the line bisecting an angle between these two lines are
Let \[ f(x)=\frac{([x]+|x|-x)x}{\sin|x|} \] be a real valued function. If \[ \alpha=\lim_{x\to0^-}f(x),\qquad \beta=\lim_{x\to0^+}f(x) \] then
The domain of derivative of real valued function \[ f(x)=(x^2-x-2)|x^2+x-6| \] is
If both foci of a hyperbola having eccentricity \(\sqrt3\) lie on x-axis and x coordinates of foci are roots of equation \[ x^2-4x+1=0 \] then length of chord passing through focus and perpendicular to transverse axis is
If a straight line \[ y=mx+c \] touches the circle \[ x^2+y^2=4 \] and parabola \[ y^2=4x \] then \(2m^2=\)
If \(\theta\) is acute angle between tangents drawn from point \((3,4)\) to ellipse \[ \frac{x^2}{25}+\frac{y^2}{9}=1 \] then \(\theta=\)
Let \(S,S'\) be foci and \(B\) one end of minor axis of an ellipse. If \[ \angle SBS'=120^\circ \] and area of triangle \(SBS'\) is \(\sqrt3\), then length of latus rectum is