List of top Mathematics Questions asked in TS EAMCET

If $f:\mathbb{R}-\left\{\frac{2a}{3}\right\}\rightarrow \mathbb{R}$ is a function defined by \[ f(x)=\frac{2x+a}{3x-2a} \] and $(f\circ f)(x)=x$ for all $x\in \mathbb{R}-\left\{\frac{2a}{3}\right\}$, then $f(3)=$}

If $f:\mathbb{R}\rightarrow\mathbb{R}$ and $g:\mathbb{R}\rightarrow\mathbb{R}$ are defined by \[ f(x)=|x+1| \] and \[ g(x)= \begin{cases} e^{-x}, & x\le 0\\ x-1, & x>0 \end{cases} \] then $(f\circ g)(-2)+(g\circ f)(2)=$}

If the function \[ f(x)=\left\{ \begin{array}{ll} \dfrac{p(1+\sin 3x)}{(\pi+6x)^2}, & -\dfrac{\pi}{2}\lt x\lt-\dfrac{\pi}{6} \\[2ex] z, & x=-\dfrac{\pi}{6} \\[2ex] \dfrac{q(\sin 12x+2\sin 6x)}{\cos^3\left(\frac{\pi+12x}{2}\right)}, & -\dfrac{\pi}{6}\lt x\lt 0 \end{array} \right. \] is continuous at \(x=-\dfrac{\pi}{6}\), then \(p+2q=\)

The general solution of the differential equation \[ \frac{dy}{dx} = x^2y^2+3x^2y-2xy^2-6xy \] is

Evaluate \[ \int_{\pi/6}^{\pi/3} \frac{dx}{\sin2x(\tan^4x-\cot^4x)} \]

If \(a,b\) are arbitrary constants, then the differential equation corresponding to family \[ y=ax^2-2abx+ab^2 \] is

The area of the region bounded by the curves \[ y=x^2-3x+3 \] \[ y=2x^2-1 \] is

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 \[ \int\frac1{2\cot x-3\tan x}\,dx \]

Evaluate \[ \int\frac{\cos x}{\sqrt{16\cos^2x+9}}dx \]

Evaluate \[ \int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \frac{x\sin x}{1+\cos2x}\,dx \]

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

If \[ f(x)=(1+x^3)(1+x^6)(1+x^{12})(1+x^{24}) \] then \(f'(-1)=\)

If \[ f(x)=\pi-\cos^{-1}\left(\frac{x^2+4x+3}{x^2+4x+5}\right) \] then \(f'(1)=\)

By application of derivatives, approximate value of \[ \sqrt[5]{242} \] is

The domain of derivative of real valued function \[ f(x)=(x^2-x-2)|x^2+x-6| \] is

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

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 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 D be harmonic conjugate of point C with respect to points \[ A(1,-3,5),\qquad B(5,-3,1) \] If C divides AB in ratio \(3:5\), then point dividing CD in ratio \(1:2\) is