List of top Questions asked in TS EAMCET- 2026

A body is thrown vertically upwards from earth with velocity \(60\text{ ms}^{-1}\). The ratio of displacements during first, second and third seconds is (\(g=10\text{ ms}^{-2}\))

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

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

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

If \(\theta\) is angle between parabolas \[ y^2=108x \] and \[ x^2=32y \] then \[ \cos2\theta= \]

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 \(m\) 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 \(2M+8m=\)

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

If \[ x=\sin2\theta+\sin3\theta,\qquad y=\cos2\theta-\cos3\theta \] then \[ \frac{d^2y}{dx^2} = \]

The domain of derivative of real valued function \[ f(x)=(x^2-x-2)|x^2+x-6| \] 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 \[ f(x)=\pi-\cos^{-1}\left(\frac{x^2+4x+3}{x^2+4x+5}\right) \] then \(f'(1)=\)

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

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

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

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 \((1,-2,2)\) 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

If the image of point \((1,-1,1)\) in the plane \[ x-2y+3z=4 \] is \((x_1,y_1,z_1)\), then \(x_1-y_1-z_1=\)

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

If \(\theta\) is acute angle between tangents drawn from point \((3,4)\) to ellipse \[ \frac{x^2}{25}+\frac{y^2}{9}=1 \] then \(\theta=\)

If \(P(t_1)\) and \(Q(t_2)\) are two points on the parabola \[ y^2=7x \] If \(t_1=2\) and \(t_2=-4\), then the length of chord \(PQ\) is

If a straight line \[ y=mx+c \] touches the circle \[ x^2+y^2=4 \] and parabola \[ y^2=4x \] then \(2m^2=\)