List of top Questions asked in TS EAMCET

A body P of mass \(1.5\text{ kg}\) moving with velocity \(10\text{ ms}^{-1}\) makes a one dimensional elastic collision with another body Q at rest. If ratio of velocities after collision is \(1:3\), then velocity of centre of mass is

A block slides down a \(30^\circ\) inclined plane. Coefficient of friction on upper half is \[ \mu_1=\frac{1}{2\sqrt3} \] and on lower half is \[ \mu_2=\frac{1}{4\sqrt3} \] Find ratio of velocities at midpoint and bottom.

A bomb of mass \(m\) at rest explodes into three parts. If these three parts move horizontally with equal speeds in different directions, then the masses of the three parts can be

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 (\(g=10\text{ ms}^{-2}\))

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

If minimum velocity of a projectile is \(15\text{ ms}^{-1}\) and maximum height reached is \(20\text{ m}\), then velocity of projection is (\(g=10\text{ ms}^{-2}\))

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

The unification of electromagnetism and optics is based on the discovery that

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

If \(B\) is magnetic induction, \(e\) is charge of electron, \(m\) is mass and \(c\) is speed of light in vacuum, then the physical quantity having dimensions of \[ \frac{4\pi mc}{Be} \] is

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

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 \(f(0)=\)

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

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

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 \(2M+8m=\)

If the real valued function \[ f(x)=\log(2x-3)-2x^2+6x-4 \] then the interval in which \(f(x)\) is increasing is

Evaluate \[ \int \frac{\cos x+\sin2x}{1-\sin x-2\sin^2x}\,dx \]

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

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

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 \(f'(1)=\)

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

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

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