List of top Questions asked in TS EAMCET

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

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 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 \[ l_1x+m_1y+n_1=0 \] and \[ l_2x+m_2y+n_2=0 \] are tangents drawn from point \((2,-1)\) to circle \[ x^2+y^2=4 \] then \(n_1+n_2=\)

If the inclination of a straight line \[ x-y+1=0 \] with another straight line \(L\) is \(30^\circ\) and \(m\) is the slope of line \(L\), then \[ m^2+1= \]

If the points with position vectors \[ x\vec i+2\vec j+y\vec k \] \[ \vec i-2\vec j+2x\vec k \] and \[ 2\vec i+3\vec j-\vec k \] are collinear, then \[ 10x-25y= \]

Let \[ \vec a=\vec i+2\vec j+\vec k \] and \[ \vec b=2\vec i-\vec j+\vec k \] be two vectors. If vector \[ \vec r=x\vec i+y\vec j+2\vec k \] is along the bisector of angle between \(\vec a\) and \(\vec b\), then \[ |\vec r|= \]

Number of solutions of equation \[ 3^{2\sin^2x}+3^{2\cos^2x}=6 \] lying in interval \[ [-\pi,\pi] \] is

An electron is moving in a stable circular orbit of radius $0.1\text{ m}$ around a thin infinitely long positively charged straight wire. If the orbital velocity of the electron around the wire is $4 \times 10^7\text{ ms}^{-1}$, then the linear charge density of the wire is nearly:}

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

The external centre of similitude for circles \[ x^2+y^2+10x-16y-11=0 \] and \[ x^2+y^2-2x+4y-4=0 \] is

If \(\alpha\in R\) and equation \[ (x-\alpha)(x-3)+1=0 \] has equal roots, then sum of squares of all values of \(\alpha\) is

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 \[ \left|\frac{m}{n}\right|= \]

A particle executes simple harmonic motion according to the equation \( x(t) = A \sin^2(\alpha t) \). If the time period of the S.H.M is 0.2 s, then the value of \( \alpha \) (in units of rad/s) is:

A car is moving with velocity V at the top of a semi-circular hill of radius 40 m such that the normal force on it is zero. Find the velocity (V) of the car. [use \( g = 10 \, \text{ms}^{-2} \)]

A monochromatic radiation of wave length $\lambda$ is incident on a hydrogen sample in ground state. The sample subsequently emits radiation of six different wave lengths, then the value of $\lambda$ is [Use $ch = 1242\text{ eV-nm}$]

A particle executes simple harmonic motion according to the equation \( x(t) = A \sin^2(\alpha t) \). If the time period of the S.H.M is 0.2 s, then the value of \( \alpha \) (in units of rad/s) is:

Which one of the following is the correct description for a mature embryo sac?

Hybridisation of carbon in ethyne (acetylene) is:

Which of the following shows the most primitive vascular system?

The transfer cells are found in:

Colostrum is rich in:

Which of the following is an ectothermic animal?

Which of the following is a correct statement about the lac operon?