List of top Questions asked in TS EAMCET

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 \[ \tanh^{-1}(x)=\log\sqrt3 \] and \[ \cosh^{-1}(y)=\log(1+\sqrt2), \] then \[ \operatorname{sech}^{-1}(xy)= \]

If \( a \) is a real number and \( 2\sinh^2 x - 3\cosh x + a = 0 \) has a solution, then the range of \( a \) is:

If \[ 1+3+5+\cdots+l_1=1521 \] and \[ 2+4+6+\cdots+l_2=1722, \] then $l_1+l_2=$

The set of all values of x satisfying \[ \sqrt{x^2-2x+1}>x+2 \] is

A function is defined as \[ f(x)= \begin{cases} 3x-1, & 0\le x\le 2,\\ \sqrt{25(x-1)}, & 2\le x<\infty. \end{cases} \] For \(f(x)\) in the interval \(\left[\frac13,3\right]\), choose the correct statement.

If $x=Sin^{-1}(cos~t)$ and $y=Tan^{-1}(cos~t)$ then $\frac{dy}{dx}=$}

If \(z\) is a complex number such that \[ \left|9z+\frac{1}{z}\right|=8, \] then the maximum value of \(|z|\) is

If $f(x)=\begin{cases}\frac{x}{|x|}when~x\ne0\\ |x|when~x=0\end{cases}$ is a real valued function, then}

If \(A,B,C\) are the vertices of a triangle \(ABC\), \[ AB=2,\qquad BC=3,\qquad CA=4, \] then \[ \overrightarrow{AB}\cdot\overrightarrow{BC} + \overrightarrow{BC}\cdot\overrightarrow{CA} + \overrightarrow{CA}\cdot\overrightarrow{AB} = \]

$[\frac{d}{dx}((sin~x)^{cos~x})]_{x=7/4}=$}

If \(A(2,1)\), \(B(4,k)\), \(C(3,4)\) are vertices of triangle right angled at B and \(k\) is not an odd number, then equation of line joining orthocentre and circumcentre is

One of the pair of lines \(x^{2}-3y^{2}-4x-6\sqrt{3}y-5=0\) is \(x+by+c=0\) \((b<0)\). If the other line intersects the curve \(x^{2}-5y^{2}-4x=0\) at two points A and B, then \(\angle AOB=\):

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 \[ \lim_{x\to0}\frac{2^{\tan x}-2^{\sin x}}{x^2\sin x}=k, \] then \(e^{2k}=\)

The term independent of \(x\) in expansion of \[ \left(\frac{\sqrt{x}}{2}-\frac{3}{x}\right)^{12} \] is

Evaluate binomial sum involving $\sum C_r \frac{2^r}{r+1}$ for $n=10$.}

If A(1,2,-3), B(2,3,-1), C(3,1,-2) are vertices of triangle ABC, then area is

If the domain and the range of the real valued function \[ f(x)=\frac{1}{\sqrt{|x|-[x]}} \] are A and B, then \(A\cap B=\) (\(R^{+}\) is set of positive real numbers and \(Z^{+}\) is set of positive integers)

If \[ x=2+\frac{7}{8}+\frac{7\cdot10}{8\cdot12}+\frac{7\cdot10\cdot13}{8\cdot12\cdot16}+\cdots, \] then \(x^3=\)

Probability for a person A to have success in one trial is \(\frac{2}{5}\). In 7 Bernoulli trials, if the probability that A has \(k\) successes is maximum, then \(k = \):

For circle \(x^2+y^2+12x-4y-9=0\), line \(x+2y-3=0\) represents

If $y=e^{2x}+sin~x$, then $2y^{\prime\prime}-5y^{\prime}+2y=$}

Direction cosines satisfy \(l-2m+n=0\), \(2l^2-3m^2+n^2=0\). Angle between lines is

The number of real roots of the equation \[ e^{3x}-2e^{2x}-e^{x}+2=0 \] is