List of top Questions asked in TS EAMCET

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 \(\angle AOB=\):
The number of real roots of the equation \[ e^{3x}-2e^{2x}-e^{x}+2=0 \] is
For circle \(x^2+y^2+12x-4y-9=0\), line \(x+2y-3=0\) represents
If \[ \frac{x^{2}+1}{(x^{4}+5x^{2}+6)(x^{6}+x^{4})} = \frac{A}{x^{4}}+\frac{B}{x^{2}}+\frac{C}{x^{2}+2}+\frac{D}{x^{2}+3}, \] then \(A-B=\):
The standard deviation of the data \[ 2,3,4,5,6,7,10,11,13,19 \] is
If \[ A= \begin{bmatrix} 1& 7& 49\\ 2& 16& 130\\ 2& 18& 170 \end{bmatrix}, \] then $\det(A)=$
If \(a\) is a real root of the equation \[ x^{3}-2x^{2}-2x-3=0 \] and \[ A= \begin{bmatrix} 1& 2& a\\ 2& a& 1\\ a& 1& 2 \end{bmatrix}, \] then \(A^{2}-A=\)
In a triangle \(ABC\), if \[ \overrightarrow{AB}=\hat{i}-2\hat{j}+3\hat{k}, \qquad \overrightarrow{BC}=3\hat{i}+2\hat{j}-2\hat{k}, \] then the triangle is
In a \(\triangle ABC\), if \(r_1=12,\; r_2=18,\; r_3=36\), then \(\Delta=\)
For parabola \(y^2=5x\), normal at P meets x-axis at Q. If PQ subtends \(60^\circ\) at vertex, slope of normal is

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

If \(a,b\) are arbitrary constants, then the differential equation corresponding to family \[ y=ax^2-2abx+ab^2 \] is
Let \([t]\) represent the greatest integer less than or equal to \(t\). If \[ x = (7\sqrt{5} + 15)^9 \quad \text{and} \quad y = (5\sqrt{7} + 13)^{11}, \] then \([x]\) and \([y]\) are:

\[ \lim_{x \rightarrow \frac{2}{3}} \frac{\sin\left(\pi \cos^2(3x-2)\right)} {9x^2-12x+4} = \ ? \] 

One of the roots of the equation \((x + 1)^4 + 81 = 0\) is
If the rate of change of volume of a cube and that of its surface area are numerically equal, then the length of its diagonal is
Consider the following Assertion and Reason Assertion: \[ \frac{1}{5\cdot9}+\frac{1}{9\cdot13}+\frac{1}{13\cdot17}+... \text{ to 10 terms }=\frac{9}{41} \] Reason: \[ \text{For all }n\in N, \quad \frac{1}{5\cdot9}+\frac{1}{9\cdot13}+... =\frac{n}{5(4n+5)} \]
Area enclosed by \(x^2-2x+y+1=0\) and \(3x+y-3=0\)
If \( A = \begin{bmatrix} \alpha & 3 & 1 2 & \beta & 6 -2 & -1 & \gamma \end{bmatrix} \) and \( AA^T = \begin{bmatrix} 35 & 28 & -13 28 & 56 & -8 -13 & -8 & 5 \end{bmatrix} \), then Trace of \( A = \)
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
Evaluate \[ e^{Sinh^{-1}(2\sqrt2)}+e^{Cosh^{-1}(3)} \]
\(\int_0^2 |2x^2-9x+9|dx=\)
If two cards are drawn at a time from a well shuffled pack of 52 cards, then the probability of getting a result containing only one king and only one spade is
If \[ f(x)=(1+x^3)(1+x^6)(1+x^{12})(1+x^{24}) \] then \(f'(-1)=\)
In triangle ABC, \[ (r_1-r)\cos\frac{B-C}{2} = ? \]