List of top Mathematics Questions asked in TS EAMCET

If the equations \[ ax^2+2bx+3c=0,\qquad 3x^2+8x+15=0 \] have a common root, where \(a,b,c\) are sides of triangle \(ABC\), then \[ \cos2A+\cos2B+\cos2C= \]

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

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

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

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

The area of the region bounded by the curves \[ y=2^x,\qquad y^2=4x \] and the lines \[ x=\frac12,\qquad x=1 \] 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 \(2M+8m=\)

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

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

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

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

If \[ A= \begin{bmatrix} 0& \alpha& \beta\\ \beta& \alpha& 0\\ \alpha& 0& \beta \end{bmatrix} \] where \(\beta& gt;\alpha& gt;0\) and \[ AA^T= \begin{bmatrix} 25& a& b\\ a& 25& 12\\ b& a& 25 \end{bmatrix} \] then \[ a+b+\alpha-\beta= \]

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 \(k = \):

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

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

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 \( -1 + i \) is a root of the equation \( x^4 + 4x^3 + 5x^2 + 2x - 2 = 0 \), then the real roots of this equation are

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:

In a \(\triangle ABC\), if \(r_1=12,\; r_2=18,\; r_3=36\), then \(\Delta=\)

If \[ A= \begin{bmatrix} 1& 7& 49\\ 2& 16& 130\\ 2& 18& 170 \end{bmatrix}, \] then $\det(A)=$

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 \(A-B=\):

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 \(A^{2}-A=\)