List of top Mathematics Questions asked in TS EAMCET

A ray from (7,2) reflects on \(2x+y=1\) and passes through (3,10). Equation of incident ray is:

Equation of the image of the pair of lines \[ ax^2+2hxy+by^2=0 \] with respect to \(y=0\) is

The locus of the centre of a circle touching the lines \[ x+2y=0 \] and \[ x-2y=0 \] is

If line \(4x-3y+c=0\) makes a chord of length 10 on circle \(x^2+y^2-2x+4y-23=0\), then \(c=\):

If the equation of a transverse common tangent drawn to the circles \[ x^2+y^2-2x-10y+1=0 \] and \[ x^2+y^2+8x+14y+1=0 \] is \[ 5x+by+c=0, \] then \(b+c=\)

Let \(S,S'\) be foci and \(B\) one end of minor axis of an ellipse. If \[ \angle SBS'=120^\circ \] and area of triangle \(SBS'\) is \(\sqrt3\), then length of latus rectum is

Evaluate \[ \lim_{x\to 0}\frac{\log(4+x)^x-\log 4^x}{\sin^2 x}. \]

\(y=4\) is the directrix of the parabola \[ x^{2}+8x+12y+k=0. \] If \(l\) is the length of its latus rectum, then \(l-k=\) ?

In a triangle ABC, if \( a = 2 \), \( \sin A = \frac{2}{3} \), \( B = \frac{\pi}{3} \), then \( \sqrt{5}b - 3c = \):

\( T_m \) denotes the number of triangles that can be formed with the vertices of a regular polygon of \( m \) sides. If \( T_{m+1} - T_m = 15 \), then \( m = \)

If \[ A=\{z=x+iy:|z-4||z-3|\}, \] \[ B=\{z=x+iy:-3\le y\le3,\;x\in N,\;y\in N\}, \] and \(C=A\cap B\), then \(n(C)=\)

A bag A contains 3 red, 2 white and 2 black balls and another bag B contains 1 red, 2 white and 4 black balls. A die is thrown to select a bag. If an odd prime number appears on the die, a ball is drawn from bag A; otherwise from bag B. If the ball drawn is black, then the probability that it is drawn from bag B is

If an acute angle \(\theta\) is used to rotate axes to remove the \(xy\)-term from \[ 4x^{2}+3xy+y^{2}+1=0, \] then \((1+\tan\theta)^2=\)

If $\alpha,\beta$ are roots of $2x^2-x-3\lambda=0$ and $\alpha,\gamma$ are roots of $2x^2+9x+2\lambda=0$, find equation of roots $2\alpha+\beta$ and $\beta+\gamma$.

\(T_1,T_2\) are points of contact of a transverse common tangent drawn to circles \[ x^2+y^2+4x-10y+4=0 \] and \[ x^2+y^2-6x+8y+9=0 \] If \(T_1T_2\) is horizontal line, midpoint of segment \(T_1T_2\) is

If the minimum value of $ax^2-7x+3a$ is $-\frac{1}{8}$, find sum of roots of $ax^2-7x+3a=0$.}

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

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

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

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

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 $\frac{dy}{dx}=$}

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

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