List of top Questions asked in TS EAMCET

If \( \lim_{x \to 0} \frac{3x^3 - (1-x^2)^{3/2}}{x^2\sin x} = p + \log q \) then pq =

If the line passing through the point \((4, -3)\) and having negative slope makes an angle of \(45^\circ\) with the line joining the points \((1,1), (2,3)\) then the sum of intercepts of that line is

If the length of the chord 2x+3y+k=0 of the circle \(x^2+y^2-2x+4y-11=0\) is \(2\sqrt{3}\), then the sum of all possible values of k is

If the equation of the circle passing through the points (-1,0), (-1,1), (1,1) is \( ax^2+ay^2+2gx+2fy-2=0 \) then \( a = \)

For the circle \( x-2=5\cos\theta \), \( y+1=5\sin\theta \) where \( \theta \) is the parameter, the line \( x=1+\frac{\sqrt{3}}{2}r \), \( y=-2+\frac{r}{2} \) where \( r \) is the parameter, is a

If a line L passing through a point A(2,3) intersects another line \( 4x-3y-19=0 \) at the point B such that \( AB=4 \), then the angle made by the line L with positive X-axis in anti-clockwise direction is

If \( (h,k) \) is the new origin to be chosen to eliminate first degree terms from the equation \( S = 2x^2 - xy - y^2 - 3x + 3y = 0 \) by translation and if \( \theta \) is the angle with which the axes are to be rotated about the origin in anticlockwise direction to eliminate xy-term from \( S = 0 \), then \( \tan 2\theta = \)

If the product of the perpendicular distances from any point on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) to its asymptotes is \( \frac{36}{13} \) and its eccentricity is \( \frac{\sqrt{13}}{3} \), then \( a - b = \)

If the slopes of the lines represented by the equation $6x^2+2hxy+4y^2 = 0$ are in the ratio 2:3, then the value of h such that both the lines make acute angles with the positive X-axis measured in positive direction is

If \( \theta \) is the angle between the circles \( x^2+y^2-4x+2y-4=0 \) and \( x^2+y^2-2x+4y-11=0 \), then \( \sin\theta = \)

The equation of the circle whose radius is 3 and which touches the circle \(x^2 + y^2 - 4x - 6y - 12 = 0\) internally at \((-1, -1)\) is

By shifting the origin to the point (-1,2) through translation of axes, if $ax^2+2hxy+by^2+2gx+2fy+c=0$ is the transformed equation of $2x'^2-x'y'+y'^2-3x'+4y'-5=0$, then $2(f+g+h) =$

Let e be the eccentricity of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \). If a=5, b=4 and the equation of the normal drawn at one end of the latus rectum that lies in the first quadrant is \(lx+my=27\), then l+m=

The lines x+y+4=0, x-2y-4=0 and 3x+4y-2=0

If the perpendicular drawn from the point (2,-3) to the straight line $4x-3y+8=0$ meets it at M(a,b) and $a^3-b^3=k^3$, then $k =$

When the coordinate axes are rotated about the origin through an angle $\frac{\pi}{4}$ in the positive direction, the equation $ax^2+2hxy+by^2=c$ is transformed to $25x'^2+9y'^2=225$, then $(a+2h+b-\sqrt{c})^2=$

The line $4x-3y+2 = 0$ intersects the circle $x^2+y^2-2x+6y+c=0$ at two points A, B and AB=8. If (1,k) is a point on the given circle and $k>0$, then $k =$

The focal distance of a point (5,5) on the parabola \( x^2-2x-4y+5=0 \) is

If L(p,q), q>3 is one end of the latus rectum of the parabola \((y-2)^2 = 3(x-1)\) then the equation of the tangent at L to this parabola is

For the parabola \(y = x^2 - 3x + 2\), match the items in list-1 to that of the items in list-2.
S is a focus, Z is intersection of axis and directrix, P is one end point of latus rectum, Q is the point on the parabola at which tangent is parallel to X-axis

The radius of the circle having three chords along y-axis, the line $y=x$ and the line $2x+3y=10$ is

If $2x-3y+5=0$ and $4x-5y+7=0$ are the equations of the normals drawn to a circle and (2,5) is a point on the given circle, then the radius of the circle is

Among the chords of the circle $x^2+y^2=75$, the number of chords having their midpoints on the line $x=8$ and having their slopes as integers is

The lines $x-2y+1=0$, $2x-3y-1=0$ and $3x-y+k=0$ are concurrent. The angle between the lines $3x-y+k=0$ and $mx-3y+6=0$ is $45^\circ$. If m is an integer, then $m-k=$

The centres of all circles passing through the points of intersection of the circles \(x^2 + y^2 + 2x - 2y + 1 = 0\) and \(x^2 + y^2 - 2x + 2y - 2 = 0\) and having radius \(\sqrt{14}\) lie on the curve