List of top Questions asked in TS EAMCET- 2025

If the curves \(y^2=12x-3\) and \(y^2=12-kx\) cut each other orthogonally then the length of the sub tangent at (1,b) on the curve \(y^2=12-kx\) is

If \( y = \tan^2(\cos^{-1}\sqrt{\frac{1+x^2}{2}}) \), then \( \frac{dy}{dx} = \)

If [x] is the greatest integer function and \( f(x) = \begin{cases} \frac{2[x]-x}{|x|} & x \neq 0 \\ 1 & x=0 \end{cases} \) is a real valued function, then f is

If the angle between the planes ax-y+3z=2a and 3x+ay+z=3a is \( \frac{\pi}{3} \) then the direction ratios of the line perpendicular to the plane (a+2)x+(a-4)y+2az=a are

If \(\alpha\) is the angle between any two diagonals of a cube and \(\beta\) is the angle between a diagonal of a cube and a diagonal of its face, which intersects this diagonal of the cube then \( \cos\alpha + \cos^2\beta = \)

If the latus rectum through one of the foci of a hyperbola \( \frac{x^2}{9} - \frac{y^2}{b^2} = 1 \) subtends a right angle at the farther vertex of the hyperbola, then \(b^2 = \)

The equation of the locus of a point whose distance from XY-plane is twice its distance from Z-axis is

If P is any point on the ellipse \( \frac{x^2}{25} + \frac{y^2}{9} = 1 \) and S, S' are its foci, then the maximum area (in sq. units) of \(\Delta SPS' = \)

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

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=

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 \( \sin\theta = \)

If the line x+y=2 cuts the circle \(x^2+y^2+2x-4y+4=0\) at two points A and B then the radius of the circle passing through A, B and orthogonal to \(x^2+y^2-2x-4y-4=0\) is

The angle between the tangents drawn from the point P(k, 6k) to the circle \(x^2+y^2+6x-6y+2=0\) is \(2\tan^{-1}(\frac{4}{3})\). If the coordinates of P are integers, then k =

A normal chord PQ drawn at a point P on the parabola \(y^2=5x\) subtends a right angle at the vertex. If P lies in the first quadrant, then the other end Q of the normal chord 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 (-1,-1) is the point of intersection of the pair of lines \(2x^2+5xy-3y^2+2gx+2fy+c=0\) then g+f=

The area of the quadrilateral formed by the lines x+2y+3=0, 2x+4y+9=0, x-2y+3=0 and 3x-6y+11=0 is

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

Among every 8 units of a product, one is likely to be defective. If a consumer has ordered 5 units of that product, then the probability that atmost one unit is defective among them is \

If two smallest squares are chosen at random on a chess board then the probability of getting these squares such that they do not have a side in common is

Let \( \vec{a} \) and \( \vec{b} \) be two vectors such that \( |\vec{a}| = |\vec{b}| \) and \( |\vec{a}+2\vec{b}| = |2\vec{a}-\vec{b}| \). If \( \vec{c} \) is a vector parallel to \( \vec{a} \) then the angle between \( \vec{b} \) and \( \vec{c} \) is

If \( \vec{a} \) and \( \vec{b} \) are two vectors such that \( |\vec{a}|=|\vec{b}|=\sqrt{6} \) and \( \vec{a} \cdot \vec{b} = -1 \), then \( |\vec{a} \times \vec{b}| \sin(\vec{a}, \vec{b}) = \)

If the volume of a tetrahedron having \( \vec{i}+2\vec{j}-3\vec{k} \), \( 2\vec{i}+\vec{j}-3\vec{k} \) and \( 3\vec{i}-\vec{j}+p\vec{k} \) as its coterminous edges is 2, then the values of p are the roots of the equation

If a=3, b=5, c=7 are the sides of a triangle ABC, then \( \cot A + \cot B + \cot C = \)

ABCD is a tetrahedron. \( \vec{i}-2\vec{j}+3\vec{k} \), \( -2\vec{i}+\vec{j}+3\vec{k} \), \( 3\vec{i}+2\vec{j}-\vec{k} \) are the position vectors of the points A, B, C respectively. \( -\vec{i}+2\vec{j}-3\vec{k} \) is the position vector of the centroid of the triangular face BCD. If G is the centroid of the tetrahedron, then GD =