List of top Questions asked in TS EAMCET

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 \( \cos\alpha + \cos^2\beta = \)

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 =

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

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 \( \sin\theta = \)

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

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

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

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=

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

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 \( |\vec{a} \times \vec{b}| \sin(\vec{a}, \vec{b}) = \)

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 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 \( x = \log_e 3 \), then \( \tanh(2x) + \operatorname{sech}(2x) = \)

Number of solutions of the equation \( \tan^2 x + 3\cot^2 x = 2\sec^2 x \) lying in the interval \( [0, 2\pi] \) is

\( \sin^{-1}(-\cos 2) + \cos^{-1}(\sin 3) + \tan^{-1}(\cot 5) = \)

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 =

Let \(p_1, p_2, p_3\) be the altitudes of a triangle ABC drawn through the vertices A, B, C respectively. If \(r_1=4, r_2=6, r_3=12\) are the ex-radii of triangle ABC then \( \frac{1}{p_1^2} + \frac{1}{p_2^2} + \frac{1}{p_3^2} = \)

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

If \( \frac{x+1}{x^3(x-1)} = \frac{a}{x} + \frac{b}{x^2} + \frac{c}{x^3} + \frac{d}{x-1} \) then

5 boys and 5 girls have to sit around a table. The number of ways in which all of them can sit so that no two boys and no two girls are together is

\((1-i\sqrt{3})^{2025}= \)

If \( A = \begin{pmatrix} 1 & 2 & 2 \\ 2 & 1 & 1 \\ 1 & 2 & 1 \end{pmatrix} \), then \( |\text{Adj}(A^2)| = \)

The correct statements about the products B and C in the given reactions are (Ethanol reacts with HCl/Anhy ZnCl$_2$ to give A. A reacts with ethanolic AgCN to give B (Minor) and C (Major)). I. B and C are functional isomers II. With H$_2$|Catalyst B gives 1$^\circ$ amine and C gives 2$^\circ$ amine III. B on acid hydrolysis gives formic acid and C gives C$_3$H$_6$O$_2$ IV. C forms isocyanate with HgO