List of top Questions asked in TS EAMCET- 2025

The set of all values of $\theta$ such that $\frac{1-i\cos\theta}{1+2i\sin\theta}$ is purely imaginary is
If $\omega \neq 1$ is a cube root of unity, then one root among the $7^{th}$ roots of $(1+\omega)$ is
If all the letters of the word ACADEMICIAN are permuted in all possible ways then the number of permutations in which no two A's are together and all the consonants are together is
The number of all possible three letter words that can be formed by choosing three letters from the letters of the word FEBRUARY so that a vowel always occupies the middle place is
The constant term in the expansion of \( \left(1+\frac{1}{x}\right)^{20} \left(30x(1+x)^{29} + (1+x)^{30}\right) \) is
When \( |x|>3 \), the coefficient of \( \frac{1}{x^n} \) in the expansion of \( x^{3/2} (3+x)^{1/2} \) is
The number of non negative integral solutions of the equation \( x+y+z+t=10 \) when \( x \ge 2, z \ge 5 \) is
Number of all possible ways of distributing eight identical apples among three persons is
All the letters of the word MOTHER are arranged in all possible ways and the resulting words (may or may not have meaning) are arranged as in the dictionary. The number of words that appear after the word MOTHER is
There are 15 stations on a train route and the train has to be stopped at exactly 5 stations among these 15 stations. If it stops at at least two consecutive stations, then the number of ways in which the train can be stopped is
If all the letters of the word MOST are permuted and the words (with or without meaning) thus obtained are arranged in the dictionary order then the rank of the word STOM when counted from the rank of the word MOST, is
The number of ways in which 6 boys and 4 girls can be arranged in a row such that between any two girls there must be exactly 2 boys is
The number of positive integral solutions of $\frac{1}{x} + \frac{1}{y} = \frac{1}{2025}$ is
The number of positive integral solutions of $xyz = 60$ is
The equation of the locus of a point which is at a distance of 5 units from a fixed point (1,4) and also from a fixed line 2x+3y-1=0 is
If the normals drawn at the points $P\left(\frac{3}{4}, \frac{3}{2}\right)$ and $Q(3,3)$ on the parabola $y^2 = 3x$ intersect again on $y^2=3x$ at R, then R =
If $\theta$ is the acute angle between the tangents drawn from the point (1,5) to the parabola $y^2 = 9x$ then
If a normal is drawn at a variable point P(x, y) on the curve $9x^2+16y^2-144=0$, then the maximum distance from the centre of the curve to the normal is
If the perpendicular distance from the focus of an ellipse $\frac{x^2}{9} + \frac{y^2}{b^2} = 1$ ($b<3$) to its corresponding directrix is $\frac{4}{\sqrt{5}}$, then the slope of the tangent to this ellipse drawn at $(\frac{3}{\sqrt{2}}, \frac{b}{\sqrt{2}})$ is
If the point P($x_1, y_1$) lying on the curve $y = x^2-x+1$ is the closest point to the line $y = x-3$ then the perpendicular distance from P to the line $3x+4y-2=0$ is
If the angle between the tangents drawn to the parabola $y^2=4x$ from the points on the line $4x-y=0$ is $\frac{\pi}{3}$, then the sum of the abscissae of all such points is
The normal at a point on the parabola $y^2=4x$ passes through a point P. Two more normals to this parabola also pass through P. If the centroid of the triangle formed by the feet of these three normals is G(2,0), then the abscissa of P is
If the percentage error in the radius of a circle is 3, then the percentage error in its area is
The midpoint of the chord of the ellipse $x^2+\frac{y^2}{4}=1$ formed on the line $y=x+1$ is
If the tangent drawn at the point $P(3\sqrt{2}, 4)$ on the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$ meets its directrix at $Q(\alpha, \beta)$ in the fourth quadrant then $\beta = $