List of top Mathematics Questions asked in AP EAMCET

The value of \( x \) such that \( \sin \left( 2 \tan^{-1} \frac{3}{4} \right) = \cos \left( 2 \tan^{-1} x \right) \) is:
If \( \tanh x = \text{sech } y = \frac{3}{5} \) and \( e^{x+y} \) is an integer, then \( e^{x+y} \) is:
In \( \triangle ABC \), if \( b + c : c + a : a + b = 7:8:9 \), then the smallest angle (in radians) of that triangle is:
In \( \triangle ABC \), if \( A, B, C \) are in arithmetic progression, \( \Delta = \frac{\sqrt{3}}{2} \) and \( r_1 r_2 = r_3 r \), then \( R \) is:
In \( \triangle PQR \), \((4\overline{i} + 3\overline{j} + 6\overline{k} )\) and \((3\overline{i} + \overline{j} + 3\overline{k} )\) are the position vectors of the vertices P, Q, R respectively. Then the position vector of the point of intersection of the angle bisector of \( P \) with \( QR \).
The distance of a point \( (2,3,-5) \) from the plane \( \vec{r} \cdot (4i - 3j + 2k) = 4 \) is:
Three numbers are chosen at random from 1 to 20. The probability that their sum is divisible by 3 is:
Two persons A and B throw three unbiased dice one after the other. If A gets the sum 13, then the probability that B gets a higher sum is:
8 teachers and 4 students are sitting around a circular table at random. The probability that no two students sit together is:
In a Binomial distribution, the difference between the mean and standard deviation is 3, and the difference between their squares is 21. Then, the ratio \( P(x = 1) : P(x = 2) \) is:
When an unfair dice is thrown, the probability of getting a number \( k \) on it is \( P(X = k) = k^2 P \), where \( k = 1, 2, 3, 4, 5, 6 \) and \( X \) is the random variable denoting a number on the dice. Then, the mean of \( X \) is:
The equation of the locus of points that are equidistant from the points \( (2,3) \) and \( (4,5) \) is:
The transformed equation of \( x^2 - y^2 + 2x + 4y = 0 \) when the origin is shifted to the point \( (-1,2) \) is:
The equation of one side of an equilateral triangle is \( x + y = 2 \), and one vertex is \( (2,-1) \). The length of the side is:
The orthocentre of the triangle formed by lines \( x + y + 1 = 0 \), \( x - y - 1 = 0 \) and \( 3x + 4y + 5 = 0 \) is:
If the slope of one of the pair of lines represented by \( 2x^2 + 3xy + Ky^2 = 0 \) is 2, then the angle between the pair of lines is:
The length of x-intercept made by the pair of lines \( 2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0 \) is:
From a point \( (1,0) \) on the circle \( x^2 + y^2 - 2x + 2y + 1 = 0 \), if chords are drawn to this circle, then locus of the poles of these chords with respect to the circle \( x^2 + y^2 = 4 \) is:
If A and B are the centres of similitude with respect to the circles \( x^2 + y^2 - 14x + 6y + 33 = 0 \) and \( x^2 + y^2 + 30x - 2y + 1 = 0 \), then midpoint of \( AB \) is:
\( C_1 \) is the circle with centre at \( (0,0) \) and radius 4, \( C_2 \) is a variable circle with centre at \( (\alpha, \beta) \) and radius 5. If the common chord of \( C_1 \) and \( C_2 \) has slope \( \frac{3}{4} \) and of maximum length, then one of the possible values of \( \alpha + \beta \) is:
If \( x - 4 = 0 \) is the radical axis of two orthogonal circles out of which one is \( x^2 + y^2 = 36 \), then the centre of the other circle is:
If the normal chord drawn at \( (2a,2a\sqrt{2}) \) on the parabola \( y^2 = 4ax \) subtends an angle \( \theta \) at its vertex, then \( \theta \) is:
If the ellipse \(4x^2 + 9y^2 = 36\) is confocal with a hyperbola whose length of the transverse axis is 2, then the points of intersection of the ellipse and hyperbola lie on the circle:
If \( e_1 \) and \( e_2 \) are respectively the eccentricities of the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and its conjugate hyperbola, then the line \( \frac{x}{2e_1} + \frac{y}{2e_2} = 1 \) touches the circle having center at the origin, then its radius is:
The orthocentre of triangle formed by points: \( (2,1,5) \), \( (3,2,3) \) and \( (4,0,4) \) is: