List of top Mathematics Questions asked in AP EAPCET

The equation of the circle passing through the origin and cutting orthogonally the circles \( x^2 + y^2 + 6x - 15 = 0 \) and \( x^2 + y^2 - 8y - 10 = 0 \) is:
For the parabola represented parametrically by \( x = t^2 + t + 1 \) and \( y = t^2 - t + 1 \), the length of the latus rectum is:
An ellipse has lengths of major and minor axes as 6 and 2 respectively. If the center is at \( (5,6) \) and the major axis lies along the line \( x - y + 1 = 0 \), then the equation of the ellipse is:
For the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \), if the length of the transverse axis is 8 and the distance between the foci is \( 2\sqrt{41} \), then the length of its latus rectum is:
If the point \( P(\sin\alpha, \cos\alpha) \) lies inside the triangle formed by the vertices \( (0, 0), \left(\frac{\sqrt{3}}{2}, 0\right), (0, \frac{\sqrt{3}}{2}) \), then \( \alpha \) lies in the interval:
The equation of bisectors of the angle between the lines given by \( 3x^2 + 5xy + 4y^2 = 0 \) is:
Suppose \( d_1 \) and \( d_2 \) are respectively the lengths of intercepts of the circle \( x^2 + y^2 = 4 \) and \( x^2 + y^2 - 10x - 14y + 65 = 0 \) on the line \( 2x - 2y = 3 \). Then which of the following is true?
If the point \( (2, \lambda) \) lies inside the circles \( x^2 + y^2 = 13 \) and \( x^2 + y^2 + x - 2y = 14 \), then \( \lambda \) lies in the set:
If \( \left(x_1, \frac{1}{x_1}\right), \left(x_2, \frac{1}{x_2}\right), \left(x_3, \frac{1}{x_3}\right), \left(x_4, \frac{1}{x_4}\right) \) lie on the boundary of a circle of radius 4, then the value of \( x_1 x_2 x_3 x_4 \) is:
The equation of the tangent to the circle \( x^2 + y^2 = 9 \) making an angle \( 60^\circ \) with the x-axis is:
The triangle formed by \( x^2 - 4xy + y^2 = 0 \) and \( x + y + 4\sqrt{6} = 0 \) is:
On the locus of the point \( P(x, y) \) equidistant from \( (3, 0) \) and \( (0, 4) \), if \( A \) and \( B \) are two points that satisfy \( 4x = 3y \) and \( x = y \) respectively, then the distance between A and B is:
If one side of an isosceles triangle is given by \( y = 2 \), and the base is provided by the points \( (2, 0) \) and \( (0, 2) \), then its area (in sq. units) is:
The straight line passing through \( (0, 0) \) and the foot of the perpendicular from \( (2, 4) \) onto the line \( x + y - 1 = 0 \) is:
If a number is chosen at random from the set \( \{1, 2, 3, \dots, 100\} \), then the probability that it is a perfect cube is:
Suppose that a book of 600 pages contains 40 print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poisson distribution. The probability that all the 10 pages selected at random have no print mistakes is:
The maximum value of the variance of a Binomial distribution with parameters \( n \) and \( p \) is:
In a set of 30 game cards, 17 are white and the rest are green. Out of the 30, 4 white and 5 green are marked “IMPORTANT”. If a card is chosen randomly from this set, the possibility of choosing a green card or an “IMPORTANT” card is:
In a toy factory, the machines A, B, and C are used to manufacture 30%, 40%, and 30% of the output respectively. The probability that a toy produced by machines A, B, and C is defective is 2%, 3%, and 1% respectively. A toy is found to be defective. The probability that it was manufactured by machine B is:
The range of the data set: \( 35, 12, 21, 24, 15, 7, 16, 12, 30, 32, 13, 17 \) is:
If \( A \) and \( B \) are two independent events such that \( P(A) = 0.3 \), \( P(B) = x \), and \( P(A \cup B) = 0.44 \), then \( x = \):
If \( C \) is the midpoint of line segment \( \overline{AB} \), and \( P \) is any point outside the line \( AB \), then:
Let \( \vec{a}, \vec{b} \) be non-collinear vectors, with \( |\vec{a}| = 2\sqrt{2} \), \( |\vec{b}| = 3 \), and the angle between them is \( 45^\circ \). Then the lengths of the diagonals of the parallelogram whose adjacent sides are \( \vec{5a} + \vec{2b} \) and \( \vec{a} - \vec{3b} \) are:
Two vertices of a triangle are at \( -\vec{i} + 3\vec{j} \) and \( 2\vec{i} + 5\vec{j} \). Its orthocenter is at \( \vec{i} + 2\vec{j} \). If the position vector of the third vertex is \( a\vec{i} + b\vec{j} \), then \( (a, b) = \):
If \( \vec{a}, \vec{b}, \vec{c} \) are vectors such that \( \vec{a} \ne 0 \), \( \vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c}) \), \( |\vec{a}| = 1 \), \( |\vec{c}| = 1 \), \( |\vec{b}| = 4 \), and the angle between \( \vec{b} \) and \( \vec{c} \) is \( \cos^{-1} \left( \frac{1}{4} \right) \). If \( \vec{b} - 2\vec{c} = \lambda \vec{a} \), then \( \lambda = \):