List of top Mathematics Questions asked in AP EAPCET

Let the circle \( S \) be concentric with the circle \( x^2 + y^2 - 2x + ky + 4 = 0 \). If one of the diameters of \( S \) lies along the line \( 3x - 2y + 4 = 0 \) and the length of the diameter is 6, then the radius of the circle \( S \) is
If the length of the chord \( 2x + 3y + k = 0 \) of the circle \( x^2 + y^2 - 6x - 8y + 9 = 0 \) is \( 2\sqrt{5} \), then one of the values of \( k \) is
If \( Q \) is the inverse point of the point \( P(2, 3) \) with respect to the circle \( x^2 + y^2 - 2x - 2y + 1 = 0 \), then the circle with \( PQ \) as diameter is
If a parabola having its axis parallel to X-axis passes through the points \( (0, -1), (6, 1) \) and \( (-2, -3) \), then the point at which this parabola cuts the X-axis is
Let \( S(1, 0) \) and \( S'(0, 1) \) be the foci of an ellipse such that \( SP + S'P = 2 \) for any point \( P \) on the ellipse. If \( A(x_1, y_1) \) and \( A'(x_2, y_2) \) are the end points of the major axis of this ellipse, then \( x_1 + x_2 + y_1 + y_2 = \)
A point on the straight line \( 3x + 5y = 15 \) which is equidistant from the coordinate axes will lie in
The equation of the line passing through the points \( \left( ct_1, \frac{c}{t_1} \right) \) and \( \left( ct_2, \frac{c}{t_2} \right) \) is
The line \( x + y = k \) meets the curve \( x^2 + y^2 - 2x - 4y + 2 = 0 \) at two points \( A \) and \( B \). If \( O \) is the origin and \( \angle AOB = 90^\circ \), then the value of \( k \) (\( k>1 \)) is
If the angle between the pair of lines \( x^2 + 2\sqrt{2} xy + ky^2 = 0, k>0 \) is \( 45^\circ \), then the area (in square units) of the triangle formed by the pair of bisectors of the angles between these lines and the line \( x + 2y + 1 = 0 \) is
The coordinates of the point \( (3, -5) \) in the new system, when the origin is shifted to the point \( (-1, -1) \) by the translation of axes, is
Let \( A(-1, 1, 2), B(1, 2, 3), C(1, 1, 6) \) be three points. If \( l_1, m_1, n_1 \) are the direction cosines of \( AB \) and \( l_2, m_2, n_2 \) are the direction cosines of \( AC \), then \( |l_1 l_2 + m_1 m_2 + n_1 n_2| = \)
If the plane \( 56x + 4y + 9z = 2016 \) meets the coordinate axes in \( A, B \) and \( C \), then the centroid of the \( \triangle ABC \) is
The sides of a triangle are \( 3x + 2y - 6 = 0 \), \( 2x - 3y + 6 = 0 \) and \( x + 2y + 2 = 0 \). If \( P(0, b) \) lies either on the triangle or inside the triangle, then \( b \) lies in the interval
In a city it is found that 10 accidents took place in a span of 50 days. Assuming that the number of accidents follow the Poisson distribution, the probability that there will be 3 or more accidents in a day in that city, is
For a binomial distribution with mean 6 and variance 2, \( P(X \ge 2) = \)
If \( A = (2, 3) \) and \( B = (-4, 5) \) are two fixed points, then the locus of a point \( P \) such that the area of \( \triangle PAB \) is 12 square units is
If one ticket is selected at random from 30 tickets each with a distinct number from 1 to 30, then the probability that the number on the selected ticket is a multiple of 3 or 5 is
A and B are independent events of a random experiment if and only if
From out of 100 enrolled students, two sections of strength 40 and 60 are formed. If you and your friend are among those 100 students, then the probability that both of you are placed in the same section is
For some real number \( \lambda \), if the area of the triangle having \( \mathbf{a} = \lambda \mathbf{i} - 3\mathbf{j} + \mathbf{k} \) and \( \mathbf{b} = 2\mathbf{i} + \lambda \mathbf{j} - 3\mathbf{k} \) as two of its sides is \( \frac{\sqrt{195}}{2} \), then the number of distinct possible values of \( \lambda \) is
Let \( \mathbf{a} = \mathbf{i} + 2\mathbf{j} + 3\mathbf{k} \) and \( \mathbf{b} = \mathbf{i} - 2\mathbf{j} - 3\mathbf{k} \) be two vectors. If \( A_1 \) is the area of the quadrilateral having \( \mathbf{a}, \mathbf{b} \) as its diagonals and \( A_2 \) is the area of the parallelogram having \( \mathbf{a}, \mathbf{b} \) as its adjacent sides, then \( A_1 : A_2 = \)
If the sum of squares of the deviations from the mean of the data \( x_i \) (\( i = 1, 2, \dots, n \)) is \( n\overline{x}^2 \), where \( \overline{x} \) is the mean of \( x_i \)'s, then the sum of squares of \( x_i \)'s is
If \( \mathbf{a} = (2x + y)\mathbf{i} + 3\mathbf{j} + 9\mathbf{k} \) and \( \mathbf{b} = 2\mathbf{i} + \mathbf{j} - (x - y)\mathbf{k} \) are two collinear vectors, then \( x^3 + 27y^3 = \)
If a point \( C \) divides the line segment joining the points with position vectors \( 2\mathbf{i} - 3\mathbf{j} + 2\mathbf{k} \) and \( 3\mathbf{i} - \mathbf{j} - 2\mathbf{k} \) in the ratio \( 2:3 \), then the distance of \( C \) from the point with position vector \( 2\mathbf{i} - \mathbf{j} + \mathbf{k} \) is
Let \( \mathbf{a} = \mathbf{i} - 2\mathbf{j} \), \( \mathbf{b} = 2\mathbf{j} + 3\mathbf{k} \), \( \mathbf{c} = p\mathbf{i} + q\mathbf{j} \) and \( \mathbf{d} = p\mathbf{j} - q\mathbf{k} \) be four vectors. If \( (\mathbf{a} \times \mathbf{b}) \cdot \mathbf{c} = 3 \) and \( (\mathbf{a} \times \mathbf{b}) \cdot \mathbf{d} = 0 \), then \( 3p + q = \)