List of top Mathematics Questions asked in AP EAMCET

Evaluate the limit: \[ \lim\limits_{x \to 2} \frac{\sqrt{1 + 4x} - \sqrt{3} + 3x}{x^3 - 8}. \]

If \( f(x) = 5x \csc(\sqrt{x}) - (x-2) \csc(\sqrt{x}) \), then \( \lim\limits_{x \to \infty} f(x^2) \) is:

Let \( \pi \) be the plane that passes through the point \( (-2,1,-1) \) and is parallel to the plane \( 2x - y + 2z = 0 \). Then the foot of the perpendicular drawn from the point \( (1,2,1) \) to the plane \( \pi \) is:

If \( P(2, \beta, \alpha) \) lies on the plane \( x + 2y - z - 2 = 0 \) and \( Q (\alpha, -1, \beta) \) lies on the plane \( 2x - y + 3z + 6 = 0 \), then the direction cosines of the line \( PQ \) are:

Consider the tetrahedron with the vertices \( A(3,2,4) \), \( B(x_1,y_1,0) \), \( C(x_2,y_2,0) \), and \( D(x_3,y_3,0) \). If the triangle \( BCD \) is formed by the lines \( y = x \), \( x + y = 6 \), and \( y = 1 \), then the centroid of the tetrahedron is:

The equation of one of the tangents drawn from the point \( (0,1) \) to the hyperbola \( 45x^2 - 4y^2 = 5 \) is:

The equation of the pair of asymptotes of the hyperbola \( 4x^2 - 9y^2 - 24x - 36y - 36 = 0 \) is:

If \( A_1, A_2, A_3 \) are the areas of the ellipse \( x^2 + 4y^2 = 4 \), its director circle, and auxiliary circle respectively, then \( A_2 + A_3 - A_1 \) is:

The equation of the normal drawn to the parabola \( y^2 = 6x \) at the point \( (24,12) \) is:

The radius of the circle which cuts the circles \( x^2 + y^2 - 4x - 4y + 7 = 0 \), \( x^2 + y^2 + 4x + 6 = 0 \), and \( x^2 + y^2 + 4x + 4y + 5 = 0 \) orthogonally is:

If a direct common tangent is drawn to the circles \( x^2 + y^2 - 6x + 4y + 9 = 0 \) and \( x^2 + y^2 + 2x - 2y + 1 = 0 \) that touches the circles at points \( A \) and \( B \), then \( AB = \):

If \( (a, b) \) is the midpoint of the chord \( 2x - y + 3 = 0 \) of the circle \( x^2 + y^2 + 6x - 4y + 4 = 0 \), then \( 2a + 3b = \):

If the inverse point of the point \( (-1, 1) \) with respect to the circle \( x^2 + y^2 - 2x + 2y - 1 = 0 \) is \( (p, q) \), then \( p^2 + q^2 = \)

The equations \( 2x - 3y + 1 = 0 \) and \( 4x - 5y - 1 = 0 \) are the equations of two diameters of the circle \( S = x^2 + y^2 + 2gx + 2fy - 11 = 0 \) and \( R \) are the points of contact of the tangents drawn from the point \( P(-2, -2) \) to this circle. If \( C \) is the centre of the circle, \( S = 0 \) is the equation of the circle, then the area (in square units) of the quadrilateral \( PQCR \) is:

If all chords of the curve \( 2x^2 - y^2 + 3x + 2y = 0 \), which subtend a right angle at the origin, always pass through the point \( (a, \beta) \), then \( (a, \beta) = \):

The area of the triangle formed by the lines represented by \( 3x + y + 15 = 0 \) and \( 3x^2 + 12xy - 13y^2 = 0 \) is:

If \( (a, \beta) \) is the orthocenter of the triangle with the vertices \( A(2, 5), B(1, 5), C(1, 4) \), then \( a + \beta = \):

Let \( \alpha \in \mathbb{R} \). If the line \( (a + 1)x + \alpha y + \alpha = 1 \) passes through a fixed point \( (h, k) \) for all \( a \), then \( h^2 + k^2 = \):

When the origin is shifted to \( (h, k) \) by translation of axes, the transformed equation of \( x^2 + 2x + 2y - 7 = 0 \) does not contain \( x \) and constant terms. Then \( (2h + k) = \):

P is a variable point such that the distance of P from A(4,0) is twice the distance of P from B(-4,0). If the line \( 3y - 3x - 20 = 0 \) intersects the locus of P at the points C and D, then the distance between C and D is:

A manufacturing company noticed that 1% of its products are defective. If a dealer orders 300 items from this company, then the probability that the number of defective items is at most one is:

7 coins are tossed simultaneously and the number of heads turned up is denoted by the random variable \( X \). If \( \mu \) is the mean and \( \sigma^2 \) is the variance of \( X \), then \( \frac{\mu^2}{P(X = 3)} \) is:

A basket contains 12 apples in which 3 are rotten. If 3 apples are drawn at random simultaneously from it, then the probability of getting at most one rotten apple is:

In a class consisting of 40 boys and 30 girls, 30% of the boys and 40% of the girls are good at Mathematics. If a student selected at random from that class is found to be a girl, then the probability that she is not good at Mathematics is:

If a number is drawn at random from the set \( \{1, 3, 5, 7, \dots, 59\} \), then the probability that it lies in the interval in which the function \( f(x) = x^3 - 16x^2 + 20x - 5 \) is strictly decreasing is: