List of top Mathematics Questions asked in AP EAPCET

If \( \frac{d^n y}{dx^n} = y_n \) and \( y = e^{\sqrt{x}} + e^{-\sqrt{x}} \), then find the value of \( 4x y_2 + 2 y_1 \).

Evaluate the limit: \[ \lim_{x \to \infty} \frac{A + e^{mx}}{x + Ae^{mx}} \]

Evaluate: \[ \lim_{n \to \infty} \sqrt{2} \left[ \frac{ \left(2 + \sqrt{2} \right)^n + \left(2 - \sqrt{2} \right)^n }{ \left(2 + \sqrt{2} \right)^n - \left(2 - \sqrt{2} \right)^n } \right] \]

The centroid of a triangle with vertices \( (a, 1, 3), (-2, b, -5), (4, 7, c) \) lies at the origin. Find \( a^2 + b^2 + c^2 \).

Find the distance between the point \( (6, 4\sqrt{3}) \) and the focus of the parabola \( y^2 = 8x \)

A ray makes angles \( \alpha, 2\alpha, 3\alpha \) with the coordinate axes OX, OY, OZ respectively. Then possible values of \( \alpha \) are:

A plane makes intercepts \(-2, \frac{4}{3}, \frac{-4}{5}\) on the X, Y, Z axes respectively. Find the direction cosines of a normal to the plane.

For the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \), the locus of the point of intersection of the tangents at the endpoints of normal chords is:

Find the distance between the directrices of the ellipse: \[ \frac{x^2}{36} + \frac{y^2}{20} = 1 \]

Find the locus of the incenter of the triangle formed by: \[ xy - 4x - 4y + 16 = 0,\quad x + y = 5 \]

Find the set of all points at a distance of at least 2 units from the point \( (-3, 0) \).

A circle passes through \( (0, a) \) and \( (b, h) \), and its center is at \( (c, 0) \). Find \( c \).

Given points \( A(-3, 3), B(1, 1), C(1, -1), D(-2, -2) \), find the angle between diagonals \( AC \) and \( BD \).

The pairs of straight lines \( 2x^2 + axy + 3y^2 = 0 \) and \( 2x^2 + bxy - 3y^2 = 0 \) share a common line, and the other lines are perpendicular. Then values of \( a \) and \( b \) are?

A circle touches the y-axis at a distance 4 units from the origin and cuts off an intercept 6 from the x-axis. Find its equation.

A circle touches both coordinate axes and its center lies on the line \( x - 2y - 3 = 0 \). What is its equation?

A circle of diameter \( R \) touches the parabola \( x^2 + y^2 - 4y = 0 \) and passes through the point \( (4, 5) \). Which of the following is correct?

Suppose a point \( P \) moves such that: \[ BP^2 - AP^2 = 121 \] where \( A = (2, 5) \), \( B = (5, 11) \). Then the locus of \( P \) is a straight line. What is the slope of this line?

Two distinct points are each at a unit distance from the line \( 4x + 3y - 10 = 0 \) and lie on the line \( x + y = 4 \). If they are separated by distance \( d \), then:

Let \( P(x, y) \) lie on one of the lines: \[ \sqrt{3}x - y + 2 = 0 \quad \text{or} \quad \sqrt{3}x + y - 2 = 0 \] and suppose it is at a distance 5 units from their point of intersection. What is the distance from \( (0, 0) \) to the foot of the perpendicular from \( P \) onto the \( y \)-axis?

If variance of a Poisson distribution is 3, find: \[ P(1<X<4) \]

From a pack of 52 cards, 3 cards are drawn at random. What is the probability that one is an ace, one is a queen, and one is a jack?

There are 4 hotels in a town. If 3 men check into the hotels in a day, what is the probability that each checks into a different hotel?

A discrete random variable \( X \sim B(n, p) \) (i.e., binomial distribution). Given: \[ P(X = 2) = P(X = 3) \] Then what is the mean of \( X \)?

Three students \( X, Y, Z \) appear for an exam. Their passing probabilities are: \[ P(X) = \frac{1}{5},\quad P(Y) = \frac{1}{4},\quad P(Z) = 1 - \frac{2}{3} = \frac{1}{3} \] What is the probability that at least two of them pass?