List of top Mathematics Questions asked in AP EAPCET

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?

Two dice are thrown simultaneously. What is the probability that the product of the numbers is even?

In \( \triangle ABC \), let \( O \) be the circumcenter and \( G \) be the centroid. Then: \[ OG^2 = ? \]

In parallelogram \( ABCD \), points \( M \) and \( N \) are midpoints of sides \( BC \) and \( CD \) respectively. Then the length \( AM + AN = \) ?

Three vectors \( \vec{a}, \vec{b}, \vec{c} \) satisfy: \[ \vec{a} + \vec{b} + \vec{c} = \vec{0},\quad |\vec{a}| = 1,\quad |\vec{b}| = 3,\quad |\vec{c}| = 4 \] Then the value of: \[ \vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a} = ? \]

Let \( \vec{OA} = -4\hat{i} + 3\hat{k} \), \( \vec{OB} = 14\hat{i} + 2\hat{j} - 5\hat{k} \), and vector \( \vec{OD} \) bisects \( \angle AOB \), with \( |\vec{OD}| = \sqrt{6} \). Then: \[ \vec{OD} = ? \]