List of top Mathematics Questions asked in AP EAPCET

Let the slopes $ m_1 $ and $ m_2 $ of the lines represented by: $$ ax^2 + 2hxy + by^2 = 0 $$ satisfy: $$ 3(m_1 - m_2) - 7 = 0 \quad \text{and} \quad m_1 m_2 - 2 = 0 $$ Then find the correct relation among $ a, b, h $.

Sides passing through vertex $ (\alpha, \beta) $ of a triangle are bisected at right angles by the lines: $$ y^2 - 8xy - ax^2 = 0 $$ Find the coordinates of the centroid of the triangle.

Find the radius of the circle that has the lines: $$ 3x - 4y + 4 = 0 \quad \text{and} \quad 6x - 8y - 7 = 0 $$ as its tangents.

Find the least distance from the point $ (10, 7) $ to the circle: $$ x^2 + y^2 - 4x - 2y - 20 = 0 $$

Let the coordinates of points A and B satisfy:
- $ x^2 + 2x - a^2 = 0 $
- $ y^2 + 4y - b^2 = 0 $ Find the equation of the circle having AB as diameter.

A circle is such that it is tangent to every line of the form: $$ (x - 2)\cos\theta + (y - 2)\sin\theta = 1 $$ for all $ \theta $. Find the equation of the circle.

Find the locus of midpoints of points of intersection of the line $$ x \cos \theta + y \sin \theta = 1 $$ with the coordinate axes.

Points $ P $ and $ Q $ lie on the lines: $$ 3x + 4y - 4 = 0 \quad \text{and} \quad 5x - y - 4 = 0 $$ The midpoint of segment $ PQ $ is $ (1, 5) $. Find the slope of the line $ PQ $.

Find the length of the intercept made by the line $ x + 1 = 0 $ between the lines: $$ 3x + 2y = 5 \quad \text{and} \quad 3x + 2y = 3 $$

Two brothers X and Y appeared for an exam. Let:
- $ A $: event that X passed
- $ B $: event that Y passed
Given: $$ P(A) = \frac{1}{7},\quad P(B) = \frac{2}{9} $$ Assuming independence, find the probability that both passed, i.e., $ P(A \cap B) $.

There are two bags:
- Bag 1: 4 red, 3 black → total = 7 balls
- Bag 2: 2 red, 3 black → total = 5 balls
A bag is chosen at random and one ball is drawn. What is the probability that the ball is red?

In a binomial distribution, if:
- Number of trials $ n $
- Mean $ = 4 $
- Variance $ = 3 $
Then find: $$ 2^{32} \cdot P\left(X = \frac{n}{2}\right) $$

For a Poisson distribution:
- Mean $ = \ell $
- Variance $ = m $
- $ \ell + m = 8 $
Then evaluate: $$ e^4 \cdot \left[1 - P(X>2)\right] $$

Given: $$ \vec{F} = 2\hat{i} + 2\hat{j} + 5\hat{k},\quad A = (1, 2, 5),\quad B = (-1, -2, -3) $$ and: $$ \overrightarrow{BA} \times \vec{F} = 4\hat{i} + 6\hat{j} + 2\lambda \hat{k} $$ Find the value of $ \lambda $.

If the mean deviation of the data: $$ 1, 1 + d, 1 + 2d, \ldots, 1 + 100d $$ from their mean is 255, then find $ d $.

What is the probability of getting a sum of 9 when two dice are thrown?

If $ A $ and $ B $ are two events such that $ P(B) \ne 0 $ and $ P(B) \ne 1 $, then: $$ P(\bar{A} \mid B) = ? $$

Three vectors of magnitudes $ a, 2a, 3a $ are along the diagonals of three adjacent faces of a cube that meet at a point. Find the magnitude of the sum of these vectors.

If $ \vec{a} $ is collinear with $ \vec{b} = 3\hat{i} + 6\hat{j} + 6\hat{k} $ and $ \vec{a} \cdot \vec{b} = 27 $, then find $ |\vec{a}| $.

Let $ \vec{a}, \vec{b}, \vec{c} $ be unit vectors such that: - $ \vec{a} \perp \text{plane of } \vec{b}, \vec{c} $ - Angle between $ \vec{b} $ and $ \vec{c} $ is $ \frac{\pi}{3} $ Find: $$ |\vec{a} + \vec{b} + \vec{c}| $$

If $ \sin\theta + \csc\theta = 4 $, then find: $$ \sin^2\theta + \csc^2\theta = ? $$

Evaluate: $$ \sin^2\left(\frac{2\pi}{3}\right) + \cos^2\left(\frac{5\pi}{6}\right) - \tan^2\left(\frac{3\pi}{4}\right) $$

In any triangle $ ABC $, evaluate: $$ \frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} $$

In triangle $ ABC $, if: $$ r_1 = 36,\quad r_2 = 18,\quad r_3 = 12 $$ then find the semi-perimeter $ s $.

In triangle $ ABC $, given: $$ a = 6,\quad b = 5,\quad c = 4,\quad \text{find } \cos 2A $$