List of top Mathematics Questions asked in AP EAPCET

If $ P(\bar{A}) = 0.3,\ P(B) = 0.4,\ P(A \cap \bar{B}) = 0.5 $, then find $ P(B / (A \cup \bar{B})) $

From the word "CURVE", how many 3-letter words can be formed out of all 2-letter or more combinations (with all distinct letters)? Find probability of getting a 3-letter word.

X denotes the number of heads in $ n $ tosses of a fair coin. If $ P(X = 4),\ P(X = 5),\ P(X = 6) $ are in arithmetic progression, find the largest possible value of $ n $.

Three numbers are chosen from 1 to 30. Find the probability that they are NOT 3 consecutive numbers.

If $ \vec{a}, \vec{b}, \vec{c} $ are three unit vectors such that $ \vec{a} \times (\vec{b} \times \vec{c}) = \frac{\sqrt{3}}{2} \vec{b} + \frac{1}{2} \vec{c} $, and $ \alpha, \beta $ are the angles between $ \vec{a}, \vec{c} $ and $ \vec{a}, \vec{b} $ respectively, then $ \alpha + \beta = ? $

The vector equation of a plane passing through the line of intersection of the planes $$ \vec{r} \cdot (\hat{i} - 2\hat{k}) = 3,\quad \vec{r} \cdot (\hat{j} + \hat{k}) = 5 $$ and also passing through the point $ \vec{r} = \hat{i} + 2\hat{j} + 3\hat{k} $ is:

Let vectors: $ \vec{A} = \hat{i} - 2\hat{j} + \hat{k},\ \vec{B} = \hat{i} + \hat{j} - 2\hat{k},\ \vec{C} = 2\hat{i} - \hat{j},\ \vec{D} = \hat{i} + \hat{j} + \hat{k} $ If $ P $ divides $ AB $ in ratio 2:1 internally, and $ Q $ divides $ CD $ in ratio 1:2 externally, find the ratio in which the point $ 5\hat{i} - 6\hat{j} - 5\hat{k} $ divides line $ PQ $

If $ \vec{a} = \hat{i} + \hat{j}, \vec{b} = 2\hat{j} - \hat{k} $ are two vectors such that $ \vec{r} \times \vec{a} = \vec{b} \times \vec{a}, \vec{r} \times \vec{b} = \vec{a} \times \vec{b} $, then the unit vector in the direction of $ \vec{r} $ is:

If the line joining points $ \vec{r}_1 = \hat{i} + 2\hat{j} $ and $ \vec{r}_2 = \hat{j} - 2\hat{k} $ intersects the plane through the points $ \vec{A} = 2\hat{i} - \hat{j},\ \vec{B} = -2\hat{j} + 3\hat{k},\ \vec{C} = \hat{k} - 2\hat{i} $ at $ T $, then find $ \vec{r}_T \cdot (\hat{i} + \hat{j} + \hat{k}) $

In triangle $ ABC $, if $ a = 5,\ b = 4,\ \cos(A - B) = \frac{31}{32} $, then $ c = ? $

If $ \tan\left( \frac{\pi}{4} + \alpha \right) = \tan^3\left( \frac{\pi}{4} + \beta \right) $, then compute: $$ \tan(\alpha + \beta) \cot(\alpha - \beta) = ? $$

If $ A + B + C + D = 2\pi $, then $$ \sin A + \sin B + \sin C + \sin D = ? $$

If $ \theta = \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{1}{7} \right) + \tan^{-1} \left( \frac{1}{13} \right) + \tan^{-1} \left( \frac{1}{21} \right) + \tan^{-1} \left( \frac{1}{31} \right) $, then $ \tan \theta = ? $

If $ \tanh^{-1} x = \coth^{-1} y = \log \sqrt{5} $, then find $ \tan^{-1}(xy) = ? $

In triangle $ ABC $, if $ C = 120^\circ $, $ c = \sqrt{19} $, and $ b = 3 $, then $ a = ? $

In triangle $ ABC $, $ 2A + C = 300^\circ $. If the circumradius is 8 times the inradius, then $ \sin\frac{C}{2} = ? $

The number of positive integers less than 10000 which contain the digit 5 at least once is

5 men and 4 women are seated in a row. If the number of arrangements in which one particular man and one particular woman are together is $ \alpha $, and the number of arrangements in which they are not together is $ \beta $, then $ \frac{\alpha}{\beta} = $

Evaluate: $$ \sin \frac{\pi}{12} \cdot \sin \frac{2\pi}{12} \cdot \sin \frac{3\pi}{12} \cdot \sin \frac{4\pi}{12} \cdot \sin \frac{5\pi}{12} \cdot \sin \frac{6\pi}{12} $$

If a team of 4 persons is to be selected out of 4 married couples to play mixed doubles tennis game, then the number of ways of forming a team in which no married couple appears is

In the binomial expansion of $ (p - q)^{14} $, if the sum of 7^th and 8^th terms is zero, then $$ \frac{p + q}{p - q} = ? $$

The numerically greatest term in the expansion of $ (x + 3y)^{13} $, when $ x = \frac{1}{2},\ y = \frac{1}{3} $, is

If $ \frac{x^4}{(x-1)(x-2)} = \frac{A}{x - 1} + \frac{B}{x - 2} $, then $$ f(-2) + A + B = ? $$

Let $ f(x) = x^2 + 2bx + 2c^2 $ and $ g(x) = -x^2 - 2cx + b^2 $, $ x \in \mathbb{R} $. If $ b $ and $ c $ are non-zero real numbers such that $ \min f(x)>\max g(x) $, then $$ \left| \frac{c}{b} \right| $$ lies in the interval

If $ x^2 - 4x + 5 + a>0 $ for all $ x \in \mathbb{R} $ whenever $ a \in (\alpha, \beta) $, then $ 4\beta + \alpha = $