List of top Mathematics Questions asked in AP EAPCET

If the ends of the hypotenuse of a right-angled triangle are $ (0, a) $ and $ (a, 0) $, then the locus of the third vertex is:
The point $ P(2, 1) $ is translated to a point $ Q $ parallel to the line $ L: x - y - 4 = 0 $ by $ 2\sqrt{5} $ units. If the point $ Q $ lies in the third quadrant, then the equation of the line passing through $ Q $ and perpendicular to $ L $ is:
Let $ \bar{a}, \bar{b}, \bar{c} $ be three vectors such that $ \bar{a} $ is perpendicular to $ \bar{b} $ and $ \bar{b} $ is perpendicular to $ \bar{c} $. If $ |\bar{a}| = 2, |\bar{b}| = 3, |\bar{c}| = 5 $ and $ |\bar{a} + \bar{b} + \bar{c}| = 4\sqrt{3} $, then the angle between $ \bar{a} $ and $ \bar{c} $ is
Let $ \bar{a} = \bar{i} + \bar{j} + \bar{k} $, $ \bar{b} = \bar{i} + \bar{j} - 2\bar{k} $, $ \bar{c} = \bar{i} - 2\bar{j} + 3\bar{k} $ and $ \bar{d} = -4\bar{i} + 5\bar{j} - 3\bar{k} $ be four vectors. If $ \bar{d} = x(\bar{b} \times \bar{c}) - \frac{7}{9}(\bar{c} \times \bar{a}) + z(\bar{a} \times \bar{b}) $, then $ x = $
The mean deviation from the mean for the data $ 6, 7, 10, 12, 13, 4, 12, 16 $ is:
A shopkeeper buys a particular type of electric bulbs from three manufacturers $ M_1, M_2, M_3 $. He buys 25% of his requirement from $ M_1 $, 45% from $ M_2 $, and 30% from $ M_3 $. Based on past experience, he found that 2% of type $ M_1 $ bulbs are defective, whereas only 1% of type $ M_1 $ and type $ M_2 $ are defective. If a bulb chosen by him at random is defective, then the probability that it was of type $ M_3 $ is:
The probability that a non-leap year contains 53 Sundays is
If $ A $ and $ B $ are two events of a random experiment such that $ P(A \cup B) = 0.65 $ and $ P(A \cap B) = 0.15 $, then $ P(A) + P(B) = ?$
If a card is drawn at random from a well shuffled pack of playing cards, then the probability that it is either an Ace or a Spade card is
In $ \triangle ABC $, if $ r $ is the inradius and $ r_1, r_2, r_3 $ are the ex-radii, then \[ \frac{1}{4} \left[ b^2 \sin 2C + c^2 \sin 2B \right] = \]

Let ABCD be a parallelogram and $ 2\bar{i} + \bar{j} $, $ 4\bar{i} + 5\bar{j} + 4\bar{k} $ and $ -\bar{i} - 4\bar{j} - 3\bar{k} $ be the position vectors of the vertices A, B, D respectively. Then the position vector of one of the points of trisection of the diagonal AC is

If $ \frac{k}{kx + 3} + \frac{3}{3x-k}= \frac{12x + 5}{(kx + 3)(3x - k)} $, then both the roots of the equation $ kx^2 - 7x + 3 = 0 $ are:

Match the items of List - A with those of the entries of List - B.

If $ \sin x \cosh y = \cos \theta $ and $ \cos x \sinh y = \sin \theta $, then find $ \sin^2 x + \cosh^2 y $.
The value of the following expression is: \[ \cos \left( \frac{\pi}{2^2} \right) \cdot \cos \left( \frac{\pi}{2^3} \right) \cdot \cos \left( \frac{\pi}{2^4} \right) ... \cdot \cos \left( \frac{\pi}{2^{10}} \right) \]
If $ \sin(\alpha + \beta) = 5 \sin(\alpha - \beta) $, then $ \frac{\sin 2\beta}{5 - \cos 2\beta} $ is:
The coefficient of $ x^2 $ in the expansion of \[ (1 - 3x)^{\frac{-1}{4}} \] is

If $ N(n) = n \prod_{r=1}^{2023} (n^2 - r^2) $ where $ n > 2023 $, then the value of $ {}^{n}C_{N-1} $ when $ n = 2024 $ is:

If $ \alpha, \beta, \gamma $ are the roots of the equation $ x^3 + 3x^2 + 4x + 5 = 0 $, then the cubic equation whose roots are $ 1 + 4\alpha, 1 + 4\beta, 1 + 4\gamma $ is:
The number of natural numbers less than 500 in which no two digits are repeated is:
The number of elements in the set $ S = \{x \in \mathbb{Z} : x^2 - 7x + 6 \le 0 \text{ and } x^2 - 3x>0 \} $ is
Arg \[ \frac{4 + 2i}{1 - 2i} + \frac{3 + 4i}{2 + 3i} \] lies in the interval \[ \text{Arg} \left( \frac{4 + 2i}{1 - 2i} + \frac{3 + 4i}{2 + 3i} \right) \]
The multiplicative inverse of $ z $ is:

Given: \[ \lim_{x \to a} \left\lfloor \left( \frac{x^3}{a} - \left\lfloor \frac{x}{a} \right\rfloor^3 \right) \right\rfloor = k, \quad \lim_{x \to a} \left( \left\lfloor \frac{x^3}{a} \right\rfloor - \left\lfloor \frac{x}{a} \right\rfloor^3 \right) = l \] Then: \[ \boxed{?} \]

The equation √5·y − √8 = 0 is the directrix of a hyperbola:

x² / a² − y² / b² = 1

and the eccentricity is e = √5 / 2. 

Find the value of a.