List of top Questions asked in AP EAMCET

Let \( \alpha \in \mathbb{R} \). If the line \( (a + 1)x + \alpha y + \alpha = 1 \) passes through a fixed point \( (h, k) \) for all \( a \), then \( h^2 + k^2 = \):
When the origin is shifted to \( (h, k) \) by translation of axes, the transformed equation of \( x^2 + 2x + 2y - 7 = 0 \) does not contain \( x \) and constant terms. Then \( (2h + k) = \):
P is a variable point such that the distance of P from A(4,0) is twice the distance of P from B(-4,0). If the line \( 3y - 3x - 20 = 0 \) intersects the locus of P at the points C and D, then the distance between C and D is:
A manufacturing company noticed that 1% of its products are defective. If a dealer orders 300 items from this company, then the probability that the number of defective items is at most one is:
7 coins are tossed simultaneously and the number of heads turned up is denoted by the random variable \( X \). If \( \mu \) is the mean and \( \sigma^2 \) is the variance of \( X \), then \( \frac{\mu^2}{P(X = 3)} \) is:
A basket contains 12 apples in which 3 are rotten. If 3 apples are drawn at random simultaneously from it, then the probability of getting at most one rotten apple is:
In a class consisting of 40 boys and 30 girls, 30% of the boys and 40% of the girls are good at Mathematics. If a student selected at random from that class is found to be a girl, then the probability that she is not good at Mathematics is:
If a number is drawn at random from the set \( \{1, 3, 5, 7, \dots, 59\} \), then the probability that it lies in the interval in which the function \( f(x) = x^3 - 16x^2 + 20x - 5 \) is strictly decreasing is:
If 12 dice are thrown at a time, then the probability that a multiple of 3 does not appear on any die is:
Mean deviation about the mean for the following data is: \[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 0-6 & 1 \\ 6-12 & 2 \\ 12-18 & 3 \\ 18-24 & 2 \\ 24-30 & 1 \\ \hline \end{array} \]
If \( \vec{a} = \hat{i} - \hat{j} + \hat{k} \), \( \vec{b} = \hat{i} + \hat{j} - 2\hat{k} \), \( \vec{c} = 2\hat{i} - 3\hat{j} - 3\hat{k} \), and \( \vec{d} = 2\hat{i} + \hat{j} + \hat{k} \) are four vectors, then \( (\vec{a} \times \vec{c}) \times (\vec{b} \times \vec{d}) = \):
A(1, 2, 1), B(2, 3, 2), C(3, 1, 3) and D(2, 1, 3) are the vertices of a tetrahedron. If \( \theta \) is the angle between the faces ABC and ABD then \( \cos \theta \) is:
If \( \vec{a} = \hat{i} - \hat{j} + \hat{k} \), \( \vec{b} = 2\hat{i} + \hat{j} + \hat{k} \) are two vectors and \( \vec{c} \) is a unit vector lying in the plane of \( \vec{a} \) and \( \vec{b} \), and if \( \vec{c} \) is perpendicular to \( \vec{b} \), then \( \vec{c} \cdot (\hat{i} + 2\hat{k}) = \):
If \( \vec{c} \) is a vector along the bisector of the internal angle between the vectors \( \vec{a} = 4\hat{i} + 7\hat{j} - 4\hat{k} \) and \( \vec{b} = 12\hat{i} - 3\hat{j} + 4\hat{k} \), and the magnitude of \( \vec{c} \) is \( 3\sqrt{13} \), then \( \vec{c} = \):
In \( \triangle ABC \), if \( AB:BC:CA = 6:4.5 \), then \( R : r = \)
In a triangle ABC, if \( BC = 5 \), \( CA = 6 \), \( AB = 7 \), then the length of the median drawn from \( B \) onto \( AC \) is:
In a triangle, if the angles are in the ratio \( 3:2:1 \), then the ratio of its sides is:
If \( \theta \) is an acute angle, \( \cosh x = K \) and \( \sinh x = \tan \theta \), then \( \sin \theta = \dots \)
If the general solution set of \( \sin x + 3 \sin 3x + \sin 5x = 0 \) is \( S \), then \[ \sin a \quad {for} \quad a \in S \quad {is} \quad \{ \sin a \mid a \in S \} = \]
For \( a \in \mathbb{R} \setminus \{0\} \), if \( a \cos x + a \sin x + a = 2K + 1 \) has a solution, then \( K \) lies in the interval:
If \( P + Q + R = \frac{\pi}{4} \), then \[ \cos \left( \frac{\pi}{8} - P \right) + \cos \left( \frac{\pi}{8} - Q \right) + \cos \left( \frac{\pi}{8} - R \right) = P + Q + R = \frac{\pi}{4}. \]
If \( \sin x + \sin y = \alpha \), \( \cos x + \cos y = \beta \), then \( \csc(x + y) \) =
Bag A contains 3 white and 4 red balls, bag B contains 4 white and 5 red balls, and bag C contains 5 white and 6 red balls. If one ball is drawn at random from each of these three bags, then the probability of getting one white and two red balls is:
If the period of the function \( f(x) = \frac{\tan 5x \cos 3x}{\sin 6x} \) is \( \alpha \), then find \( f \left( \frac{\alpha}{8} \right) \):
If \[ \frac{1}{(3x+1)(x-2)} = \frac{A}{3x+1} + \frac{B}{x-2} \quad {and} \quad \frac{x+1}{(3x+1)(x-2)} = \frac{C}{3x+1} + \frac{D}{x-2}, \] then \[ \frac{1}{(3x+1)(x-2)} = \frac{A}{3x+1} + \frac{B}{x-2}, { find } A + 3B = 0, A:C = 1:3, B:D = 2:3. \]