List of top Mathematics Questions asked in AP EAPCET

If a straight line \( L \) perpendicular to the line \( 3x - 4y = 6 \) forms a triangle of area 6 square units with coordinate axes, then the minimum perpendicular distance from the point \( (1,1) \) to the line \( L \) is:
Let \( a, b, c, d \) be non-zero numbers. If the point of intersection of the lines \( 4ax + 2ay + c = 0 \) and \( 5bx + 2by + d = 0 \) lies in the fourth quadrant and is equidistant from the two coordinate axes, then the relationship between \( a, b, c, d \) is:
If the image of the point \( (3, 8) \) in the line \( x + 3y = 7 \) is \( (\alpha, \beta) \), then \( \alpha + \beta = \)
The condition that the lines joining the origin to the points of intersection of the line \( \frac{x}{a} + \frac{y}{b} = 2 \) and the circle \( (x - a)^2 + (y - b)^2 = r^2 \) are at right angles is:
The square of the distance from the origin to the point of intersection of the pair of lines \( ax^2 + 2hxy - ay^2 + 2gx + 2fy + c = 0 \) is:
If a cubical die is thrown, then the mean and variance of the random variable \( X \), giving the number on the face that shows up, are respectively:
Students of two sections A and B of a class show the following results in a test conducted for 100 marks. Then, the comparison of variability between Section A and Section B is:
Students of two sections A and B of
If the vectors \( \vec{a} = 2\vec{i} + 3\vec{j} - \vec{k} \), \( \vec{b} = 4\vec{i} - \vec{j} + 3\vec{k} \), and \( \vec{c} = p\vec{i} + \vec{j} - \vec{k} \) are coplanar, then: \[ |\vec{a} \times \vec{c}| = ? \]
A bag contains 12 two rupee coins, 7 one rupee coins and 4 fifty paise coins. If three coins are selected at random, then the probability that the sum of the values of the three coins is not an integral multiple of a rupee is
If \( A \) and \( B \) are any two events of a random experiment and \( P(B) \neq 1 \), then: \[ P(A|B^C) = ? \]
A bag contains 10 similar balls, of which 4 are blue and 6 are red. Three balls are taken at random from the bag one after the other without replacement. The probability that all the three balls drawn are red is:
If A and B are among 20 persons who sit at random along a round table, then the probability that there are exactly six persons between A and B is:
It is observed that there will be 25 blood specimens of normal persons, if 100 blood samples are tested. If 10 specimens are sent to a laboratory for testing, then the probability of having at least two specimens of normal persons is:
Let \( x \) be a real number and \( -2<x<2 \). When \( \frac{x+1}{(x+3)(x-2)} \) is expanded in powers of \( x \), then the coefficient of \( x^3 \) is:
In \( \triangle ABC \), if \( (\sin A + \sin B)(\sin A - \sin B) = \sin C(\sin B + \sin C) \), then \( \angle A = \)
In \( \triangle ABC \), if \( A, B, C \) are in arithmetic progression, then \( \frac{c}{a} \sin 2A + \frac{a}{c} \sin 2C = \):
If \( \vec{a} = t\vec{b} \) where \( t<0 \) is a scalar, then:
Let \( \vec{a}, \vec{b}, \vec{c} \) be coinitial vectors and \( \vec{a} = 2\hat{i} - \hat{j} + 5\hat{k}, \vec{b} = 3\hat{i} + 7\hat{j} - \hat{k} \). If \( \cos(\theta) = 0 \), where \( \theta \) is the angle between \( \vec{a} \) and \( \vec{b} \), and \( \vec{c} \) is the vector along the bisector of the angle \( \angle ABC \), then the vector \( \mathbf{c} \) is:
If \( \vec{a} = 2\hat{i} - 5\hat{j} + 8\hat{k} \), \( \vec{b} = 7\hat{i} - 5\hat{j} + 3\hat{k} \), and \[ (\vec{2a} - \vec{3b}) \times (\vec{4a} + \vec{b}) = x\hat{i} + y\hat{j} + z\hat{k}, \] then \( x + y + z = \)
If \( \vec{a} \) and \( \vec{b} \) are two unit vectors with \( (\vec{a}, \vec{b}) = 0 \) and \( |\vec{a} - \vec{b}| = 1 \), then: \[ 2|\vec{a} + \vec{b}| \cos\theta = \frac{2}{|\vec{a} + \vec{b}| \cos\theta} \]
Evaluate: \( (1 + \cos\frac{\pi}{8})(1 + \cos\frac{2\pi}{8})(1 + \cos\frac{3\pi}{8}) \ldots (1 + \cos\frac{7\pi}{8}) = \)
If \( \cos\theta \), \( \sin\theta \), and \( \cot\theta \) are in geometric progression, then: \[ \sin^9\theta + \sin^6\theta + 3\sin^5\theta + \sin^3\theta + \sin^2\theta = \]
If \(3\sin^4 x + 2\cos^4 x = \frac{6}{5}\) and \(x\) is an acute angle, then \(\tan 2x =\)
If \( f_n(x) = \frac{1}{2n} \left[ \sin^{2n}x + \cos^{2n}x \right] \), then \( f_1(x) + f_2(x) - f_3(x) = \):
If \( \cosh x = \csc\theta \), then \( \coth^2\left(\frac{x}{2}\right) = \):