List of top Questions asked in AP EAPCET

A parabola having its axis parallel to the Y-axis passes through the points \(\left(0, \frac{2}{5}\right)\), \((4, -2)\), and \(\left(1, \frac{8}{5}\right)\). Then the point that lies on this parabola is:
Let the eccentricity of the ellipse \(2x^2 + ay^2 - 8x - 2ay + (8 - a) = 0\) be \(\frac{1}{\sqrt{3}}\). If the major axis of this ellipse is parallel to the Y-axis, then the equation of the tangent to this ellipse with slope 1 is:
The equation of the pair of asymptotes of the hyperbola \(\frac{(x - 3)^2}{3} - \frac{(y - 2)^2}{2} = 1\) is:
If A and B are the points of intersection of the circles \( x^2 + y^2 - 4x + 6y - 3 = 0 \) and \( x^2 + y^2 + 2x - 2y - 2 = 0 \), then the distance between A and B is:
Let \( S = 0 \) be the circle passing through the points \((2, 0)\), \((1, -2)\), and \((-1, 1)\). Then the point \((1, 2)\):
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:
If the image of the point \( (3, 8) \) in the line \( x + 3y = 7 \) is \( (\alpha, \beta) \), then \( \alpha + \beta = \)
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:
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:
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: \[ |\vec{a} \times \vec{c}| = ? \]
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
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:
If \( \vec{a} \) and \( \vec{b} \) are two unit vectors with \( (\vec{a}, \vec{b}) = 0 \) and \( |\vec{a} - \vec{b}| = 1 \), then: \[ 2|\vec{a} + \vec{b}| \cos\theta = \frac{2}{|\vec{a} + \vec{b}| \cos\theta} \]
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:
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 \(3\sin^4 x + 2\cos^4 x = \frac{6}{5}\) 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 \( \coth^2\left(\frac{x}{2}\right) = \):
A question paper has two sections A and B. Section A has 8 questions and Section B has 6 questions. A student has to answer 10 questions, choosing at least 4 from section A and at least 3 from section B. The number of ways the student can answer the paper is:
If 5 dice are rolled simultaneously, then the number of ways of getting a total of 7 from the numbers on their faces is:
If \( P(x) = 0 \) is a polynomial of least degree with integer coefficients and \( \sqrt{2} + \sqrt{3}i \) is one of its roots, then that equation is:
The sum of the fourth powers of the roots of the equation \( 16x^2 - 10x + 1 = 0 \) is: