List of top Mathematics Questions asked in AP EAPCET

A plane meets the X, Y, Z -- axes in A, B, C respectively. If the centroid of the triangle ABC is \((2, -3, 5)\) then the perpendicular distance from origin to the given plane is
The length of the latus rectum of the parabola \( y^2-4x-4y+8=0 \) is
The eccentricity of the ellipse \( 9x^2+16y^2=144 \) is
If \( ax^2 - 34xy - 5y^2 + 2x + 26y - 5 = 0 \) represents a pair of straight lines, then the value of a is
The equations of the lines perpendicular to \(x^2 - 5xy + 4y^2 = 0\) and passing through (2, 1) is
Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are \(3x+4y-4=0\) and \((2,2)\) respectively. Then, which of the following is another side of the triangle?
A point P on a line is at a distance of 4 units from the origin (0, 0). If the line makes 60\(^\circ\) with the negative direction of the x-axis, then P is
A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from this bag. Then, the probability that the ball drawn is not red is
A person P speaks truth in 75% cases and another person R in 80% cases. Then the probability that they likely to contradict each other in narrating the same event is
If X is a Poisson random variate with mean 3, then \(P(|X-3|<2)\) =
A point P(x, y) is such that the sum of squares of its distances from (a, 0) and (--a, 0) is \(2b^2\). The equation representing the locus of P is
Let \( \vec{a} = \hat{i} + x\hat{j} + \hat{k} \), \( \vec{b} = \hat{i} - \hat{j} + \hat{k} \) and \( |\vec{a}+\vec{b}| = |\vec{a}| + |\vec{b}| \) then
If \( \vec{a} = \hat{i} + 2\hat{j} + 3\hat{k} \), \( \vec{b} = 2\hat{i} + 3\hat{j} + \hat{k} \), \( \vec{c} = 8\hat{i} + 13\hat{j} + 9\hat{k} \) and \( x\vec{a} + y\vec{b} + z\vec{c} = \vec{0} \), then \( \frac{xy}{z^2} = \)
The vector \( \vec{x} \) is perpendicular to the vectors \( \vec{a} = 3\hat{i} + 2\hat{j} + 2\hat{k} \), \( \vec{b} = 18\hat{i} - 22\hat{j} - 5\hat{k} \) and makes an obtuse angle with \( \hat{j} \). If \( |\vec{x}|=14 \), then \( \vec{x} = \)
The set of real values of \( \lambda \) for which the vectors \( \lambda\hat{i} - 3\hat{j} + 5\hat{k} \) and \( 2\lambda\hat{i} - \lambda\hat{j} + \hat{k} \) are perpendicular to each other is
\( \cos\theta (\csc\theta - \sec\theta) - \cot\theta = \)
Let ABC be an acute-angled triangle with area R. Then \( \sqrt{a^2b^2-4R^2} + \sqrt{b^2c^2-4R^2} + \sqrt{c^2a^2-4R^2} = \)
In a triangle ABC, if a = 4, b = 5 and c = 7, then \( \sin(A/2) = \)
\( \frac{x^3}{(x^2+1)(x^2+3)} = \)
The value of \( \sin(\frac{5\pi}{24}) \cdot \cos(\frac{\pi}{24}) \) is
\( \frac{\sin x}{1+\cos x} + \frac{1+\cos x}{\sin x} = \)
The sum of all possible numbers that can be formed by using the digits 2,3,5,7 without repetition of digits is
If \( {}^n P_r = {}^{n-1}P_r + x \cdot {}^{n-1}P_{r-1} \quad \forall n,r \in N \text{ and } r \le n \), then x = .
If \(\alpha, \beta\) are the roots of \(ax^2+bx+c=0\), then the quadratic equation whose roots are \( \sqrt{5}\alpha, \sqrt{5}\beta \) is
The English alphabets have 5 vowels and 21 consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?