List of top Mathematics Questions asked in AP EAPCET

The square of the slope of a common tangent to the circle \(4x^2 + 4y^2 = 25\) and ellipse \(4x^2 + 9y^2 = 36\) is
If \(\theta\) is the acute angle between the asymptotes of a hyperbola \(7x^2 - 9y^2 = 63\), then \(\cos \theta =\)
The tangents drawn to the hyperbola \(5x^2 - 9y^2 = 90\) through a variable point \(P\) make angles \(\alpha\) and \(\beta\) with its transverse axis. If \(\alpha\) and \(\beta\) are complementary angles, then the locus of \(P\) is
The angle between the tangents drawn from the point (2, 2) to the circle \(x^2 + y^2 + 4x + 4y + c = 0\) is \(\cos^{-1} \left( \frac{7}{16} \right)\). If two such circles exist, then the sum of values of \(c\) is
If (a, b) is the common point of the circles \(x^2 + y^2 - 4x + 4y - 1 = 0\) and \(x^2 + y^2 + 2x - 4y + 1 = 0\), then \(a^2 + b^2 =\)
If a circle S passes through the origin and makes intercept 4 units on line \(x = 2\), then the equation of curve on which center of S lies is
A line \(L\) passes through point \(P(1, 2)\) and makes an angle of \(60^\circ\) with OX in positive direction. A and B are points on line \(L\), 4 units from P. If O is origin, then area of \(\triangle OAB\) is
The equation \((2p - 3)x^2 + 2pxy - y^2 = 0\) represents a pair of distinct lines
The equation of chord AB of ellipse \(2x^2 + y^2 = 1\) is \(x - y + 1 = 0\). If O is the origin, then \(\angle AOB =\)
A circle touches the line \(2x + y - 10 = 0\) at (3, 4) and passes through the point (1, -2). Then a point that lies on the circle is
If the equation \(3x^2 + 4y^2 - xy + k = 0\) is the transformed equation of \(3x^2 + 4y^2 - xy - 5x - 7y + 2 = 0\) after shifting the origin to \((\alpha, \beta)\), then \(\alpha + \beta = k =\)
If the intercept of a line \(L\) made between the straight lines \(5x - y - 4 = 0\) and \(3x + 4y - 4 = 0\) is bisected at the point (1, 5), then the equation of \(L\) is
If \(P\) is a variable point which is at a distance of 2 units from the line \(2x - 3y + 1 = 0\) and \(\sqrt{13}\) units from the point (5, 6), then the equation of the locus of \(P\) is
Given \(f(x) = x^2 - 5x + 4\). Out of first 20 natural numbers, if a number \(x\) is chosen at random, then the probability that the chosen \(x\) satisfies the inequality \(f(x)>10\) is
Three dice are thrown simultaneously and the sum of the numbers is noted. If A = getting sum greater than 14 and B = getting sum divisible by 3, then \(P(A \cap B) + P(A \cup B) =\)
A manufacturing company has 3 units A, B, and C which produce 25%, 35%, 40% of bulbs respectively. 5%, 4%, and 2% of their production is defective. If a bulb is found defective, the probability it came from B is
A problem in Algebra is given to two students A and B whose chances of solving it are \(\dfrac{2}{5}\) and \(\dfrac{3}{5}\) respectively. The probability that the problem is solved if both try independently is
A student has probability \(\dfrac{2}{3}\) of getting distinction in a test. Out of 5 tests, the probability that he gets distinction in at least 3 tests is
Given the PMF: \(P(X=x) = \alpha\) for \(x = 1,2\), \(= \beta\) for \(x = 4,5\), and \(= 0.3\) for \(x = 3\), with mean \(\mu = 4.2\). Find \(\sigma^2 + \mu^2\)
In a triangle ABC, if \(r_1 = 3, r_2 = 4, r_3 = 6\), then \(b =\)
If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors and \(\vec{a} \perp \vec{b}\), and \((\vec{a} - \vec{c}) \cdot (\vec{b} + \vec{c}) = 0\), and \(\vec{c} = l\vec{a} + m\vec{b} + n(\vec{a} \times \vec{b})\), then \(n^2 =\)
If the points A, B, C, D with position vectors \(\vec{i} + \vec{j} - \vec{k}, -\vec{i} + 2\vec{k}, \vec{i} - 2\vec{j} + \vec{k}, 2\vec{i} + \vec{j} + \vec{k}\) form a tetrahedron, then angle between faces ABC and ABD is
The point of intersection of the lines represented by \(\vec{r} = (\hat{i} - 6\hat{j} + 2\hat{k}) + t(\hat{i} + 2\hat{j} + \hat{k})\) and \(\vec{r} = (4\hat{j} + \hat{k}) + s(2\hat{i} + \hat{j} + 2\hat{k})\) is
Let the position vectors of the vertices of triangle ABC be \(\vec{a}, \vec{b}, \vec{c}\). If a point \(P\) on the plane of triangle has a position vector \(\vec{r}\) such that \(\vec{r} - \vec{b} = \vec{a} - \vec{c}\) and \(\vec{r} - \vec{c} = \vec{a} - \vec{b}\), then \(P\) is the
If the variance of the first \(n\) natural numbers is 10 and the variance of the first \(m\) even natural numbers is 16, then \(n : m =\)