List of top Mathematics Questions asked in AP EAMCET

If $ O(0, 0, 0), A(3, 0, 0), B(0, 4, 0) $ form a triangle then the incenter of triangle OAB is:

Suppose the axes are to be rotated through an angle $ \theta $ so as to remove the $ xy $ term from the equation $3 x^2 + 2\sqrt{3}xy + y^2 = 0 $. Then in the new coordinate system, the equation $ x^2 + y^2 + 2xy = 2 $ is transformed to:

If $540^\circ<A<630^\circ$ and $|\cos A| = \frac{5}{13}$, then $ \tan\frac{A}{2} \tan A =$

Evaluate the integral: \[ I = \int_{-5\pi}^{5\pi} \left(1 - \cos 2x \right)^{\frac{5}{2}} dx. \]

The area of the region enclosed by the curves \[ 3x^2 - y^2 - 2xy + 4x + 1 = 0 \] and \[ 3x^2 - y^2 - 2xy + 6x + 2y = 0 \] is:

If the roots of the equation $x^3 + ax^2 + bx + c = 0$ are in arithmetic progression, then:

If $ \frac{3 - 2i \sin \theta}{1 + 2i \sin \theta}$ is a purely imaginary number, then $ \theta $ is:

The differential equation of the family of hyperbolas having their centers at origin and their axes along the coordinate axes is:

Find the differential equation representing the family of circles having their centers on the Y-axis. Given that $ y_1 = \frac{dy}{dx} $ and $ y_2 = \frac{d^2y}{dx^2} $.

The point (a, b) is the foot of the perpendicular drawn from the point (3, 1) to the line x + 3y + 4 = 0. If (p, q) is the image of (a, b) with respect to the line 3x - 4y + 11 = 0, then $\frac{p}{a} + \frac{q}{b} = $

Evaluate the limit: \[ \lim\limits_{x \to 2} \frac{\sqrt{1 + 4x} - \sqrt{3} + 3x}{x^3 - 8}. \]

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:

The angle between the line with the direction ratios $ (2, 5, 1) $ and the plane $ 8x + 2y - z = 4 $ is given by

If the coefficients of the $ r^{th} $, $ (r+1)^{th $, and $ (r+2)^{th} $ terms in the expansion of $ (1 + x)^n $ are in the ratio $ 4:15:42 $, then $ n - r $ is:}

A ray of light passing through the point (2, 3) reflects on the Y-axis at a point P. If the reflected ray passes through the point (3, 2) and P = (a, b), then 5b = ?

Let P be any point on the circle x² + y² = 25. Let L be the chord of contact of P with respect to the circle x^2 + y^2 = 9. The locus of the poles of the lines L with respect to the circle x² + y² = 36 is:

The foot of the perpendicular drawn from a point $ A(1,1,1) $ onto a plane $ \pi $ is $ P(-3,3,5) $. If the equation of the plane parallel to the plane $ \pi $ and passing through the midpoint of $ AP $ is \[ ax - y + cz + d = 0, \] then $ a + c - d $ is:

If the circle S = 0 cuts the circles x² + y² - 2x + 6y = 0, x² + y² - 4x - 2y + 6 = 0, and x² + y² - 12x + 2y + 3 = 0 orthogonally, then the equation of the tangent at (0, 3) on S = 0 is:

The locus of a variable point which forms a triangle of fixed area with two fixed points is:

If the area of the triangle formed by the straight lines $-15x^2 + 4xy + 4y^2 = 0$ and $x = a$ is $200 \, {sq. units}$, then $|a| =$

If $ \alpha, \beta $ ($\alpha<\beta$) are the values of $ x $ such that the determinant of the matrix \[ \begin{bmatrix} x - 2 & 0 & 1 \\ 1 & x + 3 & 2 \\ 2 & 0 & 2x - 1 \end{bmatrix} \] is zero (i.e., the matrix is singular), then the value of $ 2\alpha + 3\beta + 4\gamma $ is:

If $ A = \begin{bmatrix} 2 & 3 \\ 1 & k \end{bmatrix} $ is a singular matrix, then the quadratic equation having the roots $ k $ and $ \frac{1}{k} $ is:

If the mean deviation about the mean is $m$ and the variance is $\sigma^2$ for the following data, then $m + \sigma^2 =$ % Data table \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 7 & 9 \\ \hline f & 4 & 24 & 28 & 16 & 8 \\ \hline \end{array} \]

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:

In $ \triangle ABC $, if $ AB:BC:CA = 6:4.5 $, then $ R : r = $