List of top Mathematics Questions asked in AP EAMCET

The length of the tangent drawn from the point $ \left(\frac{k}{4}, \frac{k}{3}\right) $ to the circle $ x^2 + y^2 + 8x - 6y - 24 = 0 $ is:

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} = $

If $ (a, b) $ is the stationary point of the curve $ y = 2x - x^2 $, then the area bounded by the curves $ y = 2x - x^2 $, $ y = x^2 - 2x $, and $ x = a $ is:

If the circles $ S = x^2 + y^2 - 14x + 6y + 33 = 0 $ and $ S' = x^2 + y^2 - a^2 = 0 $ (where $ a \in \mathbb{N} $) have 4 common tangents, then the possible number of values of $ a $ is:

A Circle S passes through the points of intersection of the circles $ x^2 + y^2 - 2x + 2y - 2 = 0 $ and $ x^2 + y^2 + 2x - 2y + 1 = 0 $. If the centre of this circle S lies on the line $ x - y + 6 = 0 $, then the radius of the circle S is:

The normal drawn at $ (1,1) $ to the circle $ x^2 + y^2 - 4x + 6y - 4 = 0 $ is:

If the circles $ x^2 + y^2 + 2ax + 2y - 8 = 0 $ and $ x^2 + y^2 - 2x + ay - 14 = 0 $ intersect orthogonally, then the distance between their centers is:

Find the equation of a line passing through the intersection of $ 3x + y - 4 = 0 $ and $ x - y = 0 $, and making a $ 45^\circ $ angle with $ x - 3y + 5 = 0 $.

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:

If the area of the circum-circle of the triangle formed by the line 2x + 5y + a = 0 and the positive coordinate axes is $\frac{29\pi}{4}$ sq. units, then |a| =

The equation of one side of an equilateral triangle is $ x + y = 2 $, and one vertex is $ (2,-1) $. The length of the side is:

The equation of a line which makes an angle of $ 45^\circ $ with each of the pair of lines \[ xy - x - y + 1 = 0 \] is:

If a variable straight line passing through the point of intersection of the lines x - 2y + 3 = 0 and 2x - y - 1 = 0 intersects the X and Y axes at A and B respectively, then the equation of the locus of a point which divides the segment AB in the ratio -2 : 3 is:

In a triangle ABC, if $ (r_1 + r_2) \csc^2 \frac{C}{2} = $

In $ \triangle ABC $, given: \[ a = 26, \quad b = 30, \quad \cos C = \frac{63}{65} \] Find $ c $.

If $ H $ is the orthocenter of $ \triangle ABC $ and $ AH = x $, $ BH = y $, $ CH = z $, then evaluate: \[ \frac{abc}{xyz} \]

In a triangle ABC, if $ r : R = 1 : 3 : 7 $, then $ \sin(A + C) + \sin B = $

If a running track of 500 ft. is to be laid out enclosing a playground, the shape of which is a rectangle with a semicircle at each end, then the length of the rectangular portion such that the area of the rectangular portion is maximum is (in feet).

In a triangle ABC, if $ a = 13, b = 14, c = 15 $, then $ r_1 = $

In $\Delta ABC$ if $B = 90^\circ$ then $2(r + R) = $

If the direction cosines of two lines are given by \[ l + m + n = 0 \quad \text{and} \quad mn - 2lm - 2nl = 0, \] then the acute angle between those lines is:

If the angle $ \theta $ between the line $ \frac{x + 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{2} $ and the plane $ 2x - y + \sqrt{\lambda}z + 4 = 0 $ is such that $ \sin \theta = \frac{1}{3} $, then the value of $ \lambda $ is: