List of top Questions asked in AP EAMCET- 2024

If the reflection of a point $ A(2,3) $ in the X-axis is $ B $; the reflection of $ B $ in the line $ x + y = 0 $ is $ C $ and the reflection of $ C $ in $ x - y = 0 $ is $ D $, then the point of intersection of the lines $ CD, AB $ is:

The area (in square units) of the triangle formed by the lines 6x² + 13xy + 6y² = 0 and x + 2y + 3 = 0 is:

The perpendicular distance from the point $ (-1,1,0) $ to the line joining the points $ (0,2,4) $ and $ (3,0,1) $ 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 = ?

Consider the point $ P(\alpha, \beta) $ on the line $ 2x + y = 1 $. If the points $ P $ and $ (3,2) $ are conjugate points with respect to the circle $ x^2 + y^2 = 4 $, then find $ \alpha + \beta $:

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 circle S = x² + y² − 2x − 4y + 1 = 0 cuts the y-axis at A, B (OA: OB). If the radical axis of S ≡ 0 and S′ = x² + y² − 4x − 2y + 4 = 0 cuts the y-axis at C, then the ratio in which C divides AB is:

If $ A = (1,2,3), B = (3,4,7) $ and $ C = (-3,-2,-5) $ are three points then the ratio in which the point C divides AB externally is

The locus of the point of intersection of perpendicular tangents drawn to the circle $ x^2 + y^2 = 10 $ is:

The angle subtended by the chord $ x + y - 1 = 0 $ of the circle $ x^2 + y^2 - 2x + 4y + 4 = 0 $ at the origin is:

A line $ L $ passes through $ (1,2,-3) $ and $ (3,3,-1) $, and a plane $ \pi $ passes through $ (2,1,-2), (-2,-3,6), (0,2,-1) $. If $ \theta $ is the angle between $ L $ and $ \pi $, then $ 27 \cos^2 \theta = $ ?

If $ (a, b) $ and $ (c, d) $ are the internal and external centres of similitude of the circles \[ x^2 + y^2 + 4x - 5 = 0 \] and \[ x^2 + y^2 - 6y + 8 = 0 \] respectively, then $ (a + d)(b + c) $ is:

The area of the triangle formed by the pair of lines $ 23x^2 - 48xy + 3y^2 = 0 $ with the line $ 2x + 3y + 5 = 0 $ is:

The equation $ 2x^2 - 3xy - 2y^2 = 0 $ represents two lines $ L_1 $ and $ L_2 $. The equation $ 2x^2 - 3xy - 2y^2 - x + 7y - 3 = 0 $ represents another two lines $ L_3 $ and $ L_4 $. Let $ A $ be the point of intersection of lines $ L_1 $ and $ L_3 $, and $ B $ be the point of intersection of lines $ L_2 $ and $ L_4 $. The area of the triangle formed by the lines $ AB $, $ L_3 $, and $ L_4 $ is: .

If the perpendicular distance from $ (1,2,4) $ to the plane $ 2x + 2y - z + k = 0 $ is 3, then $ k $ is:

The orthocentre of the triangle formed by lines $ x + y + 1 = 0 $, $ x - y - 1 = 0 $ and $ 3x + 4y + 5 = 0 $ is:

If $ (1,3) $ is the midpoint of a chord of the circle $ x^2 + y^2 - 4x - 8y + 16 = 0 $, then the area of the triangle formed by that chord with the coordinate axes is:

The triangle $ PQR $ is inscribed in the circle \[ x^2 + y^2 = 25. \] If $ Q = (3,4) $ and $ R = (-4,3) $, then $ \angle QPR $ is:

A line $ L $ passing through the point $ P(-5,-4) $ cuts the lines $ x - y - 5 = 0 $ and $ x + 3y + 2 = 0 $ respectively at $ Q $ and $ R $ such that \[ \frac{18}{PQ} + \frac{15}{PR} = 2, \] then the slope of the line $ L $ is:

If the lines $ 3x+y-4=0 $, $ x - \alpha y + 10 = 0 $, $ \beta x + 2y + 4 = 0 $ and $ 3x + y + k = 0 $ represent the sides of a square, then find $ \alpha \beta (k+4)^2 $.

Point (-1, 2) is changed to (a, b) when the origin is shifted to the point (2, -1) by translation of axes. Point (a, b) is changed to (c, d) when the axes are rotated through an angle of 45$^{\circ}$ about the new origin. (c, d) is changed to (e, f) when (c, d) is reflected through y = x. Then (e, f) = ?

The transformed equation of $ x^2 - y^2 + 2x + 4y = 0 $ when the origin is shifted to the point $ (-1,2) $ is:

If the coordinate axes are rotated by $ 45^\circ $ about the origin in the counterclockwise direction, then the transformed equation of $ y^2 = 4ax $ is:

The combined equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve $ x^2 + y^2 + xy + x + 3y + 1 = 0 $ and the line $ x + y + 2 = 0 $ is:

If the line through the point $ P(5,3) $ meets the circle $ x^2 + y^2 - 2x - 4y + \alpha = 0 $ at $ A(4, 2) $ and $ B(x_1, y_1) $, then $ PA \times PB = $: