List of top Mathematics Questions asked in AP EAPCET

In the Argand plane, the values of \( z \) satisfying the equation \( |z - 1| = |i(z + 1)| \) lie on:
If \( A = \begin{bmatrix} 2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2 \end{bmatrix} \) is expressed as a sum of a symmetric matrix \( P \) and a skew-symmetric matrix \( Q \), then \( P^T - Q^T \) equals:
If \( f : \mathbb{R} \setminus \{0\} \to \mathbb{R} \) is defined by \( f(x) = x + \frac{1}{x} \), then the value of \( \left(f(x)\right)^2 \) is:
If \( y = y(x) \) is the solution of the differential equation \[ x \frac{dy}{dx} = y + xe^{-\frac{y}{x}}, \quad y(1) = \log e \] , then \( y(e) = \)
If \[ f(x) = \lim_{n \to \infty} n^2 \left( \frac{1}{x^n} - \frac{1}{x^{n+1}} \right), x>0, \] then \[ \int x f(x) \, dx = ? \]
Evaluate the following integral: \[ \int \frac{1 - \cos x}{\cos x(1 + \cos x)} \, dx \]
If \( g(x) \) is an antiderivative of \( f(x) = 1 + 2 \log 2 \) and the graph of \( y = g(x) \) passes through the point \( \left( -1, -\frac{1}{2} \right) \), then the curve meets the Y-axis at
The area bounded by the curves \( y = x^2 \) and \( y - 6 = -|x| \) is:
If \( \theta \) is the angle made by the normal drawn to the curve \[ x = e^t \cos t, \quad y = e^t \sin t \] at the point \( (1, 0) \) with the X-axis, then \( \theta = \):
If a normal drawn at a point \( P \) to the curve \( y = \sin x \) passes through the origin, then the locus of \( P \) is:
An extreme value of \( f(x) = \frac{4}{\sin x} + \frac{1}{1 - \sin x} \) in \( (0, \frac{\pi}{2}) \) is:
If the tangent drawn to the curve \( y = x^3 \) at point \( (\alpha, \beta) \) cuts again the curve at another point \( (\alpha_1, \beta_1) \), then \( \frac{\beta_1}{\beta} = \):
Evaluate the integral \[ \int \frac{dx}{(2ax + x^2)^{3/2}} \]
If a normal drawn to the ellipse \[ \frac{x^2}{4} + \frac{y^2}{3} = 1 \] touches the hyperbola \[ \frac{x^2}{4} - \frac{y^2}{3} = 1, \] then the square of the slope of that normal is:
If \( f(x) = 3x + \frac{12}{x} \) is continuous on \( \mathbb{R} - \{0\} \) and \( M \) is its maximum value, then \( \displaystyle \lim_{x \to M} f(x) = \):
Let \( \ell \) be the directrix of the parabola \( 9y^2 + 12y + 9x - 14 = 0 \), and \( \ell_1 \) be the line passing through the vertex of this parabola and the origin. If \( (h, k) \) is the point of intersection of \( \ell \) and \( \ell_1 \), then \( h + k = \):
Let the point \( L \) lying in the first quadrant be one end of a latus rectum of the ellipse \[ \frac{x^2}{4} + \frac{y^2}{3} = 1 \] Let \( P \) and \( Q \) be the points where the normal drawn at \( L \) meets the major and minor axes. Then the distance between \( P \) and \( Q \) is:
Let X-axis be the transverse axis and Y-axis be the conjugate axis of a hyperbola \( H \). Let the eccentricity of \( H \) be the reciprocal of the eccentricity of the ellipse \[ \frac{x^2}{4} + \frac{y^2}{2} = 1 \] If \( (5, 4) \) lies on \( H \), then the length of the transverse axis is:
The distance of the origin from the external centre of similitude for the circles \[ x^2 + y^2 - 8x - 10y - 8 = 0 \quad \text{and} \quad x^2 + y^2 + 2x - 2y - 2 = 0 \] is:
The equation of the line common to the pair of lines \[ (p^2 - q^2)x^2 + (q^2 - r^2)xy + (r^2 - p^2)y^2 = 0 \] and \[ (l - m)x^2 + (m - n)xy + (n - l)y^2 = 0 \] is:
If \( A(2, 3, 5), B(\alpha, 3, 3), C(7, 5, \beta) \) are the vertices of a triangle. If the median through \( A \) is equally inclined with the coordinate axes, then \( \frac{\beta}{\alpha} = \):
Let the locus of the point of intersection of the perpendicular tangents drawn to the circle \[ x^2 + y^2 + 6x - 4y - 12 = 0 \] be the circle \( S \). Then the equation of the tangent drawn to \( S \) which is perpendicular to the line \( 6x - 4y + k = 0 \) is:
The equation of the plane passing through the point \( (1, 2, 2) \) and perpendicular to the planes \[ x - y + 2z = 3 \quad \text{and} \quad 2x - 2y + z + 12 = 0 \] is:
In \( \triangle ABC \), if the midpoints of the sides \( AB, BC, CA \) are respectively \( (l, 0, 0), (0, m, 0), (0, 0, n) \), then: \[ \frac{AB^2 + BC^2 + CA^2}{l^2 + m^2 + n^2} = ? \]
The lines \( L_1: y - x = 0 \) and \( L_2: 2x + y = 0 \) intersect the line \( L_3: y + 2 = 0 \) at points \( P \) and \( Q \) respectively. The bisector of the acute angle between \( L_1 \) and \( L_2 \) intersects \( L_3 \) at \( R \). Statement-1: \( PR : RQ = 2\sqrt{2} : \sqrt{5} \) Statement-2: In any triangle, the bisector of an angle divides the triangle into two similar triangles.