List of top Mathematics Questions asked in AP EAPCET

A question paper has two sections A and B. Section A has 8 questions and Section B has 6 questions. A student has to answer 10 questions, choosing at least 4 from section A and at least 3 from section B. The number of ways the student can answer the paper is:
If 5 dice are rolled simultaneously, then the number of ways of getting a total of 7 from the numbers on their faces is:
If \( P(x) = 0 \) is a polynomial of least degree with integer coefficients and \( \sqrt{2} + \sqrt{3}i \) is one of its roots, then that equation is:
If \( -3 + ix^2y \) and \( x^2 + y + 4i \) are complex conjugates, then \( x = \):
If \( z = 1 + \cos\theta - i\sin\theta \) and \( 0<\theta<\pi \), then \[ \left[ |z - 1|^2 \cdot \frac{|z|^2}{4} \right]^{1/2} = \]
In the Argand plane, the values of \( z \) satisfying the equation \( |z - 1| = |i(z + 1)| \) lie on:
The sum of the fourth powers of the roots of the equation \( 16x^2 - 10x + 1 = 0 \) is:
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 \( f(x) = 3x + \frac{12}{x} \) is continuous on \( \mathbb{R} - \{0\} \) and \( M \) is its maximum value, then \( \displaystyle \lim_{x \to M} f(x) = \):
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:
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:
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: