List of top Mathematics Questions asked in AP EAMCET

The set of all real values of \( c \) for which the equation \[ zz' + (4 - 3i)z + (4+3i)z + c = 0 \] represents a circle is:

Let \( T_1 \) be the tangent drawn at a point \( P(\sqrt{2}, \sqrt{3}) \) on the ellipse \( \frac{x^2}{4} + \frac{y^2}{6} = 1 \). If \( (a, \beta) \) is the point where \( T_1 \) intersects another tangent \( T_2 \) to the ellipse perpendicularly, then \( a^2 + \beta^2 = \):

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 \( \alpha + \beta \):

Evaluate the integral \( \int \frac{dx}{\sqrt{\sin^3 x \cdot \cos (x - \alpha)}} \):

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 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:

In a triangle, if the angles are in the ratio \( 3:2:1 \), then the ratio of its sides is:

The real valued function \( f: \mathbb{R} \to \left[ \frac{5}{2}, \infty \right) \) defined by \( f(x) = \left| 2x + 1 \right| + \left| x - 2 \right| \) is:

The rate of change of \( x^{\sin x} \) with respect to \( (\sin x)^x \) is:

If the period of the function \( f(x) = \frac{\tan 5x \cos 3x}{\sin 6x} \) is \( \alpha \), then find \( f \left( \frac{\alpha}{8} \right) \):

If \[ \cos \alpha + 4 \cos \beta + 9 \cos \gamma = 0 \quad \text{and} \quad \sin \alpha + 4 \sin \beta + 9 \sin \gamma = 0, \] then \[ 81 \cos (2\gamma - 2\alpha) - 16 \cos (2\beta - 2\alpha) = ? \]

If \( \omega \) is the cube root of unity, then: \[ \frac{a + b\omega + c\omega^2}{c + a\omega + b\omega^2} = \frac{a + b\omega + c\omega^2}{b + c\omega + a\omega^2} \]

If the slope of one of the pair of lines represented by \( 2x^2 + 3xy + Ky^2 = 0 \) is 2, then the angle between the pair of lines is:

If \( a \) is in the 3rd quadrant, \( \beta \) is in the 2nd quadrant such that \( \tan \alpha = \frac{1}{7}, \sin \beta = \frac{1}{\sqrt{10}} \), then \[ \sin(2\alpha + \beta) = \]

If the matrix is:
\(\left| \begin{array}{ccc} a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c \end{array} \right|>0, \text{ then } abc>?\)

Evaluate the expression: \[ \sin^2 76^\circ + \sin^2 16^\circ - \sin 76^\circ \sin 16^\circ \]

If \( \alpha, \beta, \gamma \) are the roots of the determinant equation: \[ \begin{vmatrix} 1-x & -2 & 1
-2 & 4-x & -2
1 & -2 & 1-x \end{vmatrix} = 0 \] then \( \alpha \beta + \beta \gamma + \gamma \alpha \) is:

For \(|x|<\frac{1}{\sqrt{2}}\) the coefficient of \(x\) in the expansion of \(\frac{(1-4x)^2(1-2x^2)^{1/2}}{(4-x)^{3/2}}\) is

Find the general solution of the differential equation \( ( \sin y \cos^2 y - x \sec^2 y ) dy = (\tan y) dx \).

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:

If \( P \) is a point which divides the line segment joining the focus of the parabola \( y^2 = 12x \) and a point on the parabola in the ratio 1:2, then the locus of \( P \) is:

The set of all real values of \(x\) satisfying the inequality \(\frac{7x^2 - 5x - 18}{2x^2 + x - 6}<2\) is

Equation of the line touching both parabolas \( y^2 = 4x \) and \( x^2 = -32y \) is:

If \( y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \cdots \infty}}} \), then the value of \( \frac{d^2y}{dx^2} \) at \( (\pi,1) \) is: