List of top Mathematics Questions asked in AP EAMCET

The normal drawn at a point \( (2, -4) \) on the parabola \( y^2 = 8x \) cuts again the same parabola at \( (\alpha, \beta) \). Then \( \alpha + \beta \) is:
The interval containing all the real values of \( x \) such that the real valued function \[ f(x) = \sqrt{x} + \frac{1}{\sqrt{x}} \] is strictly increasing is:
The general solution of \( 2 \cos^2 x - 2 \tan x + 1 = 0 \) is:
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:
Evaluate the expression \[ 2 \cot h^{-1}(4) + \sec h^{-1}\left( \frac{3}{5} \right). \]
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 \( (a, \beta) \) is the orthocenter of the triangle with the vertices \( A(2, 5), B(1, 5), C(1, 4) \), then \( a + \beta = \):

For real values of $ x $ and $ a $, if the expression $ \frac{x+a}{2x^2 - 3x + 1} $ assumes all real values, then:

If the pair of lines represented by \[ 3x^2 - 5xy + P y^2 = 0 \] and \[ 6x^2 - xy - 5y^2 = 0 \] have one line in common, then the sum of all possible values of \( P \) is:
If \( a \) is a rational number, then the roots of the equation \( x^2 - 3ax + a^2 - 2a - 4 = 0 \) are:
Evaluate the integral $$ I = \int_1^5 \left( |x - 3| + |1 - x| \right) \, dx $$
If \( x \) is real and \( \alpha, \beta \) are maximum and minimum values of \( \frac{x^2 - x + 1}{x^2 + x + 1} \) respectively, then \( \alpha + \beta = \):
Simplify the expression: \( 4 + \frac{1}{4 + \frac{1}{4 + \frac{1}{4 + \cdots}}} \)
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: .
Equation of the line touching both parabolas \( y^2 = 4x \) and \( x^2 = -32y \) 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:
tan 9$^\circ$ - tan 27$^\circ$ - tan 63$^\circ$ + tan 81$^\circ$ =
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 vectors \[ \mathbf{a} = 2i - j + k, \quad \mathbf{b} = i + 2j - 3k, \quad \mathbf{c} = 3i + pj + 5k \] are coplanar, find \( p \).
Evaluate the integral \( \int \frac{\sin^{-1} \left(\frac{x}{\sqrt{a + x}}\right) \sqrt{a + x}}{dx} \):
If \( P \) is the greatest divisor of \( 49^n + 16n - 1 \) for all \( n \in \mathbb{N} \), then the number of factors of \( P \) is:
If $\alpha_1, \alpha_2, \alpha_3, \alpha_4, \alpha_5$ are the roots of the equation $$ x^5 - 5x^4 + 9x^3 - 9x^2 + 5x - 1 = 0, $$ then find the value of $$ \frac{1}{\alpha_1^2} + \frac{1}{\alpha_2^2} + \frac{1}{\alpha_3^2} + \frac{1}{\alpha_4^2} + \frac{1}{\alpha_5^2}. $$
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 \[ \sin(2\alpha + \beta) = \]
For \( a \in \mathbb{R} \setminus \{0\} \), if \( a \cos x + a \sin x + a = 2K + 1 \) has a solution, then \( K \) lies in the interval:
The equation \( x^4 - x^3 - 6x^2 + 4x + 8 = 0 \) has two equal roots. If \( \alpha, \beta \) are the other two roots of this equation, then \( \alpha^2 + \beta^2 = \):