List of top Mathematics Questions asked in AP EAPCET

If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 + ax^2 + bx + c = 0 \), then \( (\alpha + \beta - 2\gamma)(\beta + \gamma - 2\alpha)(\gamma + \alpha - 2\beta) = \)
If the roots of the equation \[ x^3 + p x^2 + q x + r = 0 \] are in arithmetic progression, then which of the following is always true?
In a triangle \(ABC\), if \(r_1 : r_2 = 3 : 4\) and \(r_1 : r_3 = 2 : 3\), then find the ratio \(a : b : c\).
The equation \[ x^{\frac{3}{4}(\log_{x} x)^2 + \log_{x} x^{-\frac{5}{4}}} = \sqrt{2} \] has
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $5x^3 - 4x^2 + 3x - 2 = 0$, then $\alpha^3 + \beta^3 + \gamma^3$ equals
If \( \sinh^{-1}(2) + \sinh^{-1}(3) = \alpha \), then \( \sinh\alpha = \) ?
If the axes are translated to the orthocentre of the triangle formed by points \(A(7,5), B(-5,-7), C(7,-7)\), then the coordinates of the incentre of the triangle in the new system are?
If \(A(\cos \alpha, \sin \alpha)\), \(B(\sin \alpha, -\cos \alpha)\), and \(C(1, 2)\) are the vertices of \(\triangle ABC\), then find the locus of its centroid.
When the axes are rotated through an angle \( \theta \) about the origin in the anticlockwise direction and then translated to the new origin (2, -2), if the transformed equation of \( x^2+y^2=4 \) is \( X^2+Y^2+aX+bY+c=0 \), then \( a+b+c= \):
Let \( A(5,4) \) and \( B(5,-4) \) be two points. If \( P \) is a point in the coordinate plane such that \( |APB| = \frac{\pi}{4} \), then the point \( P \) lies on the curve:
The transformed equation of \( 3x^2 - 4xy = r^2 \) when the coordinate axes are rotated about the origin through an angle of \( \tan^{-1}(2) \) in positive direction is
If \( \text{sech}^{-1}x = \log 2 \) and \( \text{cosech}^{-1}y = -\log 3 \), then \( (x+y) = \)
When the axes are rotated through an angle \( \theta \) about the origin in the anticlockwise direction and then translated to the new origin (2, -2), if the transformed equation of \( x^2+y^2=4 \) is \( X^2+Y^2+aX+bY+c=0 \), then \( a+b+c= \):
Evaluate: \(\tanh^{-1}\left(\frac{1}{3}\right) + \coth^{-1}(3) =\)
Let \( A(5,4) \) and \( B(5,-4) \) be two points. If \( P \) is a point in the coordinate plane such that \( |APB| = \frac{\pi}{4} \), then the point \( P \) lies on the curve:
If the equation \(3x^2 + 4y^2 - xy + k = 0\) is the transformed equation of \(3x^2 + 4y^2 - xy - 5x - 7y + 2 = 0\) after shifting the origin to \((\alpha, \beta)\), then \(\alpha + \beta = k =\)
In \( \triangle ABC \), if \( r = 3 \) and \( R = 5 \) then \( \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} = \)
In \(\triangle ABC\), if \(a : b : c = 4 : 5 : 6\), then \( \dfrac{\cos A + 3 \cos C}{\cos B} = \)
If \(P\) is a variable point which is at a distance of 2 units from the line \(2x - 3y + 1 = 0\) and \(\sqrt{13}\) units from the point (5, 6), then the equation of the locus of \(P\) is
If A(1,0), B(0,-2), C(2,-1) are three fixed points, then the equation of the locus of a point P such that area of \( \triangle \text{PAB} \) is equal to area of \( \triangle \text{PAC} \) is
Domain of the real-valued function \(f(x) = \log(x^2 - 1) + x \, \coth^{-1}x\) is
The coordinate axes are rotated about the origin in the counterclockwise direction through an angle \( 60^\circ \). If \( a \) and \( b \) are the intercepts made on the new axes by a straight line whose equation referred to the original axes is \( x + y = 1 \), then \( \dfrac{1}{a^2} + \dfrac{1}{b^2} = \, ? \)
In \( \triangle ABC \), if \( r = 3 \) and \( R = 5 \) then \( \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} = \)
If the distance of a variable point \(P\) from a point \(A(2,-2)\) is twice the distance of \(P\) from the Y-axis, then the equation of locus of \(P\) is:
If A(1,0), B(0,-2), C(2,-1) are three fixed points, then the equation of the locus of a point P such that area of \( \triangle \text{PAB} \) is equal to area of \( \triangle \text{PAC} \) is