List of top Mathematics Questions asked in AP EAPCET

If $I = \int_{1}^{3} \sqrt{3 + x + x^2} dx$, then $I$ lies in the interval
Let \( n \in (0, \infty) \). If for all the curves \( y = x^n \log x \) for distinct values of \( n \), we have \( y = x - 1 \) as the tangent at a fixed point \((\alpha, \beta)\), then \(\alpha + \beta = \):
The equation of the normal to the curve \( y = \cosh x \) drawn at the point nearest to the origin is:
If \( f(x) \) is a function such that \( f'(x) = \sqrt{f^2(x) - 1} \) and \( f(0) = 1 \), then \( f(1) = \):
If \(\int \frac{dx}{1 + \sin x} = \tan \left( \frac{x}{2} - \theta \right) + C\), then \(\theta =\):
\(A(-2, 9)\) and \(B(1, 6)\) are two points on the curve \(y = x^2 + 5\). The coordinates of the point \(C\) on the curve such that the tangent drawn at \(A\) is parallel to the chord \(BC\) is:
If all the normals drawn to the curve \( y = \frac{1 + 3x^2}{3 + x^2} \) at the points of intersection of \( y = \frac{1 + 3x^2}{3 + x^2} \) and \( y = 1 \) pass through the point \( (\alpha, \beta) \), then \( 3\alpha + 2\beta = \):
Let \( S_n = 1 + 3x + 9x^2 + 27x^3 + \ldots + n \text{ terms} -\frac{1}{3}<x<\frac{1}{3} \). If \( f(x) = S_n \), then \( f(x) \) is discontinuous at the point \( x = \):
The locus of the point on the curve \( y = \sin x \) where the tangent drawn at that point always passes through the point \( (0, \pi) \) is:
Let \([ \cdot ]\) denote the greatest integer function.
Assertion (A): \(\lim_{x \to \infty} \frac{[x]}{x} = 1\)
Reason (R): \(f(x) = x - 1\), \(g(x) = [x]\), \(h(x) = x\) and \(\lim_{x \to \infty} \frac{f(x)}{x} = \lim_{x \to \infty} \frac{h(x)}{x} = 1\):
\( f(x) \) and \( g(x) \) are differentiable functions such that \( \frac{f(x)}{g(x)} = \) a non-zero constant. If \( \frac{f'(x)}{g'(x)} = \alpha(x) \) and \( \left( \frac{f(x)}{g(x)} \right)' = \beta(x) \), then \( \frac{\alpha(x) - \beta(x)}{\alpha(x) + \beta(x)} = \):
Let X-axis be the transverse axis and Y-axis be the conjugate axis of a hyperbola H. Let \( x^2 + y^2 = 16 \) be the director circle of H. If the perpendicular distance from the centre of H to its latus rectum is \( \sqrt{34} \), then \( a + b = \):
A parabola having its axis parallel to the Y-axis passes through the points \(\left(0, \frac{2}{5}\right)\), \((4, -2)\), and \(\left(1, \frac{8}{5}\right)\). Then the point that lies on this parabola is:
Let the eccentricity of the ellipse \(2x^2 + ay^2 - 8x - 2ay + (8 - a) = 0\) be \(\frac{1}{\sqrt{3}}\). If the major axis of this ellipse is parallel to the Y-axis, then the equation of the tangent to this ellipse with slope 1 is:
The equation of the pair of asymptotes of the hyperbola \(\frac{(x - 3)^2}{3} - \frac{(y - 2)^2}{2} = 1\) is:
\( \lim_{x \to -9} \frac{(2.5)^{81 - x^2} - (0.4)^{x + 9}}{x + 9} = \)
If the chord of contact of the point \( P(1, 1) \) with respect to the circle \( S = x^2 + y^2 + 4x + 6y - 3 = 0 \) meet the circle \( S = 0 \) at A and B, then the area of \( \triangle PAB \) is:
If A and B are the points of intersection of the circles \( x^2 + y^2 - 4x + 6y - 3 = 0 \) and \( x^2 + y^2 + 2x - 2y - 2 = 0 \), then the distance between A and B is:
If the points \( (k, 1, 5), (1, 0, 3), (7, -2, m) \) are collinear, then \( (k, m) = \)
If a line \( L \) makes angles \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) with the positive X-axis and positive Y-axis respectively, then the angle made by \( L \) with the positive direction of the Z-axis is:
The equation of a plane passing through \( (-1, 2, 3) \) and whose normal makes equal angles with the coordinate axes is:
Let \( S = 0 \) be the circle passing through the points \((2, 0)\), \((1, -2)\), and \((-1, 1)\). Then the point \((1, 2)\):
If the acute angle between the pair of tangents drawn from the origin to the circle \( x^2 + y^2 - 4x - 8y + 4 = 0 \) is \( \alpha \), then \( \tan \alpha = \)
Let \( C \) be the centre and \( A \) be one end of a diameter of the circle \( x^2 + y^2 - 2x - 4y - 20 = 0 \). If \( P \) is a point on \( AC \) such that \( CP : PA = 2 : 3 \), then the locus of \( P \) is:
The Cartesian form of the curve given by \( x = \frac{a}{2}\left(t + \frac{1}{t}\right) \), \( y = \frac{a}{2}\left(t - \frac{1}{t}\right) \), where \( t \) is a parameter, is: