List of top Mathematics Questions asked in AP EAMCET

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

Evaluate the integral \( \int \frac{dx}{x(x^4 + 1)} \):
A value of \(c\) according to the Lagrange's mean value theorem for \(f(x) = (x - 1)(x - 2)(x - 3)\) in \([0,4]\) is:
The acute angle between the curves \(x^2 + y^2 = x + y\) and \(x^2 + y^2 = 2y\) is:
The length of the subnormal at any point on the curve \( y = \left(\frac{x}{2024}\right)^k \) is constant if the value of \( k \) is:
If \( p_1 \) and \( p_2 \) are the perpendicular distances from the origin to the tangent and normal drawn at any point on the curve \( x^{2/3} + y^{2/3} = a^{2/3} \) respectively. If \( k_1 p_1^2 + k_2 p_2^2 = a^2 \), then \( k_1 + k_2 = \)
In the interval \([0, 3]\), the function \(f(x) = |x - 1| + |x - 2|\) is:
If \(y = t^2 + t^3\) and \(x = t - t^4\), then \(\frac{d^2y}{dx^2}\) at \(t = 1\) is:
If \(f(x) = \begin{cases} 2x + 3, & \text{if } x \leq 1 \\ 2ax + bx, & \text{if } x > 1 \end{cases}\) is differentiable \(\forall x \in \mathbb{R}\), then \(f(2) =\)
Determine the values of \(a\) and \(b\) for which the function \(f(x)\) defined as: \[ f(x) = \begin{cases} 1 + |\sin x|^{\left(\frac{a}{|\sin x|}\right)} & \text{if } \frac{-\pi}{6} < x < 0, \\ b & \text{if } x = 0, \\ e^{\left(\frac{\tan 2x}{\tan 3x}\right)} & \text{if } 0 < x < \frac{\pi}{6} \end{cases} \] is continuous at \(x = 0\).
Evaluate the limit: \[ \lim_{x \to 0} \frac{e^{x} - a - \log(1+x)}{\sin x} = 0, { then find } a. \]
Evaluate the limit: \[ \lim_{x \to \frac{\pi}{4}} \frac{4\sqrt{2} - (\cos x + \sin x)^5}{1 - \sin 2x} = \]
The direction cosines of the line of intersection of the planes \( x + 2y + z - 4 = 0 \) and \( 2x - y + z - 3 = 0 \) are:
If \( l_1 \) and \( l_2 \) are the lengths of the perpendiculars drawn from a point on the hyperbola \( 5x^2 - 4y^2 - 20 = 0 \) to its asymptotes, then \( \frac{l_1^2 l_2^2}{100} = \)
If a directrix of a hyperbola centered at the origin and passing through the point \( (4, -2\sqrt{3}) \) is \( \sqrt{5}x = 4 \) and \( e \) is its eccentricity, then \( e^2 = \)
If the chord of the ellipse \( \frac{x^2}{4} + \frac{y^2}{9} = 1 \) having \((1,1)\) as its middle point is \( x + \alpha y = \beta \), then:
Equation of a tangent line of the parabola \(y^2 = 8x\), which passes through the point \((1, 3)\) is:
The radical center of the circles \(x^2 + y^2 + 2x + 3y + 1 = 0\), \(x^2 + y^2 - x + y + 3 = 0\), and \(x^2 + y^2 - 3x + 2y + 5 = 0\) is:
If the locus of the mid points of the chords of the circle \(x^2 + y^2 = 25\) that subtend a right angle at the origin is given by \( \frac{x^2}{a^2} + \frac{y^2}{a^2} = 1\), then \(|a| =\)
The circle \(x^2 + y^2 - 8x - 12y + \alpha = 0\) lies in the first quadrant without touching the coordinate axes. If \((6, 6)\) is an interior point to the circle, then the range of \(\alpha\) is:
The equation of the straight line passing through the point of intersection of the lines represented by \(x^2 + 4xy + 3y^2 - 4x - 10y + 3 = 0\) and the point \((2,2)\) is:
If the line \(2x - 3y + 5 = 0\) is the perpendicular bisector of the line segment joining \(1, -2\) and \((a, b)\), then \(a + b =\)
The circumcentre of the triangle formed by the lines \(x + y + 2 = 0\), \(2x + y + 8 = 0\) and \(x - y - 2 = 0\) is
If the origin is shifted to remove the first degree terms from the equation \(2x^2 - 3y^2 + 4xy + 4x + 4y - 14 = 0\), then with respect to this new co-ordinate system, the transformed equation of \(x^2 + y^2 - 3xy + 4y + 3 = 0\) is
The probability that a man failing to hit a target is \(\frac{1}{3}\). If he fires 4 times, then the probability that he hits the target at least thrice is