List of top Mathematics Questions asked in AP EAPCET

Evaluate: \[ \int_{0}^{\pi/4} e^{\tan^2 \theta} \sin^2 \theta \tan \theta \, d\theta = \]
Evaluate: \[ \int_{\pi/4}^{5\pi/4} \left(\cos t |\sin t| + \sin t |\cos t|\right) dt = \]
If \( f(x) = \max(\sin x, \cos x) \) and \( g(x) = \min(\sin x, \cos x) \), then \[ \int_0^{\pi/2} f(x) dx + \int_0^{\pi/2} g(x) dx = \]
If \( 2x - y + c \log(|x - 2y - 4|) = k \) is the general solution of \[ \frac{dy}{dx} = \frac{2x - 4y - 5}{x - 2y + 2} \] then \( c = \):
If the straight line \( x\cos\alpha + y\sin\alpha = p \) touches the curve \( \left( \frac{x}{a} \right)^n + \left( \frac{y}{b} \right)^n = 2 \) at the point (a, b), and \( \frac{1}{a^2} + \frac{1}{b^2} = \frac{k}{p^2} \), then \( k = \):
Condition that two curves \( y^2 = 4ax \) and \( xy = c^2 \) cut orthogonally is:
A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is:
Two particles P and Q located at the points \( P(t, t^3 - 16t - 3) \), \( Q(t+1, t^3 - 6t - 6) \) are moving in a plane. The minimum distance between the points in their motion is:
If \( f(x) = \int_{x^2}^{\cos^2 x} (2x \tan^2 x - 2x - 6 \tan x) dx \), and \( f(0) = \pi \), then \( f(x) = \):
If \( \int e^{\sqrt{x}} / \sqrt{x} (x + \sqrt{x}) dx = e^{\sqrt{x}}[Ax + B\sqrt{x} + C] + K \), then \( A + B + C = \):
If \( \int \frac{1 + \sqrt{\tan x}}{\sin 2x} dx = A \log \tan x + B \tan x + C \), then \( 4A - 2B = \):
If $x \neq 0$ and $f(x)$ satisfies $8f(x) + 6f\left(\dfrac{1}{x}\right) = x + 5$, then $\dfrac{d}{dx} \left(x^2 f(x)\right)$ at $x = 1$ is
Calculate $\dfrac{d}{dx} \left(\lim_{y \to 2} \dfrac{1}{y-2} \left(\dfrac{1}{x} - \dfrac{1}{x+y-2}\right)\right)$
The number of those tangents to the curve $y^2 - 2x^3 - 4y + 8 = 0$ which pass through the point $(1, 2)$ is
If $[\cdot]$ denotes greatest integer function, then $\lim_{x \to 3} \dfrac{[-x]}{x} =$
If $l, m$ $(l<m)$ are roots of $ax^2 + bx + c = 0$, then $\lim_{x \to a} \left| \dfrac{ax^2 + bx + c}{ax^2 + bx + c} \right|$ =
If $(2, 3, c)$ are the direction ratios of a ray passing through the point $C(5, q, 1)$ and also the midpoint of the line segment joining the points $A(p, -4, 2)$ and $B(3, 2, -4)$, then $c(p + 7q) = $
Suppose a parabola passes through $(0, 4)$, $(1, 9)$ and $(4, 5)$ and has its axis parallel to the $y$-axis. Then the equation of the parabola is
The focal distances of the point $\left(\dfrac{4}{\sqrt{5}}, \dfrac{3}{\sqrt{5}}\right)$ on the ellipse $\dfrac{x^2}{4} + \dfrac{y^2}{9} = 1$ are
If the normal to the rectangular hyperbola $x^2 - y^2 = 1$ at the point $P(\tfrac{\pi}{4})$ meets the curve again at $Q(\theta)$, then $\sec^2\theta + \tan\theta =$
If the vertices and foci of a hyperbola are respectively $(\pm3,0)$ and $(\pm4,0)$ then the parametric equations of that hyperbola are
If the equation of the plane which is at a distance of $\dfrac{1}{\sqrt{3}}$ units from the origin and perpendicular to a line whose directional ratios are $(1, 2, 2)$ is $x + py + qz + r = 0$, then $\sqrt{p^2 + q^2 + r^2} =$
If $x$-coordinate of a point $P$ on the line joining the points $Q(2,2,1)$ and $R(5,2,-2)$ is $4$, then the $y$-coordinate of $P$ is
A line passing through $P(2, 3)$ and making an angle of $30^\circ$ with the positive direction of $x$-axis meets $x^2 - 2xy - y^2 = 0$ at $A$ and $B$. Then the value of $PA \cdot PB$ is
For any real number $t$, the point $\left( \dfrac{8t}{1 + t^2}, \dfrac{4(1 - t^2)}{1 + t^2} \right)$ lies on a/an