List of top Mathematics Questions asked in AP EAPCET

In a triangle $ABC$, $\dfrac{a}{b} = 2 + \sqrt{3}$ and $\angle C = 60^\circ$. Then the measure of $\angle A$ is
Suppose a parabola with focus at $(0,0)$ has $x - y + 1 = 0$ as its tangent at the vertex. Then the equation of its directrix is
If the point \( (2, \lambda) \) lies inside the circles \( x^2 + y^2 = 13 \) and \( x^2 + y^2 + x - 2y = 14 \), then \( \lambda \) lies in the set:
If the curves \( y = x^3 - 3x^2 - 8x - 4 \) and \( y = 3x^2 + 7x + 4 \) touch each other at a point \( P \), then the equation of the common tangent at \( P \) is
The set of all \( x \) for which \( \sin x \leq x \) is:
Condition that two curves \( y^2 = 4ax \) and \( xy = c^2 \) cut orthogonally is:
If \( \int \frac{1 + \sqrt{\tan x}}{\sin 2x} dx = A \log \tan x + B \tan x + C \), then \( 4A - 2B = \):
If the point $(a, 8, -2)$ divides the line segment joining the points $(1, 4, 6)$ and $(5, 2, 10)$ in the ratio $m:n$, then $\dfrac{2m}{n} - \dfrac{a}{3} =$

The mean deviation about the mean for the given data:  

Marks Obtained0–2020–4040–6060–8080–100
Number of Students10812911
Evaluate: \[ \lim_{x \to 0} \frac{\sqrt{11 + |x|} - 6\sqrt{2 + |x|}}{6 - 2\sqrt{2 + |x|}} \]
Evaluate the integral \( \int \frac{x^2 - 2}{x^3 \sqrt{x^2 - 1}} \, dx \)
Let $$ I_n = \int (\cos^n x + \sin^n x) \, dx,\quad \text{and} \quad \frac{n - 1}{n} I_{n - 2} = \frac{\sin x \cos x}{n} f(x) $$ Then, what is $ f(x) $?
Let \( \vec{OA} = -4\hat{i} + 3\hat{k} \), \( \vec{OB} = 14\hat{i} + 2\hat{j} - 5\hat{k} \), and vector \( \vec{OD} \) bisects \( \angle AOB \), with \( |\vec{OD}| = \sqrt{6} \). Then: \[ \vec{OD} = ? \]
If $\vec{a} + \vec{b} + \vec{c} = 0$, and $|\vec{a}| = 7$, $|\vec{b}| = 5$, $|\vec{c}| = 3$, then the angle between $\vec{b}$ and $\vec{c}$ is
By eliminating the arbitrary constants from \[ y = (a + b)\sin(x + c) - de^{x + te^t} \] the differential equation obtained is of order:
Evaluate: \( 1 + \cot^2 30^\circ - \sec^2 45^\circ \)
The length of the intercept on the line $4x - 3y - 10 = 0$ by the circle $x^2 + y^2 - 2x + 4y - 26 = 0$ is
The equation of the tangent to the circle \( x^2 + y^2 = 9 \) making an angle \( 60^\circ \) with the x-axis is:
Suppose, in triangle $\triangle ABC$, $x - y + 5 = 0$, $x + 2y = 0$ are respectively the equations of the perpendicular bisectors of the sides $AB$ and $AC$. If $A$ is $(1, -2)$, the equation of the line joining $B$ and $C$ is
In a square ABCD of side length a, suppose AB and AD are along the coordinate axes. Then the circle that circumscribes the square is
If the equation of the tangent to the circle \(x^2+y^2=a^2\) at \(P(x_1, y_1)\) is \(x x_1 + y y_1 = K\), then K =
If \( f(x) = \int \cos^{-1} \left( \frac{x}{\sqrt{a + x}} \right) dx + C \), then \( f'(a) = \)
The normal to the curve y = f(x) at the points (3, 4) makes an angle \( \frac{3\pi}{4} \) with positive x-axis then \(f'(3) = \)
By simplifying the expression: $$ i^{18} - 3i^7 + i^2(1 + i^4)(i^{22}) $$ we get:
If $(a, b, c)$ are the direction ratios of a line joining the points $(4, 3, -5)$ and $(-2, 1, -8)$, then the point $P = (a, 3b, 2c)$ lies on the plane