List of top Mathematics Questions asked in AP EAPCET

The distance between the points \[ (1,2) \quad \text{and} \quad (4,6) \] is:

The number of integers that satisfy both the inequalities \[ x^2-2x+8>0 \] and \[ x^2-3x+2\le 0 \] is:

The area (in sq. units) of the region bounded between the curve \( y=x^{2}+5x+1 \) and the line \( 7x-y+1=0 \) is

If \( f(x)=|x-2|(3^{4|x|}-1) \) is a real valued function, then the set of points at which f is not differentiable, is

The value of \( \lim_{x\rightarrow0}\frac{e^{2x^{2}}-\cos 2x}{x^{2}} = \)

If the angle between the planes \( \lambda x-2y+3z+1=0 \) and \( 2x+3y-\lambda z+\lambda=0 \) is \( \cos^{-1}(\frac{12}{49}) \) and \( \lambda\in\mathbb{Z} \), then the sum of the perpendicular distances from the origin to these planes is

\( A(1,2,3) \), \( B(3,4,k) \), \( C(2,1,4) \) form an isosceles triangle. If \( AB=BC \), then the area of \( \triangle ABC \) is

The value of \( \lim_{x\rightarrow\infty}\frac{x^{3}+2x^{2}\sin x-4x \cos x}{\sqrt{(3x^{2}+2x \cos x)^{3}}} = \)

If the lengths of the sides of a triangle a, b, c \( (a>b>c) \) are in arithmetic progression and the greatest angle is twice the smallest, then a: b: \( c= \)

The partial fraction decomposition of \( \frac{x^{4}+24 x^{2}+28}{(x^{2}+1)^{3}} \) is

If the sum of two roots of the cubic equation $x^3 - 5x^2 - 2x + 24 = 0$ is $2$, then the roots of the equation are:

If $y = e^{a \sin^{-1} x}$, then $(1 - x^2) y_2 - x y_1 =$

The equation of the parabola with focus at $(3, 0)$ and directrix $x + 3 = 0$ is:

The distance between the parallel lines $5x + 12y - 3 = 0$ and $5x + 12y + 10 = 0$ is:

The variance of the first $n$ even natural numbers is:

If \( \begin{vmatrix} 1 & 2 & 3 - \lambda 0 & -1 - \lambda & 2 1 - \lambda & 1 & 3 \end{vmatrix} = A\lambda^3 + B\lambda^2 + C\lambda + D \), then \( D + A = \)

The value of the limit \( \lim_{n \to \infty} \left( \frac{1}{1^2 + n^2} + \frac{2}{2^2 + n^2} + \frac{3}{3^2 + n^2} + \cdots + \frac{n}{n^2 + n^2} \right) \) is equal to:

If the direction ratios of two lines are given by $ l + m + n = 0 $ and $ mn - 2ln + lm = 0 $, then the angle between the lines is:

If $y = \sqrt{\tan x + \sqrt{\tan x + \sqrt{\tan x + \dots \infty}$, then $(2y - 1)\frac{dy}{dx} =$

The integral $\int \frac{dx}{x(x^4 + 1)} =$

The value of the limit $\lim_{x \to 0} \frac{e^{3x} - e^{-2x}}{\sin 4x}$ is:

The distance of the point $(1, 2)$ from the line $3x + 4y - 32 = 0$ measured parallel to the line $x - y = 0$ is:

If $\vec{a}$, $\vec{b}$, and $\vec{c}$ are three unit vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, then the value of $\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}$ is:

The foot of the perpendicular from the point $(1, 3)$ to the line $x + y - 2 = 0$ is:

The length of the tangent from the point $(3, 4)$ to the circle $x^2 + y^2 - 2x - 4y + 1 = 0$ is: