List of top Mathematics Questions asked in AP EAPCET

If $f(x) = \cot^{-1}\left( \dfrac{x^n + x^{-n}}{2} \right)$, then $f'(1) = $

Let $f: \mathbb{R}^+ \rightarrow \mathbb{R}^+$ be a function satisfying $f(x) - x = \lambda$ (constant), $\forall x \in \mathbb{R}^+$ and $f(xf(y)) = f(y) + x$, $\forall x, y \in \mathbb{R}^+$. Then $\displaystyle \lim_{x \to 0} \dfrac{(f(x))^{\frac{5}{3}} - 1}{(f(x))^{\frac{2}{3}} - 1}$ is

If $\displaystyle \lim_{x \to 0} \dfrac{|x|}{\sqrt{x^4 + 4x^2 + 5}} = k$, $\displaystyle \lim_{x \to 0} x^4 \sin\left(\dfrac{1}{3\sqrt{x}}\right) = l$, Then $k + l = $

If $\displaystyle \lim_{x \to \infty} x^n \log_e x = 0$, then $\log_e 12 =$

For any two nonzero real numbers $a$ and $b$, if the line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ is a tangent to the circle $x^2 + y^2 = 1$, then which of the following is true?

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 pole of the line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ with respect to the circle $x^2 + y^2 = c^2$ is

If the tangent at the point $P$ on the circle $x^2 + y^2 + 6x + 6y = 2$ meets the straight line $5x - 2y + 6 = 0$ at a point $Q$ on the y-axis, then the length of $PQ$ 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

The eccentric angle of a point on the ellipse $x^2 + 3y^2 = 6$ lying at a distance of 2 units from its centre is

Let origin be the centre, $(\pm 3, 0)$ the foci and $\dfrac{3}{2}$ be the eccentricity of a hyperbola. Then the line $2x - y - 1 = 0$

The locus of a variable point whose chord of contact w.r.t. the hyperbola $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ subtends a right angle at the origin is

A stick of length $r$ units slides with its ends on coordinate axes. Then the locus of the midpoint of the stick is a curve whose length is

The least distance from origin to a point on the line $y = x + 3$ which lies at a distance of 2 units from $(0,3)$ is

Starting from the point $A(-3,4)$, a moving object touches $2x + y - 7 = 0$ at $B$ and reaches $C(0,1)$. If the object travels along the shortest path, the distance between $A$ and $B$ is

Suppose a triangle is formed by $x + y = 10$ and the coordinate axes. Then the number of points $(x, y)$ where $x$ and $y$ are natural numbers, lying inside the triangle is

For $\alpha \in \left[0, \dfrac{\pi}{2} \right]$, the angle between the lines represented by
$[x \cos\theta - y] \left[ (\cos\theta + \tan\alpha)x - (1 - \cos\theta \tan\alpha)y \right] = 0$ is

The locus of centers of the circles, possessing the same area and having $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ as their common tangent, is

If the lines represented by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ intersect on the x-axis, which of the following is in general incorrect

The mean deviation about the mean for the following data:
5, 6, 7, 8, 6.9, 13, 12, 15

If $x$ is chosen at random from the set $\{1,2,3,4\}$ and $y$ is chosen at random from the set $\{5,6,7\}$, then the probability that $xy$ will be even is

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X \sim B(16, 0.25)$ and $Y \sim P(2)$. Then the sum of the variances of $X$ and $Y$ is