List of top Questions asked in AP EAPCET

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

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?

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

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

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

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

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

If 6 is the mean of a Poisson distribution, then $P(X \geq 3) =$

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

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

Let $\vec{a}, \vec{b}, \vec{c}$ be the position vectors of the vertices of a triangle $ABC$. Through the vertices, lines are drawn parallel to the sides to form the triangle $A'B'C'$. Then the centroid of $\Delta A'B'C'$ is

Let $\vec{a} = xi + yj + zk$ and $x = 2y$. If $|\vec{a}| = 5\sqrt{2}$ and $\vec{a}$ makes an angle of $135^\circ$ with the z-axis then $\vec{a} =$

The point of intersection of the lines \[ \vec{r} = 2\vec{b} + t(6\vec{c} - \vec{a}) \quad \text{and} \quad \vec{r} = \vec{a} + s(\vec{b} - 3\vec{c}) \text{ is:} \]

In a triangle ABC, $r_1 \cot \dfrac{A}{2} + r_2 \cot \dfrac{B}{2} + r_3 \cot \dfrac{C}{2} = $ ?

In quadrilateral ABCD, $\vec{AB} = \vec{a},\ \vec{BC} = \vec{b},\ \vec{DA} = \vec{a} - \vec{b}$. M is midpoint of BC and X lies on DM such that $\vec{DX} = \dfrac{4}{5}\vec{DM}$. Then the points A, X and C:

Given vectors $3\vec{a} - 5\vec{b}$ and $2\vec{a} + \vec{b}$ are mutually perpendicular, and so are $\vec{a} + 4\vec{b}$ and $-\vec{a} + \vec{b}$. Find the acute angle between $\vec{a}$ and $\vec{b}$:

If $(1 + \tan1^\circ)(1 + \tan2^\circ)\dots(1 + \tan45^\circ) = 2^n$, then $n =$ ?