List of top Questions asked in AP EAPCET

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

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

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

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

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 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 $\vec{b}$:

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 $\vec{a} =$

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

The value of $\dfrac{\sin\theta + \sin3\theta}{\cos\theta + \cos3\theta}$ is:

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

Simplify: $\dfrac{\cos\theta}{1 - \tan\theta} + \dfrac{\sin\theta}{1 - \cot\theta}$

In a triangle ABC, if $a \ne b$, then \[ \frac{a\cos A - b\cos B}{a\cos B - b\cos A} + \cos C = ? \]

If $\cosech\,x = \dfrac{4}{5}$, then $\sinh x = $ ?

The value of $\dfrac{1 + \tanh x}{1 - \tanh x} =$ ?

In a triangle ABC, $a = 2,\ b = 3,\ c = 4$, then $\tan\left(\dfrac{A}{2}\right) = $ ?

The number of real roots of the equation \[ \frac{\sqrt{x}}{\sqrt{1 - x}} + \frac{\sqrt{1 - x}}{\sqrt{x}} = \frac{13}{6} \] is:

If $4^x - 3^{x - \frac{1}{2}} = 3^{x + \frac{1}{2}} - 2^{2x - 1}$, then the value of $x$ is: