List of top Questions asked in AP EAPCET

If $(2, 3, c)$ are the direction ratios of a ray passing through the point $C(5, q, 1)$ and also the midpoint of the line segment joining the points $A(p, -4, 2)$ and $B(3, 2, -4)$, then $c(p + 7q) = $
If the equation of the plane which is at a distance of $\dfrac{1}{\sqrt{3}}$ units from the origin and perpendicular to a line whose directional ratios are $(1, 2, 2)$ is $x + py + qz + r = 0$, then $\sqrt{p^2 + q^2 + r^2} =$
If the pair of straight lines $9x^2 + axy + 4y^2 + 6x + by - 3 = 0$ represents two parallel lines then
A line passing through $P(2, 3)$ and making an angle of $30^\circ$ with the positive direction of $x$-axis meets $x^2 - 2xy - y^2 = 0$ at $A$ and $B$. Then the value of $PA \cdot PB$ is
For any real number $t$, the point $\left( \dfrac{8t}{1 + t^2}, \dfrac{4(1 - t^2)}{1 + t^2} \right)$ lies on a/an
The area of the circle passing through the points $(5, \pm2)$, $(1,2)$ is
The ratio of the largest and shortest distances from the point $(2, -7)$ to the circle $x^2 + y^2 - 14x - 10y - 151 = 0$ is
A circle has its centre in the first quadrant and passes through $(2, 3)$. If this circle makes intercepts of length 3 and 4 respectively on $x = 2$ and $y = 3$, its equation is
The image of the point $(3, 4)$ with respect to the radical axis of the circles $x^2 + y^2 + 8x + 2y + 10 = 0$ and $x^2 + y^2 + 7x + 3y + 10 = 0$ is
A manager decides to distribute Rs. 20000 between two employees X and Y. He knows X deserves more than Y, but does not know how much more. So, he decides to arbitrarily break Rs. 20000 into two parts and gives X the bigger part. Then, the chance that X gets twice as much as Y or more is
Which of the following is \textbf{not} a property of a Binomial distribution?
In a Binomial distribution $B(n, p)$, if the mean and variance are 15 and 10 respectively, then the value of the parameter $n$ is
Suppose $P$ and $Q$ are the midpoints of the sides $AB$ and $BC$ of a triangle where $A(1, 3)$, $B(3, 7)$ and $C(7, 15)$ are vertices. Then the locus of $R$ satisfying $AC^2 + QR^2 = PR^2$ is
Suppose $\triangle ABC$ is an isosceles triangle with $\angle C = 90^\circ$, $A = (2, 3)$ and $B = (4, 5)$. Then the centroid of the triangle is
If the points of intersection of the coordinate axes and $|x + y| = 2$ form a rhombus, then its area 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
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
If $P$, $Q$ are two points on the curve $y = 2x^2$ in the rectangular Cartesian coordinate system such that $\vec{OP} \cdot \vec{i} = -1$, $\vec{OQ} \cdot \vec{i} = 2$, then $\vec{OQ} - 4\vec{OP} =$
If the equation of the plane passing through the point $A(-2, 1, 3)$ and perpendicular to the vector $3\vec{i} + \vec{j} + 5\vec{k}$ is $ax + by + cz + d = 0$, then $\dfrac{a + b}{c + d} =$
If the mean of the data $p,6,6,7,8,11,15,16$ is 3 times $p$, then the mean deviation of the data from its mean is
In a box, there are 8 red, 7 blue, and 6 green balls. One ball is picked randomly. The probability that it is neither red nor green is
For two events $A$ and $B$, a true statement among the following is
Five-digit numbers are formed using digits 1,2,3,4,5 without repetition. Then the probability that the randomly chosen number is divisible by 4 is
In a triangle $ABC$, $2(bc \cos A + ac \cos B + ab \cos C) =$
If $4 + 6(e^{2x} + 1)\tanh x = 11\cosh x + 11\sinh x$, then $x =$