List of top Questions asked in AP EAPCET- 2022

The equation of directrix of parabola \(x^2 + 8x + 12y + 4 = 0\) is

For any real number \(\lambda \neq 1\), the centre of the circle that passes through \(A(1, \lambda)\), \(B(\lambda, 1)\), and \(C(\lambda, \lambda)\) is

The shortest distance from the line \(3x + 4y = 25\) to the circle \(x^2 + y^2 - 6x + 8y = 0\) is

The straight line \(x \cos \alpha + y \sin \alpha = p\) cuts the circle \(x^2 + y^2 - a^2 = 0\) at A and B. Then the equation of circle having AB as diameter is

Suppose the pairs of straight lines \(x^2 - 2axy - y^2 = 0\) and \(x^2 - 2bxy - y^2 = 0\) are such that each pair bisects the angles between the other two. Then \(ab =\)

For a triangle formed by \((0,0)\), \((4,0)\), and \((3,4)\), the orthocenter is

Suppose a triangle of area 27 sq. units is formed by \(18x^2 - 9xy + y^2 = 0\) and \(y = c\). Then the centroid of the triangle is

Given two points \(Q(3,4)\) and \(R(1,2)\). What is the point \(P(x,y)\) on the line \(2x - y - 1 = 0\) for which \(PQ + PR = QR\) holds?

If a point \(P(\alpha, \beta)\) on the line \(y = 1\) is such that the two distinct chords drawn on \(x^2 + y^2 - \alpha x - y = 0\) from \(P\) are bisected by the x-axis, then

Suppose the vertices of a triangle are given by \(A(0,3)\), \(B(-2,0)\), and \(C(6,1)\). For \((\alpha, \alpha + 1)\) to lie inside the triangle, \(\alpha\) should lie in the interval

A special lottery is to be held to select a student who will live in the only deluxe room available in a hostel. 100 III year, 150 II year, and 200 I year students have applied for the room. Each III year student’s name is placed in the lottery 3 times, each II year student’s name 2 times, and each I year student’s name 1 time. The probability that a III year student gets the room is

In \(\Delta ABC\), if \(A = (1,2)\), and \(B\) and \(C\) lie on \(y = x + \alpha\) (where \(\alpha\) is variable), then the locus of the orthocenter of the triangle is

Four cards are drawn at random from a pack of 52 playing cards. The probability of getting all four cards of the same suit is

The discrete random variables \(X\) and \(Y\) are independent from one another and are defined as \(X \sim B(n_1, 0.5)\) and \(Y \sim B(n_2, 0.4)\). If the variance of both \(X\) and \(Y\) is 6, then \(\sqrt{n_1+n_2} =\)

The probability that A wakes up before the alarm rings is 0.4. Then, the mean and variance of the number of times A wakes up before the alarm rings in the next 7 days, respectively are:

A box contains 6 bottles of \(V_1\) drink, 3 bottles of \(V_2\) drink, and 4 bottles of \(V_3\) drink. If three bottles are drawn at random, find the probability that the three are not of the same variety.

One card is drawn at random from a well shuffled pack of 52 cards. The probability that the card drawn is a face card (Jack, Queen, and King only) is

The mean deviation about the median for the following data: \(6,3,4,9,2,7,11\) is:

If \(G(2,-1,2)\) is the centroid of tetrahedron \(OABC\) where \(O = (0,0,0)\) and \(G_1\) is the centroid of \(\Delta ABC\), then \(|OG_1| = ?\)

Let \(\vec{e_1}, \vec{e_2}\) be two non-collinear unit vectors such that \(|\vec{e_1}+\vec{e_2}| = \sqrt{3}\). Then evaluate \[ (2\vec{e_1}-5\vec{e_2}) \cdot (3\vec{e_1}+\vec{e_2}). \]

Let \[ \vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}, \quad \text{where } a_1, a_2, a_3 \text{ and } |\vec{a}| \text{ are rational numbers.} \] If \(\vec{a}\) makes an angle of \(45^\circ\) with \[ \vec{b} = \sqrt{2} \hat{i} + 3 \sqrt{2} \hat{j} + 4 \hat{k}, \] then \(\vec{a}\) lies in which plane?

A, B, C, D are any 4 points and \[ |AB \times CD + BC \times AD + CA \times BD| = \lambda (\text{Area of } \Delta ABC) \] then \(\lambda = ?\)

\(A(2,1,2), B(1,0,0), C(1+\sqrt{3},\sqrt{3},-\sqrt{6})\) are vertices of a triangle. If the length of the median drawn through \(A\) is \(\lambda\sqrt{9-2\sqrt{3}+2\sqrt{6}}\), then \(\lambda=\)

In a triangle ABC, if \(a - 2b + c = 0\), then \[ \cot \frac{A}{2} \cdot \cot \frac{C}{2} = ? \]

If \[ 2 \sin 2\theta = \sqrt{3}, \] then \(\theta =\)?