List of top Questions asked in AP EAPCET- 2022

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 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?

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

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 \(\sqrt{n_1+n_2} =\)

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

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

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:

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

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.

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

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 \(\lambda = ?\)

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 \[ (2\vec{e_1}-5\vec{e_2}) \cdot (3\vec{e_1}+\vec{e_2}). \]

\(A(2,1,2), B(1,0,0), C(1+\sqrt{3},\sqrt{3},-\sqrt{6})\) 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 \(\lambda=\)

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?

In a triangle ABC, if \(a = 13, b = 14, c = 15\), then \[ \sin \frac{A}{2} = ? \]

In a triangle ABC, the expression \[ (b+c) \sin \frac{A}{2} \] is equal to:

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

If one solution of the equation \[ \cosh x - \frac{4}{5} \sinh x = 1 \text{ is } x = 0, \] then the other solution is:

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

Evaluate \[ \cos \frac{7\pi}{12}. \]

Evaluate \[ \cos^4 \frac{\pi}{24} - \sin^4 \frac{\pi}{24}. \]

If \[ \frac{x}{(x-1)(x^2+1)^2} = \frac{1}{4} \left[\frac{1}{x-1} - \frac{x+1}{x^2+1}\right] + y, \] then \(y =\)