List of top Questions asked in AP EAPCET- 2022

Suppose the pairs of straight lines \[ 2x^2+axy+3y^2=0 \] and \[ 2x^2+bxy-3y^2=0 \] are such that they have one common line with the other two remaining perpendicular. Then the values of \(a\) and \(b\) respectively are:

Suppose \(P(x,y)\) lying on \[ \sqrt{3}x-y+2=0 \] or \[ \sqrt{3}x+y-2=0 \] is at a distance of \(5\) units from their point of intersection. Then the distance from \((0,0)\) to the foot of the perpendicular of \(P\) onto the \(y\)-axis is

If two distinct points lying at a unit distance from \[ 4x+3y-10=0 \] and passing through \[ x+y=4 \] are separated by a distance \(d\), then the value of \(d\) is

Suppose a point \(P\) moves so that \[ BP^2-AP^2=121, \] where \(A\) and \(B\) are \((2,5)\) and \((5,11)\) respectively. Then the locus of \(P\) is a straight line, whose slope is:

It is given that the discrete random variable \[ X\sim B(n,p) \] and \[ P(X=2)=P(X=3). \] Then mean of \(X\) is

There are \(4\) hotels in a town. If \(3\) men check into the hotels in a day, then the probability that each checks into a different hotel is

If \(3\) is the variance of Poisson distribution, then \[ P(1\lt x\lt 4)= \] is:

Two dice are thrown simultaneously. The probability of getting two numbers whose product is even is:

From a pack of \(52\) cards, \(3\) cards are drawn at random. Then, the probability that one is ace, one is queen and one is jack is:

Three students \(X,Y\) and \(Z\) appear for an examination. The probability of \(X\) passing the examination is \(\frac{1}{5}\), the probability of \(Y\) passing the examination is \(\frac{1}{4}\), and the probability of \(Z\) failing the examination is \(\frac{2}{3}\). The probability that at least two of them pass the exam is

In \(\triangle ABC\), \(O\) is the circumcenter and \(G\) is the centroid, then \[ OG^2= \] is:

Three vectors \(\vec{a},\vec{b},\vec{c}\) satisfy the condition \[ \vec{a}+\vec{b}+\vec{c}=\vec{0}. \] If \[ |\vec{a}|=1,\quad |\vec{b}|=3,\quad |\vec{c}|=4, \] then \[ \vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{c}+\vec{c}\cdot\vec{a} = \] is:

Let \[ \overrightarrow{OA}=-4\hat{i}+3\hat{k},\quad \overrightarrow{OB}=14\hat{i}+2\hat{j}-5\hat{k}. \] \(\overrightarrow{OD}\) bisects \(\angle AOB\) and \[ |\overrightarrow{OD}|=\sqrt{6}, \] then \(\overrightarrow{OD}=\)

The mean deviation about the mean for the following data:

is:

If the position vectors of the points \(A,B,C,D\) are \[ 7\hat{i}-4\hat{j}+7\hat{k},\quad \hat{i}-6\hat{j}+10\hat{k},\quad -\hat{i}-3\hat{j}+4\hat{k},\quad 5\hat{i}-\hat{j}+5\hat{k} \] respectively, then \(ABCD\) is

In a triangle \(ABC\), \[ s\left[\frac{r_1-r}{a}+\frac{r_2-r}{b}+\frac{r_3-r}{c}\right] = \] is:

A farmer owns a triangular plot in Guntur. He measures the lengths of the sides of his property as \(4\) cm, \(5\) cm and \(7\) cm. Then the area of land of the farmer in sq. cm is

In a triangle, if \[ b=5,\quad c=6,\quad \tan\frac{A}{2}=\frac{1}{\sqrt{2}}, \] then \[ a= \] is:

Let \(x\in \mathbb{R}\) and \(|x|\lt 1\). Then \[ \tanh^{-1}x= \]

\(M\) and \(N\) are the mid points of the sides \(BC\) and \(CD\) of a parallelogram \(ABCD\) respectively, then \[ \overrightarrow{AM}+\overrightarrow{AN}= \]

If \[ \operatorname{cosech}x=\frac{4}{5}, \] then \[ \cosh x= \] is:

Let \(\alpha,\beta\) be two real numbers such that \[ \pi\lt (\alpha-\beta)\lt 3\pi. \] If \[ \sin\alpha+\sin\beta=-\frac{21}{65} \] and \[ \cos\alpha+\cos\beta=-\frac{2}{65}, \] then \[ \cos\left(\frac{\beta-\alpha}{2}\right)= \]

Simplify \[ \sec^2 x+5\tan x+5= \]

In a triangle \(ABC\), \[ \tan \frac{A}{2}\tan \frac{B}{2} +\tan \frac{B}{2}\tan \frac{C}{2} +\tan \frac{C}{2}\tan \frac{A}{2} = \]

If \[ \cos\theta-\sin\theta=\sqrt{5}\sin\theta, \] then \[ \cos\theta+4\sin\theta \] is equal to: