List of top Questions asked in AP EAPCET- 2022

The circle touching the \(y\)-axis at a distance \(4\) units from the origin and cutting off an intercept \(6\) from \(x\)-axis is:

The distance of the point \[ (6,4\sqrt{3}) \] from the focus of \[ y^2=8x \] is:

Suppose a circle passes through \((0,a)\) and \((b,h)\) having its centre at \((c,0)\). Then the value of \(c\) is

For a circle of diameter \(R\), touching \[ x^2+y^2-4y=0 \] and passing through \((4,5)\), which of the following is correct?

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 \(P(x,y)\) 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

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:

The locus of the incentre of the triangle formed by the lines \[ xy-4x-4y+16=0 \] and \[ x+y=5 \] is

If \(A(-3,3)\), \(B(1,1)\), \(C(1,-1)\) and \(D(-2,-2)\) are the vertices of a quadrilateral, the angle between the diagonals \(AC\) and \(BD\) is:

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

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:

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:

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

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

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

The mean deviation about the mean for the following data:

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 \(\overrightarrow{OD}=\)

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

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

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