List of top Questions asked in AP EAPCET- 2022

For \(\alpha\) belonging to an interval of length \(\beta\), suppose \((\alpha,-\alpha)\) is an interior point of the ellipse \[ 4x^2+5y^2=1. \] Then \[ (6\beta-4)^{201}+201= \]

From any point on the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1, \] tangents are drawn to the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=2. \] The area of the figure formed by the chord of contact of that point and the asymptotes is:

Statement 1: The eccentricity of the hyperbola \[ 9x^2-16y^2-72x+96y-144=0 \] is \[ \frac{5}{4}. \] Statement 2: The eccentricity of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] is \[ \sqrt{1+\frac{b^2}{a^2}}. \]

Suppose the angle between the tangents drawn from \((0,0)\) to the circle \[ (x+\lambda)^2+(y+1)^2=\lambda^2 \] is \(\frac{\pi}{2}\). Then \(\lambda\) satisfies:

The circle \[ x^2+y^2-4x-8y+16=0 \] rolls up along the tangent drawn to it at \((2+\sqrt3,3)\) by \(2\) units. The equation of the circle in the new position is:

For \(a,b,h>0\), if the slope of one of the lines represented by \[ a^2x^2+2hxy+b^2y^2=0 \] is twice that of the other, then the value of \[ \frac{h}{ab} \] is:

Suppose \(A\) and \(B\) are the points at which the line \[ x+y-\lambda=0 \] meets the pair of straight lines \[ x^2+y^2-2x-4y+2=0. \] If \(\angle AOB=90^\circ\), then the value of \(\lambda\) is:

If a circle of radius \(3\) passes through the point \((7,3)\) and has its centre on the line \[ x-y-1=0, \] then its equation among the following is:

Number of circles intersecting \[ x^2+y^2=4,\quad x^2+y^2-2x-3=0 \] and \[ x^2+y^2-2y-3=0 \] orthogonally is:

If the segments of the straight lines \[ x+y=6 \] and \[ x+2y=4 \] are two diameters of a circle passing through \((6,2)\), then the equation of that circle is:

The line on which the lines \[ ax+by=1 \] and \[ bx+ay=1 \] with \(a\neq 0\neq b\), intersect for any real values of \(a\) and \(b\), is:

For \(x\) and \(y\) satisfying \[ |x|+|y|=|x-3|+|y-2|, \] which of the following is correct?

A random variable \(X\) follows the binomial distribution and \[ X\sim B(n,0.3). \] If the mean of \(X\) is three times as large as the standard deviation of \(X\), then \(n=\)

If a line \(AB\) of length \(r\) moves such that \(A\) and \(B\) always lie respectively on the \(x\)-axis and the line \[ y=6x, \] then the locus of the midpoint of \(AB\) is

All points inside the triangle with vertices at \((1,3)\), \((5,0)\) and \((-1,2)\) must necessarily satisfy:

In a Binomial distribution, if \(p=q\) and \(n\geq 4\), then \[ 2^nP(X=5)= \]

Two dice are thrown simultaneously. The probability of getting a multiple of \(2\) on one die and a multiple of \(3\) on the other die is:

Two persons \(A\) and \(B\) take part in a shooting competition. \(A\) can hit the target with probability \(0.6\), and \(B\) can hit the target with probability \(0.8\). \(A\) has the first shot, after which they strike alternately. Then, the probability that \(A\) wins the competition is:

A box has \(6\) black, \(4\) red, \(2\) white and \(3\) blue shirts. When \(2\) shirts are picked at random, the probability that either both are white or both are blue is:

The mean deviation from the median for the following data is:

If \[ \vec{a}=4\vec{i}+6\vec{j},\quad \vec{b}=3\vec{j}+4\vec{k} \] and \(\vec{c}\) is the projection vector of \(\vec{a}\) on \(\vec{b}\), then \(\vec{c}\) and \(|\vec{c}|\) respectively are:

The distance between a point \(P\) whose position vector is \[ 5\vec{i}+\vec{j}+3\vec{k} \] and the line \[ \vec{r}=(3\vec{i}+7\vec{j}+\vec{k})+t(\vec{j}+\vec{k}) \] is:

If the points \[ \vec{P}=\vec{i}+2\vec{j},\quad \vec{Q}=4\vec{i}+6\vec{j},\quad \vec{R}=5\vec{i}+7\vec{j},\quad \vec{S}=a\vec{i}+b\vec{j} \] are the consecutive vertices of a parallelogram \(PQRS\), then

Three unbiased coins are tossed. Then, the probability of getting at most two heads is:

In a triangle \(ABC\), if \(r_1=12\), \(r_2=18\) and \(r_3=36\), then \(b=\)