List of top Questions asked in AP EAPCET- 2022

If \(e_1\) and \(e_2\) are the eccentricities of the hyperbola \[ 16x^2-9y^2=1 \] and its conjugate respectively, then \(3e_1=\)

Evaluate \[ \lim_{x\to -\infty}\log_e(\cosh x)+x \]

If \(a,b,c\) are three distinct real numbers and \[ \lim_{x\to \infty} \frac{(b-c)x^2+(c-a)x+(a-b)} {(a-b)x^2+(b-c)x+(c-a)} = \frac{1}{2} \] then \(a+2c=\)

Let the plane \(\pi\) pass through the point \((1,0,1)\) and perpendicular to the planes \[ 2x+3y-z=2 \] and \[ x-y+2z=1. \] Let the equation of the plane passing through the point \((11,7,5)\) and parallel to the plane \(\pi\) be \[ ax+by-z+d=0. \] Then \[ \frac{a}{b}+\frac{b}{d}= \]

If \(P\) divides the line segment joining the points \(A(1,2,-1)\) and \(B(-1,0,1)\) externally in the ratio \(1:2\) and \(Q=(1,3,-1)\), then \(PQ=\)

If the direction cosines of a line are \[ \left( \frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}} \right) \] and \(c-a=4\), then \(ca=\)

The locus of point of intersection of tangents at the ends of normal chord of the hyperbola \[ x^2-y^2=a^2 \] is

If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] is \(90^\circ\), then its eccentricity is

Which of the following represents a parabola?

Suppose that the \(x\)-coordinates of the points \(A\) and \(B\) satisfy \[ x^2+2x-a^2=0 \] and their \(y\)-coordinates satisfy \[ y^2+4y-b^2=0. \] Then the equation of the circle with \(AB\) as its diameter is

The radical centre of the three circles \[ x^2+y^2-1=0, \] \[ x^2+y^2-8x+15=0 \] and \[ x^2+y^2+10y+24=0 \] is

A circle is such that \[ (x-2)\cos\theta+(y-2)\sin\theta=1 \] touches it for all values of \(\theta\). Then the circle is

The radius of the circle having \[ 3x-4y+4=0 \] and \[ 6x-8y-7=0 \] as its tangents is

Suppose the slopes \(m_1\) and \(m_2\) of the lines represented by \[ ax^2+2hxy+by^2=0 \] satisfy \[ 3(m_1-m_2)-7=0 \] and \[ m_1m_2-2=0. \] Then which of the following is true?

Suppose that the sides passing through the vertex \((\alpha,\beta)\) of a triangle are bisected at right angles by the lines \[ y^2-8xy-9x^2=0. \] Then the centroid of the triangle is

The least distance of the point \((10,7)\) from the circle \[ x^2+y^2-4x-2y-20=0 \] is

A bag contains \(4\) red and \(3\) black balls. A second bag contains \(2\) red and \(3\) black balls. One bag is selected at random. If from the selected bag, one ball is drawn at random, then the probability that the ball drawn is red is

The locus of midpoints of points of intersection of \[ x\cos\theta+y\sin\theta=1 \] with the coordinate axes is

In a Binomial distribution, if \(n\) is the number of trials and the mean and variance are \(4\) and \(3\) respectively, then \[ 2^{32}\cdot P\left(X=\frac{n}{2}\right)= \]

Suppose \(P\) and \(Q\) lie on \[ 3x+4y-4=0 \] and \[ 5x-y-4=0 \] respectively. If the midpoint of \(PQ\) is \((1,5)\), then the slope of the line passing through \(P\) and \(Q\) is

The length of intercept of \[ x+1=0 \] between the lines \[ 3x+2y=5 \] and \[ 3x+2y=3 \] is

Suppose that the three points \(A\), \(B\) and \(C\) in the plane are such that their \(x\)-coordinates as well as \(y\)-coordinates are in G.P. with the same common ratio. Then the points \(A\), \(B\) and \(C\)

For a Poisson distribution, if mean \(=\ell\), variance \(=m\) and \[ \ell+m=8, \] then \[ e^4\left[1-P(X\gt 2)\right]= \]

The probability of getting a sum \(9\) when two dice are thrown is

Two brothers \(X\) and \(Y\) appeared for an exam. Let \(A\) be the event that \(X\) has passed the exam and \(B\) be the event that \(Y\) has passed. The probability of \(A\) is \[ \frac17 \] and of \(B\) is \[ \frac29. \] Then, the probability that both of them pass the exam is