List of top Questions asked in AP EAPCET- 2022

A plane meets the \(X, Y, Z\)-axes in \(A, B, C\) respectively. If the centroid of the triangle \(ABC\) is \((2,-3,5)\), then the perpendicular distance from origin to the given plane is

If the centroid of a triangle with vertices \[ (4,p,-3),\quad (-1,-1,2),\quad (3,5,-8) \] is given by the midpoint of \[ (1,4,-2) \] and \[ (q,2,-4), \] then \(p^2+q^2=\)

If \((1,2)\) is the focus, \(x+2y=0\) is the directrix and \(\sqrt{2}\) is the eccentricity of a hyperbola, then the equation of the hyperbola is

The foci of the ellipse \[ 9x^2+25y^2=225 \] are

The locus of the point of intersection of the lines \[ \sqrt3x-y-4\sqrt3k=0 \] and \[ \sqrt3kx+ky-4\sqrt3=0 \] for different real values of \(k\) is a hyperbola \(H\). If \(e\) is the eccentricity of \(H\), then \(4e^2=\)

If the directrix of the parabola \[ x^2+4y-6x+\lambda=0 \] is \(y+1=0\), then which of the following is correct?

Suppose \(A(2,3)\) and \(B\) are the points of intersections of two circles. The points \(P\) lying on one circle and \(Q\) lying on the other circle are such that \(BP\) and \(BQ\) constitute the diameters of the circles respectively. If the slopes of the radical axis and \(PQ\) are \(\frac{3}{4}\) and \(\frac{a}{b}\) respectively, then the value of \(3a+4b\) is

The equation of circle with centre \((2,-3)\) and touching \(x\)-axis is

In a square \(ABCD\) of side length \(a\), suppose \(AB\) and \(AD\) are along the coordinate axes. Then the circle that circumscribes the square is

The equations of the lines perpendicular to \[ x^2-5xy+4y^2=0 \] and passing through \((2,1)\) is:

The straight line touching the circle \[ x^2+y^2-2x-3=0 \] and remaining normal to the circle \[ x^2+y^2-4y-6=0 \] is

The ratio of the areas of the greatest and the smallest circles touching \[ (x\pm 1)^2+(y\pm 1)^2=1 \] is

If \[ ax^2-34xy-5y^2+2x+26y-5=0 \] represents a pair of straight lines, then the value of \(a\) is:

Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are \(3x+4y-4=0\) and \((2,2)\) respectively. Then, which of the following is another side of the triangle?

A point \(P\) on a line is at a distance of \(4\) units from the origin \((0,0)\). If the line makes \(60^\circ\) with the negative direction of the \(x\)-axis, then \(P\) is

If \(X\) is a Poisson random variable with mean \(3\), then \[ P(|X-3|\lt 2) = \] is equal to:

A point \(P(x,y)\) is such that the sum of squares of its distances from \((a,0)\) and \((-a,0)\) is \(2b^2\). The equation representing the locus of \(P\) is:

Suppose \(ABOC\) is a rhombus in the first quadrant with \(O\) being the origin. If the vertices \(B\) and \(C\) of \(\triangle ABC\) lie respectively on \[ y=\frac{4}{3}x \] and \[ y=0, \] and the side \(BC\) passes through \[ \left(\frac23,\frac23\right), \] then the midpoint of \(BC\) is

Person A can solve \(90\%\) of the problems given in the book and Person B can solve \(70\%\). Then the probability that at least one of them will solve the problem selected at random from the book is:

A person \(P\) speaks truth in \(75\%\) cases and another person \(R\) in \(80\%\) cases. Then the probability that they are likely to contradict each other in narrating the same event is

A bag contains \(3\) white, \(2\) blue and \(5\) red balls. One ball is drawn at random from this bag. Then, the probability that the ball drawn is not red is

From a well shuffled pack of \(52\) cards, two cards are drawn at random. Then, the probability of both the cards being kings is:

During the winter months in a certain village in Scotland, the probability of a day having severe fog is \(0.6\). The probability that in a given week there will be exactly two days with severe fog is:

The set of real values of \(\lambda\) for which the vectors \[ \lambda \hat{i}-3\hat{j}+5\hat{k} \] and \[ 2\lambda \hat{i}-\lambda \hat{j}+\hat{k} \] are perpendicular to each other is

\(\vec{a},\vec{b}\) are two vectors such that \(|\vec{a}|=\sqrt{3}\), \(|\vec{b}|=\sqrt{2}\). If \(\vec{x}\) is a unit vector satisfying \(\vec{x}\times \vec{a}=\vec{b}\), then \(\vec{x}=\)