List of top Questions asked in AP EAPCET- 2022

Two particles \(P\) and \(Q\) located at the points \[ P(t,t^3-16t-3),\qquad Q(t+1,t^3-6t-6) \] are moving in a plane. The minimum distance between the points in their motion is

If \[ f(x)= \begin{cases} \dfrac{x^2\log(\cos x)}{\log(1+x)}, & x\neq 0 \\ 0, & x=0 \end{cases} \] then at \(x=0\), \(f(x)\) is

Let \[ f(x)= \begin{cases} \dfrac{1}{|x|}, & \text{for } |x|\gt 1 \\[0.3cm] ax^2+b, & \text{for } |x|\leq1 \end{cases} \] If \[ \lim_{x\to1}f(x) \quad \text{and} \quad \lim_{x\to-1}f(x) \] exist, then the possible values of \(a\) and \(b\) are

If \(x\neq0\) and \(f(x)\) satisfies \[ 8f(x)+6f\left(\frac{1}{x}\right)=x+5, \] then \[ \frac{d}{dx}\left(x^2f(x)\right) \] at \(x=1\) is

If \(l,m\;(l\lt m)\) are roots of \(ax^2+bx+c=0\), then \[ \lim_{x\to \alpha}\frac{|ax^2+bx+c|}{ax^2+bx+c}= \]

If \((2,3,c)\) are the direction ratios of a ray passing through the point \(C(5,q,1)\) and also the midpoint of the line segment joining the points \(A(p,-4,2)\) and \(B(3,2,-4)\), then \(c(p+7q)=\)

If the vertices and foci of a hyperbola are respectively \((\pm 3,0)\) and \((\pm 4,0)\), then the parametric equations of that hyperbola are

If \([\,]\) denotes greatest integer function, then \[ \lim_{x\to -\frac{3}{5}}\frac{1}{x}\left[\frac{-1}{x}\right] \] is

If the equation of the plane which is at a distance of \(\dfrac{1}{3}\) units from the origin and perpendicular to a line whose directional ratios are \((1,2,2)\) is \[ x+py+qz+r=0 \] then \[ \sqrt{p^2+q^2+r^2}= \]

If \(x\)-coordinate of a point \(P\) on the line joining the points \(Q(2,2,1)\) and \(R(5,2,-2)\) is \(4\), then the \(y\)-coordinate of \(P\) is

Suppose a parabola passes through \((0,4)\), \((1,9)\) and \((4,5)\) and has its axis parallel to the \(y\)-axis. Then the equation of the parabola is

A circle has its centre in the first quadrant and passes through \((2,3)\). If this circle makes intercepts of length \(3\) and \(4\) respectively on \(x=2\) and \(y=3\), its equation is

The image of the point \((3,4)\) with respect to the radical axis of the circles \[ x^2+y^2+8x+2y+10=0 \] and \[ x^2+y^2+7x+3y+10=0 \] is

The focal distances of the point \(\left(\dfrac{4}{\sqrt{5}},\dfrac{3}{\sqrt{5}}\right)\) on the ellipse \(\dfrac{x^2}{4}+\dfrac{y^2}{9}=1\) are

The ratio of the largest and shortest distances from the point \((2,-7)\) to the circle \[ x^2+y^2-14x-10y-151=0 \] is

If the normal to the rectangular hyperbola \[ x^2-y^2=1 \] at the point \(P\left(\frac{\pi}{4}\right)\) meets the curve again at \(Q(\theta)\), then \[ \sec^2\theta+\tan\theta= \]

For any real number \(t\), the point \(\left(\dfrac{8t}{1+t^2},\dfrac{4(1-t^2)}{1+t^2}\right)\) lies on a/an

A line passing through \(P(2,3)\) and making an angle of \(30^\circ\) with the positive direction of \(x\)-axis meets \[ x^2-2xy-y^2=0 \] at \(A\) and \(B\). Then the value of \(PA\cdot PB\) is

If the points of intersection of the coordinate axes and \(|x+y|=2\) form a rhombus, then its area is

Suppose, in triangle \(\triangle ABC\), \(x-y+5=0\), \(x+2y=0\) are respectively the equations of the perpendicular bisectors of the sides \(AB\) and \(AC\). If \(A=(1,-2)\), the equation of the line joining \(B\) and \(C\) is

The area of the circle passing through the points \((5,\pm 2)\), \((1,2)\) is

If the pair of straight lines \[ 9x^2+axy+4y^2+6x+by-3=0 \] represents two parallel lines, then

Which of the following is not a property of a Binomial distribution?

Suppose \(P\) and \(Q\) are the midpoints of the sides \(AB\) and \(BC\) of a triangle where \(A(1,3)\), \(B(3,7)\) and \(C(7,15)\) are vertices. Then the locus of \(R\) satisfying \[ AC^2+QR^2=PR^2 \] is

A manager decides to distribute Rs. \(20000\) between two employees \(X\) and \(Y\). He knows \(X\) deserves more than \(Y\), but does not know how much more. So, he decides to arbitrarily break Rs. \(20000\) into two parts and gives \(X\) the bigger part. Then, the chance that \(X\) gets twice as much as \(Y\) or more is