List of top Mathematics Questions asked in AP EAPCET

A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is

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 \(x\neq0\) 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 \[ \lim_{x\to \alpha}\frac{|ax^2+bx+c|}{ax^2+bx+c}= \]

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

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

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 \(x\)-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

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 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 \[ \sqrt{p^2+q^2+r^2}= \]

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

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

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

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 \[ \sec^2\theta+\tan\theta= \]

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

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

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

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

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

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

Suppose \(\triangle ABC\) is an isosceles triangle with \(\angle C=90^\circ\), \(A=(2,3)\) and \(B=(4,5)\). Then the centroid of the triangle is