List of top Questions asked in AP EAPCET

The closest point on the parabola \[ y=x^2+7x+2 \] to the straight line \[ y=3x-2 \] is

If the vertical angle of a cone is \(60^\circ\) and the rate of change of its total surface area is \(2\sqrt{3}\,\text{cm}^2/\text{sec}\), then the rate of change of its volume (in \(\text{cm}^3/\text{sec}\)) when its radius is \(5\) cm is:

Approximate value of \( \sqrt[3]{345} \), when it is calculated with the application of derivatives, is

If the displacement of a particle at time $t$ ($0 < t < \pi$) is given by $s = 3 \sin 2t - 6 \cos t$, then the acceleration for the values of $t$ at which its velocity is zero is:

If \(f(x)=ax^{3}+bx^{2}+cx+1\) attains an extreme value \(2\) at \(x=1\) and another extreme value at \(x=\frac{2}{3}\), then \(2b+3c\) is equal to

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be such that $f(2+x)=f(2-x)\,\,\forall x\in\mathbb{R}$. If $f(x)$ is twice differentiable such that $f^{\prime}(1)=0$, then which one of the following is true?

If the rate of increase in the surface area of a cube is 6 sq. cm./sec., then the rate of increase in its volume (in c. c./sec), when the length of its edge is 12 cm, is

The function \(f(x) = \frac{x}{2} + \frac{2}{x}\) has a local minimum at

If a sector of maximum area is made with a wire of length 40 cm, then the area (in sq cms) of that sector is

If a cylindrical tank of radius 3 m is filled with water at the rate of \(\frac{3}{2} \, m^3/sec \), then the rate of change of its water level in (m/sec) is:

The cubic equation \[ 2x^3-3x^2+6x+2=0 \]

If the local maximum 'M' and local minimum 'm' of the function $f(x)=x-\frac{x^{2}}{2}-xe^{2-x}$ exist at $x=\alpha$ and $x=\beta$ respectively, then $2\alpha m+\beta M=$

The equation of the conjugate hyperbola of the hyperbola $x^{2}-4y^{2}-2x-8y-19=0$ is

If the major axis of an ellipse subtends an angle of $120^{\circ}$ at one end of its minor axis and the length of its semi latus rectum is $\frac{4}{\sqrt{3}}$, then the sum of the lengths of its axes is

The equation of the tangent to the parabola $y^2 = 8x$ which is parallel to the line $2x - y + 5 = 0$ is:

If the eccentricity of a hyperbola is $\sqrt{3}$, then the eccentricity of its conjugate hyperbola is:

The equation of the parabola with focus at $(3, 0)$ and directrix $x + 3 = 0$ is:

Through the focus of the parabola $x^{2}-4x-8y+44=0$, if tangents are drawn to another parabola $y^{2}=20x$, then the sum of the Y - coordinates of the points of contact of these tangents is

If the distance of a point P on an ellipse from its focus (1, 2) is half of the distance of P from its corresponding directrix \( x+y=0 \), then the point of intersection of the given directrix and its major axis, is

A chord is drawn through the focus of the parabola \(y^2=6x\) such that its perpendicular distance from the vertex is \(\frac{\sqrt5}{2}\). Then its slope can be:

Let S be the focus of the parabola \( y^{2}=36x \) and let the line \( x+by+c=0 \) intersect the parabola at the points Q and R. If the centroid of \( \triangle QRS \) is (57,0), then -c is

If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is:

A normal is drawn to the hyperbola \( 9x^{2}-16y^{2}=144 \) at one of the ends of its latus rectum. If that end lies in the third quadrant and the equation of the normal is \( ax+by+c=0 \) then \( \frac{b+c}{a} = \)

If $y=mx+c$, $m>0$ is a common tangent to the parabolas $y^{2}=8x$ and $y^{2}=1+4x$, then $m+c=$

A perpendicular is drawn through the vertex \(O\) of the parabola \(y^2=8x\) to any non-vertical tangent meeting the parabola at \(P\). Then \(OP.OQ=\)