List of top Mathematics Questions asked in AP EAPCET

If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ passes through the origin, has radius 3, and its center lies on the line $x + y = 4$, then $g + f =$

If the lines joining the origin to the points of intersection of the line $y = mx + 1$ and the circle $x^2 + y^2 = 1$ are perpendicular to each other, then the value of $m^2$ is:

If the equation \[ x^2-6x+y^2+8y+9=0 \] represents a circle, then its radius is:

If \(P(3,4)\) is a fixed point and \(Q\) is a variable point on the circle \[ x^2+y^2=16, \] then the locus of the midpoint of \(PQ\) is

If \[ \log_2(x-1)+\log_2(x+1)=3, \] then \(x\) is equal to:

If for all \(x\in\mathbb{R}\), \[ \frac{1}{3} < \frac{x^2-2x+4}{x^2+2x+4} <3, \] then the values of \[ \frac{9\cdot 3^{2x}+6\cdot 3^x+4} {9\cdot 3^{2x}-6\cdot 3^x+4} \] lie between

If \[ \log_2(x-1)+\log_2(x-3)=3, \] then the value of \(x\) is

The evaluation of the indefinite integral $\int \frac{dx}{\sin x + \sin 2x}$ is:

The value of $\lim_{x \to \infty} \left(\frac{x+6}{x+1}\right)^{x+4}$ is:

If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of $\sum_{r=1}^{100} \left[ \frac{r}{5} \right]$ is:

A divisor of \[ 3^{6n}+56n-1,\qquad n\in\mathbb{N} \] is

The general solution of the differential equation \[ \frac{dy}{dx}+\frac{y}{x}=x^2 \] is

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

The surface area of a sphere is \(49\pi\) sq.cm. If it is increased by \(0.016\) sq.cm., then the approximate increase in its volume (in c.c.) 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:

The length of the tangent drawn at the point \(P(1, 3\sqrt{3})\) on the curve is \(\frac{x^2}{3} + \frac{y^2}{27} = 4\):

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

The surface area of a cube is 150 sq. cm. If it is increased by 0.025 sq. cm, then the approximate increase in its volume (in c.c.) 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 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 \(f(x)=ax^{3}+bx^{2}+cx+1\) attains an extreme value \(2\) at \(x=1\) and another extreme value at \(x=\frac{2}{3}\), then \(2b+3c\) is equal to

The length of the normal drawn to the curve \( 2x^{3}+2y^{3}=9xy \) at the point (2, 1) is

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 $2\alpha m+\beta M=$

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?