List of top Questions asked in AP EAPCET

The period of the function \[ f(x)=\log(\cos x)+\cot^4\left(\frac{x}{2}\right)+\sin(3x+7) \] is

For \(\theta\in\left(0,\frac{\pi}{2}\right)\), if the complete range of \[ (\cot^2\theta-\cos^2\theta)(\tan^2\theta-\sin^2\theta) \] is \((\alpha,\beta]\), then \(\beta-\alpha=\)

If \[ \tan\alpha=-\frac{7}{24}, \qquad \sec\beta=\frac{61}{60} \] and both \(\alpha,\beta\) lie in the same quadrant, then \[ \cos(\alpha+\beta)= \]

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

The equation of the common chord of the circles $x^2 + y^2 - 4x - 4y = 0$ and $x^2 + y^2 - 6x - 8y + 10 = 0$ is:

If the circle $x^2 + y^2 + 2x - 2y + c = 0$ cuts the circle $x^2 + y^2 - 4x - 6y + 11 = 0$ orthogonally, then the value of $c$ is:

The length of the intercept made by the circle $x^2 + y^2 - 10x + 4y + 9 = 0$ on the x-axis 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 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 \[ \log_2(x-1)+\log_2(x+1)=3, \] 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:

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

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 slope of the normal to the curve $y = 2x^2 + 3\sin x$ at $x = 0$ 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:

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