List of top Mathematics Questions asked in AP EAPCET

Let A, A' be the end points of major axis, S, S' be the foci and B, B' be the end points of minor axis of an ellipse E. If $\angle \text{BAB}' = 60^\circ$, then $\angle \text{SBS}' =$
The equation of the pair of asymptotes of the hyperbola $x^2 - 2y^2 - 8x + 8y + 4 = 0$ is
Let the points $P_1(\frac{\pi}{4}), P_2(\frac{3\pi}{4}), P_3(\frac{5\pi}{4}), P_4(\frac{7\pi}{4})$ lie on the hyperbola $\frac{x^2}{9} - \frac{y^2}{16} = 1$. Then they form:
If $f(g(x+y)) = f(g(x)) + f(g(y))$, $g(1)=2$, $f(2)=1$, then $g(f(x))$ is discontinuous on:
The polar of a point with respect to the circle \( x^2 + y^2 - 10x + 12y - 3 = 0 \), which is not a tangent and not a chord of contact, is:

If $f(x) = \frac{1 - x + \sqrt{9x^2 + 10x + 1}}{2x}$, then $\lim_{x \to -1^-} f(x) =$

Which one of the following functions is discontinuous at $x=1$?
If the tangent to the curve $x^3y^2 + \dfrac{x^2}{y} = 5$ is parallel to X-axis, then a point on its locus is:

Given \( f(x) = \begin{cases} \frac{1}{2}(b^2 - a^2), & 0 \le x \le a \\[6pt] \frac{1}{2}b^2 - \frac{x^2}{6} - \frac{a^3}{3x}, & a<x \le b \\[6pt] \frac{1}{3} \cdot \frac{b^3 - a^3}{x}, & x>b \end{cases} \). Then:

The area (in sq units) of the triangle formed by the normal at point $(1,0)$ on the curve $x = e^{\sin y}$ with coordinate axes is:
If the tangent drawn to the curve $(x^2+1)(y-3)=x$ at a point P, lying in the first quadrant, is a horizontal line, then the equation of the normal at the point P is
The slope of the tangent at any point $(x,y)$ on the curve is equal to the product of the coordinates of that point. If the equation of the normal to the curve at the point $(\sqrt{2},e)$ is $ax+by=1$, then $\dfrac{b}{a}=$
The curve represented by $x = t^5 + 5t^3 + 20t + 7$ and $y = 4t^3 - 3t^2 - 18t + 3$ is decreasing in the interval

$\displaystyle \int \frac{dx}{\sin(x-a)\cos(x-b)} =$

If $I_n = \int \tan^n x \, dx \quad (n>1)$, then $I_4 + I_6 =$

If $\int \sqrt{x}(1-x^3)^{-1/2} dx = \frac{2}{3}g(f(x))+c$, then

$\int \frac{x^2}{(x^2-1)(x^2+1)} dx =$

Let $f:\mathbb{R} \to \mathbb{R}$ be a differentiable function such that $|f(x)-f(y)| \le 2|x-y|^{3/2} \ \forall x,y \in \mathbb{R}$. If $f(0)=1$, then $\int_0^1 f^2(x)dx=$
$\int_0^\pi x \sin^3 x \cos^2 x\ dx =$
If $\int_0^{2\pi} |x \sin x| dx = k\pi$, then $k=$

$\displaystyle \int_{\frac{1}{25}}^{1} x^{-2} e^{x^{-1/2}} dx =$

The area (in sq. units) bounded by the curves $y=\frac{8}{x}$, $y=2x$ and $x=4$ is

Which one of the following is a linear differential equation?
If $X=x+h, Y=y+k$ transforms $\frac{dy}{dx} = \frac{2x+3y-7}{3x+2y-8}$ to a homogeneous differential equation, then $(h,k)=$
If $\log y$ is an integrating factor of $\frac{dx}{dy}+P(y)x=Q(y)$, then $P(y)=$