List of top Mathematics Questions asked in AP EAPCET

The integral $\int \frac{1}{\cos^2 x (1 - \tan x)^2} \, dx =$
The integral $\int \frac{e^x (1 + x)}{\cos^2(x e^x)} \, dx =$
If $f(x) = \frac{k \cos x}{\pi - 2x}$ for $x \neq \frac{\pi}{2}$ and $f\left(\frac{\pi}{2}\right) = 3$ is continuous at $x = \frac{\pi}{2}$, then the value of $k$ is:
If $x = a \cos^3 t$ and $y = a \sin^3 t$, then the value of $\frac{dy}{dx}$ at $t = \frac{\pi}{4}$ is:
A balloon, which always remains spherical, has a variable radius. The rate at which its volume is increasing with respect to its radius $r$ when $r = 5$ cm is:
If $y = \tan^{-1}\left(\frac{\sin x + \cos x}{\cos x - \sin x}\right)$, then $\frac{dy}{dx} = $
If a line makes angles $45^\circ$ and $60^\circ$ with the positive $x$ and $y$ axes respectively, then the acute angle it makes with the $z$-axis is:
If $A$ and $B$ are two events such that $P(A) = 0.4$, $P(B) = 0.8$ and $P(B|A) = 0.6$, then $P(\bar{A} \cap B) =$
Let $\vec{a}$ and $\vec{b}$ be two unit vectors. If the angle between them is $\theta$, then $\cos(\theta/2) =$
If $\vec{a} = \vec{i} + \vec{j} + \vec{k}$, $\vec{b} = 4\vec{i} + 3\vec{j} + 4\vec{k}$ and $\vec{c} = \vec{i} + \alpha\vec{j} + \beta\vec{k}$ are linearly dependent vectors and $|\vec{c}| = \sqrt{3}$, then:
The number of terms in the expansion of $(x + y + z)^{10}$ is:
If $\frac{3x + 4}{(x-1)(x-2)^2} = \frac{A}{x-1} + \frac{B}{x-2} + \frac{C}{(x-2)^2}$, then $A + B + C =$
If the roots of the quadratic equation $x^2 - 2px + q^2 = 0$ are real and distinct, then:
If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, then $A^2 - 5A - 2I =$
If $z = \frac{\sqrt{3} + i}{2}$, then $z^{101} + z^{103} =$
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:
If $\sinh^{-1}(x) = \log 3$ and $\cosh^{-1}(y) = \log\left(\frac{3}{2}\right)$, then $\tanh^{-1}(x - y) =$
If \( 3\sqrt{2}x - 4y = 12 \) is a tangent to the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) and \(\frac{5}{4}\) is its eccentricity, then \( a^2 - b^2 = \)
If the normal drawn to the hyperbola \( xy = 16 \) at (8, 2) meets the hyperbola again at a point \((\alpha, \beta)\), then \( |\beta| + \frac{1}{|\alpha|} = \)
If \( \tan \theta = \frac{4}{3} \), find the value of \( \sin \theta \) in the first quadrant.
If \( \tan \theta = \frac{3}{4} \) and \( \theta \) is acute, find \( \sin 2\theta \):
The domain of the function $f(x) = \ln\left(\frac{1}{\sqrt{x^2-4x+4}}\right) + \sin^{-1}(x^2-2)$ is
The number of turning points of the curve $f(x) = 2\cos x - \sin 2x$ in the interval $[-\pi, \pi]$ is
The circles $$ x^2 + y^2 - 2x - 4y - 4 = 0 $$ and $$ x^2 + y^2 + 2x + 4y - 11 = 0 $$ ...
If the line $$ 4x - 3y + 7 = 0 $$ touches the circle $$ x^2 + y^2 - 6x + 4y - 12 = 0 $$ at $ (\alpha, \beta) $, then find $ \alpha + 2\beta $.