List of top Mathematics Questions asked in AP EAPCET

Let $ A = \begin{bmatrix} 2 & 1 & 3 & -1 \\1 & -2 & 2 & -3 \end{bmatrix}, B = \begin{bmatrix} 2 & 1 & 0 & 3 \\1 & -1 & 2 & 3 \end{bmatrix} $, and the equation $ 2A + 3B - 5C = 0 $. Find the matrix $ C $.

The number of ordered pairs $ (x, y) $ for which $ A = \begin{pmatrix} 1 & 2 & 1 \\ 2 & 2 & x \\ y & 1 & 2 \end{pmatrix} $ is a singular and symmetric matrix is:
The domain of the function $ y = f(x) $, where $ x $ and $ y $ are related by $ 2^x + 2^y = 2 $, is:
The range of the function $ f(x) = \begin{cases} 4x - 1, & x>3 \\ x^2 - 2, & -2 \leq x \leq 3 \\ 3x + 4, & x<-2 \end{cases} $ is:

At $ x = \frac{\pi^2}{4} $, $ \frac{d}{dx} \left( \operatorname{Tan}^{-1}(\cos \sqrt{x}) + \operatorname{Sec}^{-1}(e^x) \right) = $
At $ x = \frac{\pi^2}{4} $, $ \frac{d}{dx} \left( \operatorname{Tan}^{-1}(\cos \sqrt{x}) + \operatorname{Sec}^{-1}(e^x) \right) = $

The particular solution of the differential equation \[ \frac{dx}{dy} = \frac{\sin y(1 + y \cot y)}{x \log(x^2 e)}, \quad y(1) = 0 \] Options:
Let $ a $ and $ b $ be arbitrary constants and $ C $ be a fixed constant. If $ y = ae^{2x} + bxe^{2x} + C $ is the general solution of a differential equation, then the order of that differential equation is:
The differential equation \[ y^2 \, dx + (3xy - 1) \, dy = 0 \] is:
$ \int_{0}^{\frac{\pi}{2}} \frac{\sum_{n=0}^{4} \sin \left( \frac{n\pi}{4} + x \right)}{\cos x + \sin x} dx = $
If $ \int_{n}^{n+1} g(x) \, dx = n^2 $, $ \forall n \in Z $, then the value of $ \int_{-3}^{3} g(x) \, dx $ is
If $ a = 2n $ and $ b = 2m+1 $ for all $ m, n \in \mathbb{N} $, then \[ \int_{-\pi}^{\pi} e^{\sin^2 x} \cot^{b}(2n+1) x \, dx = \]
If $ S_n = \int_0^{\frac{\pi}{2}} \frac{\sin((2n-1)x)}{\sin x} \, dx $, and $ n $ is an integer, then $ S_{n+1} - S_n = $:
$\int e^{-2x} \left( \frac{1 - \sin 2x}{1 + \cos 2x} \right) dx =$
If $ f(x) = \frac{x}{(1 + nx^n)^{1/n}} $ for $ n \geq 2 $, then \[ \int x^{n-2} f(x) \, dx = \]
The maximum value of $ a $ such that the second derivative of $ x^4 + ax^3 + \frac{3x^2}{2} + 1 $ is positive for all real $ x $ is
In the interval $ \left( \frac{1}{e}, e \right) $, a decreasing function among the following functions is:
The integral \[ \int \frac{1 + x \cos x}{x \left[ 1 - x^2 \left( e^{\sin x} \right)^2 \right]} \, dx \] Options:
$\int \frac{dx}{(x-1)\sqrt{x+2}} =$
Let $ f : \mathbb{R} \to \mathbb{R} $ be a continuous function. If $ px + my + n = 0 $ is a tangent drawn to the curve $ y = f(x) $ at $ x = \alpha $, then at $ x = 0 $, the value of \[ \frac{d}{dx} \left( f(\alpha e^{2x}) \right) \]
If the height of a cone of greatest volume that can be inscribed in a sphere of radius $ R $ is $ kR $, then the ratio of the volume of the cone to the volume of the sphere is:
If a function $ f(x) $ defined on $ [a, b] $ is discontinuous at $ x = \alpha \in (a, b) $, then:
Assertion (A): If $ f(x) $ is not continuous at $ x = a $, then it is not differentiable at $ x = a $. Reason (R): If $ f(x) $ is differentiable at a point, then it is continuous at that point.
If $ f(x) $ is differentiable on $ \mathbb{R} $, $ f(x)f'(-x) - f(-x)f'(x) = 0 $, $ f(0) = 3 $, and $ f(3) = 9 $, then $ (1 + f(-3))^3 + 1 $ is:
Let $ e $ be the eccentricity of the ellipse $ \frac{x^2}{4} + \frac{y^2}{9} = 1 $. If $ \frac{1}{e} $ is the eccentricity of a hyperbola, then the eccentricity of its conjugate hyperbola is:
The line $ x + y + 2 = 0 $ intersects the circle $ x^2 + y^2 + 4x - 4y - 4 = 0 $ in two points $ A $ and $ B $. Let $ S = x^2 + y^2 + 2gx + 2fy + c = 0 $ be a different circle passing through the points $ A $ and $ B $. If the distance of the centre of $ S $ from $ AB $ is $ \sqrt{2} $, then $ g + f + c = $: