List of top Mathematics Questions asked in AP EAPCET

The rank of the matrix \( \begin{bmatrix} 2 & -3 & 4 & 0 \\ 5 & -4 & 2 & 1 \\ 1 & -3 & 5 & -4 \end{bmatrix} \) is
If \( P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} \) is the adjoint of a matrix \( A \) and \( \det(A) = 4 \), then the value of \( \alpha \) is:
If \( 11^{12} - 11^2 = k(5 \times 10^9 + 6 \times 10^9 + 33 \times 10^8 + 110 \times 10^7 + \ldots + 33) \), then find the value of \( k \).
If \( f(x) = (x+1)^2 - 1, x \ge -1 \), then \( \{x \mid f(x) = f^{-1}(x)\} \) is:
Let \( [t] \) denote the greatest integer function and \( [t - m] = [t] - m \) when \( m \in \mathbb{Z} \). If \( k = 2[2x - 1] - 1 \) and \( 3[2x - 2] + 1 = 2[2x - 1] - 1 \), then the range of \( f(x) = [k + 5x] \) is:
Evaluate \( \int \frac{\sec^2 x}{\sin^7 x} \, dx - \int \frac{7}{\sin^7 x} \, dx \):
In triangle $ ABC $, if $ a = 13 $, $ b = 8 $, $ c = 7 $, then $ \cos(B+C) = $
In a triangle ABC, if \((r_1 - r_3)(r_1 - r_2) - 2r_2r_3 = 0\), then \(a^2 - b^2 =\)
If $ \alpha, \beta, \gamma $ are the roots of the equation $ x^3 + px^2 + qx + r = 0 $, then $ \alpha^3 + \beta^3 + \gamma^3 = $
The set of all real values of $x$ such that \[ f(x) = \frac{[x] - 1}{\sqrt{[x]^2 - [x] - 6}} \] is a real valued function is
If a function $f : \mathbb{Z} \to \mathbb{Z}$ is defined by $f(x) = x - (-1)^x$, then $f(x)$ is
If $(3 + 4i)^{2025} = 5^{2023}(x + iy)$, then find $\sqrt{x^2 + y^2}$.
If \[ \left(\frac{\cos \theta + i \sin \theta}{\sin \theta + i \cos \theta}\right)^{2024} + \left(\frac{1 + \cos \theta + i \sin \theta}{1 - \cos \theta + i \sin \theta}\right)^{2025} = x + iy, \] and $x + y$ at $\theta = \frac{\pi}{2}$ is
If \(x\) is a real number, then the number of solutions of \(\tan^{-1}\left(\sqrt{x(x+1)}\right) + \sin^{-1}\left(\sqrt{x^2 + x + 1}\right) = \dfrac{\pi}{2}\) is
Domain of the real-valued function \(f(x) = \log(x^2 - 1) + x \, \coth^{-1}x\) is
One of the latus recta of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ subtends an angle $2 \tan^{-1} \left(\frac{3}{2}\right)$ at the centre of the hyperbola. If $b^2 = 36$ and $e$ is the eccentricity of the hyperbola, then find $\sqrt{a^2 + e^2}$.
If $L$ is the normal drawn to the parabola $y^2 = 8x$ at the point $t = \frac{1}{\sqrt{2}}$, then the foot of the perpendicular drawn from the focus of the parabola onto the normal $L$ is:
If the acute angle between the circles $S \equiv x^2 + y^2 + 2kx + 4y - 3 = 0$ and $S^1 \equiv x^2 + y^2 - 4x + 2ky + 9 = 0$ is $\cos^{-1}\left(\frac{3}{8}\right)$ and the centre of $S^1 = 0$ lies in the first quadrant, then the radical axis of $S = 0$ and $S^1 = 0$ is:
If \((1+x)^n = \sum_{r=0}^n \binom{n}{r} x^r\), then the value of \[ C_0 + (C_0 + C_1) + (C_0 + C_1 + C_2) + \cdots + (C_0 + C_1 + \cdots + C_n) \] is:
Evaluate the integral \[ \int_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}} \frac{1}{\left(x + \sqrt{1 - x^2}\right) \cdot \left(1 - x^2\right)} \, dx = \]
The area of the region (in sq. units) enclosed between the curves \( y = |x| \), \( y = [x] \) and the ordinates \( x = -1, x = 0, x = 1 \) is
\( \int \frac{1 + x + \sqrt{x + x^2}}{\sqrt{x + \sqrt{1 + x}}} dx = \)
If \( \int \frac{dx}{(x-1)^2(x-3)^2 = \sqrt{f(x)} + c \), then \( f(-1) - f(0) = \)}
Evaluate the integral $\displaystyle \int_0^{\frac{\pi{2}} \log(\tan x + \cot x)\, dx$}
Evaluate the integral \[ \int_{0}^{\pi} x \cdot \sin x \cdot \int_{x}^{5} \frac{\cos x}{x} \cdot dx = \]