List of top Mathematics Questions asked in AP EAPCET

If \( z = 1 + \cos\theta - i\sin\theta \) and \( 0<\theta<\pi \), then \[ \left[ |z - 1|^2 \cdot \frac{|z|^2}{4} \right]^{1/2} = \]
In the Argand plane, the values of \( z \) satisfying the equation \( |z - 1| = |i(z + 1)| \) lie on:
If \( 1, \omega, \omega^2 \) are the cube roots of unity and \( f(x, y) = (x + y)(x\omega + y\omega^2)(x\omega^2 + y\omega) \), then \( f(2, 3) \) is:
If \( \csc\theta \) and \( \cot\theta \) are the roots of \( cx^2 + bx + a = 0 \) where \( bc \neq 0 \), then evaluate \( b^2(b^2 - 4ac) \):
If \( A + 2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix} \) and \( 2A - B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix} \), then \( \text{Tr}[A] - \text{Tr}[B] \) equals:
If \( A = \begin{bmatrix} 2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2 \end{bmatrix} \) is expressed as a sum of a symmetric matrix \( P \) and a skew-symmetric matrix \( Q \), then \( P^T - Q^T \) equals:
The sum of the distinct values of \( x \) for which the matrix \( A = \begin{bmatrix} 1 & 1 & x \\ 1 & x & 1 \\ x & 1 & 1 \end{bmatrix} \) has no inverse, is:
If \( f : \mathbb{R} \setminus \{0\} \to \mathbb{R} \) is defined by \( f(x) = x + \frac{1}{x} \), then the value of \( \left(f(x)\right)^2 \) is:
The range of the real valued function \( f(x) = \sqrt{9 - x^2} \) is:
If \( y = y(x) \) is the solution of the differential equation \[ x \frac{dy}{dx} = y + xe^{-\frac{y}{x}}, \quad y(1) = \log e \] , then \( y(e) = \)
The order and degree of the differential equation \[ 3x^2 \frac{d^2 y}{dx^2} - \sin\left( \frac{d^3 y}{dx^3} \right) + \cos(xy) = 0 \] are:
Let \( c_1, c_2, c_3, c_4 \) be arbitrary constants. The order of the differential equation corresponding to \[ y = c_1 e^x + c_2 e^{\log_e x} + c_3 \sin^2 x - c_4 (\cos^5 x - 1) \] is:
If \( 5f(x) + 3f\left( \frac{1}{x} \right) = 2 - \frac{1}{x}, x \ne 0 \), then \( \int_1^2 f\left( \frac{1}{x} \right) dx = \)
If \[ f(x) = \lim_{n \to \infty} n^2 \left( \frac{1}{x^n} - \frac{1}{x^{n+1}} \right), x>0, \] then \[ \int x f(x) \, dx = ? \]
Evaluate the following integral: \[ \int \frac{1 - \cos x}{\cos x(1 + \cos x)} \, dx \]
If \( g(x) \) is an antiderivative of \( f(x) = 1 + 2 \log 2 \) and the graph of \( y = g(x) \) passes through the point \( \left( -1, -\frac{1}{2} \right) \), then the curve meets the Y-axis at
If \[ \int \frac{x^3}{\sqrt{1 + x^2}} \, dx = A(1 + x^2)^{\frac{3}{2}} + B(1 + x^2)^{\frac{1}{2}} + C, \text{ then } A + B = \]
Evaluate the integral: \[ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1 + \sqrt{\cot x}} \, dx = \]
The area bounded by the curves \( y = x^2 \) and \( y - 6 = -|x| \) is:
If \( m \in \mathbb{Z}^+, n = 2m \) and \[ \int_0^{\frac{\pi}{2}} \sin^n x \cos^m x \, dx = K(m) \int_0^{\frac{\pi}{2}} \sin^m x \, dx, \text{ then } \frac{2^{n-1}(m - 1)!}{(2m - 1)!} \cdot K(m) = \]
If \( \alpha \in \mathbb{R} \setminus \{-1\} \) and \[ f(x) = |x| + \alpha |x|(|x| - 1), \] then the number of points at which \( f(x) \) is not differentiable is:
An extreme value of \( f(x) = \frac{4}{\sin x} + \frac{1}{1 - \sin x} \) in \( (0, \frac{\pi}{2}) \) is:
If \[ f(t) = \frac{t}{2} - \frac{1}{4} \log(2t - 1), \] then \[ f'\left( \frac{t + 1}{2t + 1} \right) = ? \]
If the tangent drawn to the curve \( y = x^3 \) at point \( (\alpha, \beta) \) cuts again the curve at another point \( (\alpha_1, \beta_1) \), then \( \frac{\beta_1}{\beta} = \):
If \( \theta \) is the angle made by the normal drawn to the curve \[ x = e^t \cos t, \quad y = e^t \sin t \] at the point \( (1, 0) \) with the X-axis, then \( \theta = \):