List of top Questions asked in AP ECET- 2025

If \( A = \begin{pmatrix} 2 & x + 9 \\ 1 & 2x \end{pmatrix} \) is invertible, then \( x \neq \):
The coefficient of \( (y-2) \) in the Taylor's series expansion of \( f(x, y) = x^2 + xy + y^2 \) in powers of \( (x-1) \) and \( (y-2) \) is:
The equation of the circle with extremities \( (1, 3) \) and \( (5, 7) \) of the diameter is:
The centre of the circle of curvature for the curve \( y = e^x \) at \( (0, 1) \) is:
The integral value of \( \int \frac{\cos 2x}{\sin^2 x \cos^2 x} \, dx = \):
The curvature of the straight line \( y = 2x + 3 \) at \( (1, 5) \) is: