List of top Questions asked in AP ECET- 2025

If \((2,0)\) is the vertex and \(y\)-axis is the directrix of a parabola, then its focus is
The eccentricity of the ellipse \(16x^2+7y^2=112\) is
If length of the tangent is \(8\text{ cm}\) and the distance between the center of the circle and the external point is \(11\text{ cm}\), then the area of the circle is
The value of \(\displaystyle \lim_{x\to\infty}\frac{4x^3-x+1}{x^2-4x(1-x^2)\) is}
In a circle with center \(O\), a \(6\text{ cm}\) long chord is at a distance \(4\text{ cm}\) from the center. Then the length of diameter is
The length of the tangent from the point \((5,1)\) to the circle \(x^2+y^2+6x-4y-3=0\) is
The value of \(\cos\frac{5\pi}{17}+\cos\frac{7\pi}{17}+2\cos\frac{11\pi}{17}\cos\frac{\pi}{17}\) is
If \(\sin\theta-\cos\theta=\frac{4}{5}\), then the value of \(\sin\theta+\cos\theta=\)
The real part of \(\frac{1+2i}{(2-i)^2\) is}
Modulus of the complex number \(\frac{(1+i)^{10{(2i-4)^4}\) is equal to}
\(\sin^6\theta+\cos^6\theta+3\sin^2\theta\cos^2\theta=\)
The maximum value of \(3\cos\theta+4\sin\theta\) is
If \(\sin5x+\sin3x+\sin x=0\), then the value of \(x\) other than zero lying between \(0\leq x\leq \frac{\pi}{2}\) is
The general solution of the equation \(\tan^2x=1\) is
If \[ \frac{3x-1}{(x-1)(x-2)(x-3)} = \frac{A}{x-1} + \frac{B}{x-2} + \frac{C}{x-3}, \] then the values of \((A,B,C)\) are
If \(\sin\theta=\frac{3}{5}\), then \(\cos\theta=\)
If \(\cos\theta\cosec\theta=-1\) and \(\theta\) lies in the second quadrant, then \(\cos\theta=\)
If \(5\sin\theta=4\), then the value of \(\frac{\cosec\theta-\cot\theta}{\cosec\theta+\cot\theta}\) is
For real \(x\), if \(x+\frac{1}{x}=2\cos\theta\), then \(\cos\theta\) is
If \[ \frac{2x+5}{(x-1)(x+3)} = \frac{A}{x-1} + \frac{B}{x+3}, \] then \[ A+B = \; ? \]
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 \( \int \frac{\cos 2x}{\sin^2 x \cos^2 x} \, dx = \):