List of top Questions asked in AP ECET CSE

The value of \( \lim_{x\to\infty} \frac{4x^3 - x + 1}{x^2 - 4x(1-x^2)} \) is

The eccentricity of the ellipse \(16x^2 + 7y^2 = 112\) is

If (2,0) is the vertex and y-axis is the directrix of a parabola then its focus is

The equation of the parabola with focus (2, 0) and vertex (1, 0) is

If length of the tangent is 8 cm and the distance between the center of the circle and the external point is 11 cm, then the area of the circle is

The length of the tangent from the point (5, 1) to the circle \(x^2 + y^2 + 6x - 4y - 3 = 0\) is

In a circle with center O, a 6cm long chord is at a distance 4 cm from the center. Then the length of diameter is

Modulus of the complex number \(\frac{(1+i)^{10}}{(2i-4)^4}\) is equal to

The real part of \(\frac{1+2i}{(2-i)^2}\) is

If \(\sin \theta - \cos \theta = \frac{4}{5}\) then the value of \(\sin \theta + \cos \theta =\)

The value of \(\cos\frac{5\pi}{17} + \cos\frac{7\pi}{17} + 2\cos\frac{11\pi}{17}\cos\frac{\pi}{17}\) is

The general solution of the equation \(\tan^2 x = 1\) is

The maximum value of \(3 \cos \theta + 4 \sin \theta\) is

\(\sin^6 \theta + \cos^6 \theta + 3\sin^2 \theta \cos^2 \theta =\)

For real x and if \(x + \frac{1}{x} = 2 \cos \theta\) then \(\cos \theta\) is

If \(5 \sin \theta = 4\) then the value of \(\frac{\csc \theta - \cot \theta}{\csc \theta + \cot \theta}\) is

If \(\cos \theta \csc \theta = -1\) and \(\theta\) lies in the second quadrant then \(\cos \theta =\)

If \(\sin \theta = \frac{3}{5}\), then \(\cos \theta =\)

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 \(\frac{2x+5}{(x-1)(x+3)} = \frac{A}{x-1} + \frac{B}{x+3}\), then A+B =

If A = \(\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}\), then \((AB)^T =\)

If A = \(\begin{bmatrix} x & 3 \\ 2 & 4 \end{bmatrix}\) and A\(^{-1}\) = \(\begin{bmatrix} -2 & 1.5 \\ 1 & -0.5 \end{bmatrix}\), then the value of x is

If the matrix A is of order 3x3 and the system of equations AX = B has a unique solution, what can be concluded about the determinant of A?

If A = \(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\) and the determinant of A is 5, then determinant of the matrix 2A is

If the matrix A = \(\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}\), then which of the following is true?