List of top Mathematics Questions asked in AP ECET

The equation of the ellipse with foci at \((\pm 3,0)\) and the eccentricity as \(1/3\) is:

The length of the latus rectum and eccentricity of the Hyperbola \(9x^2-16y^2=144\) are

The line \(y=mx+2\) is a tangent to the parabola \(y^2=8x\) if

If the parabola \(y^2=4ax\) passes through the point \((3,2)\), then the length of its latus rectum is:

The equation of a circle whose Centre is \((2,-1)\) and which passes through the point \((3,6)\) is

The equation of a circle whose Centre is \((-3,2)\) and area is \(176\) units is

The conjugate of \( (1+i)^3 \) is

If \( z_1=4i^{40}-5i^{35}+6i^{17}+2,\ z_2=-1+i \), then \( |z_1+z_2|= \)

\[ \tan^{-1}1+\tan^{-1}2+\tan^{-1}3= \]

\[ \cos 6^\circ \sin 24^\circ \cos 72^\circ= \]

If \( \cos\theta=\frac{1}{2}\left(a+\frac{1}{a}\right) \), then \(4\cos^3\theta-3\cos\theta=\)

\[ \tan 9^\circ-\tan 27^\circ-\tan 63^\circ+\tan 81^\circ= \]

\[ \frac{\tan x-1+\sec x}{\tan x-\sec x+1} = \]

If \( \tan\theta+\sec\theta=\sqrt{3} \), then the principal value of \( \theta \) in \( [0,2\pi] \) 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?

If \[ \sin^{-1}\frac{5}{x}+\sin^{-1}\frac{12}{x}=\frac{\pi}{2}, \] then \(x=\)

If \(2\sin^{-1}x=\sin^{-1}k\), then \(k=\)

If \(\tan A=\frac{1}{2}\) and \(\tan B=\frac{1}{3}\), then \(A+B=\)

If \[ \frac{x+4}{(x+2)^2(x+3)} = \frac{A}{(x+2)^2} + \frac{B}{x+2} + \frac{C}{x+3}, \] then \(A+B+C=\)

If \[ \frac{x}{(x-1)^2(x+2)} = \frac{A}{(x-1)^2} + \frac{2}{9(x-1)} + \frac{B}{x+2}, \] then \(A+B=\)

If \[ \begin{bmatrix} x+y & 2 1 & x-y \end{bmatrix} = \begin{bmatrix} 4 & 2 1 & 2 \end{bmatrix}, \] then the values of \(x\) and \(y\) are:

The number of solutions of the equation \( \sin 2x-\cos 2x=2-\sin 2x \) lying in the interval \( [0,\pi] \) is

The particular integral of \(\displaystyle \frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=e^{-2x}\) is

The solution of the differential equation \(\displaystyle \frac{dy}{dx}+\frac{y}{x}=x^2\) under the condition that \(y(1)=1\) is

The solution of the differential equation \(\displaystyle \frac{d^3y}{dx^3}+3\frac{d^2y}{dx^2}+2\frac{dy}{dx}=0\) is