List of top Mathematics Questions asked in AP ECET

\[ \int \frac{dx}{\sin^2x\cos^2x}= \]

If \[ z=x^2y^3+e^y\sin x, \] then \[ \frac{\partial^2 z}{\partial x\partial y}= \]

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

\[ \lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x= \]

Slope of the tangent to the curve \[ y=9x^2+7x^4+5 \] at the point \(x=1\) is

If \[ y=\sqrt{x+\sqrt{x+\sqrt{x+\cdots\infty}}}, \] then \[ \frac{dy}{dx}= \]

\[ \lim_{x\to 0}\frac{\sqrt{1+x}-1}{x}= \]

If \[ y=\frac{a\cos x+b\sin x+c}{\sin x}, \] then \[ \frac{dy}{dx}= \]

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

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

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

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

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

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

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

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

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

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

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