List of top Questions asked in AP ECET

If \[ 2^x+2^y=2^{x+y}, \] then \[ \frac{dy}{dx}= \]

If \[ y+\sin^{-1}(1-x^2)=e^x, \] then \[ \frac{dy}{dx}= \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Which of the following is a Metamorphic rock?

Granite is an example of

Which type of rock is formed from cooling Lava or Magma?