List of top Mathematics Questions asked in AP ECET

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

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 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}

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

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 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 \(\tan^2x=1\) is

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

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

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

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

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

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

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

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

\(\displaystyle \int_{0}^{\pi/2}\frac{\cos 2x}{\sin x+\cos x}\,dx=\)

The order of the differential equation whose general solution is \(y=a\sin x+b\cos x\), where \(a\) and \(b\) are arbitrary constants, is

The RMS value of \(x^2\) in \([0,1]\) is

The differential equation \(\displaystyle \frac{dy}{dx}=-\left(\frac{x+y}{1+x^2}\right)\) is