List of top Mathematics Questions on argand plane asked in UPSEE

The number of the distinct real roots of the equation $\begin{vmatrix}\sin x&\cos x&\cos x\\ \cos x&\sin x&\cos x\\ \cos x&\cos x&\sin x\end{vmatrix} = 0 $ , in the interval $ - \frac{\pi}{4} \le x \le \frac{\pi}{4}$ is

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3 - 3x^2 + 3x + 7 = 0$, and w is cube root of unity, then the value of $\frac{\alpha-1}{\beta-1} + \frac{\beta-1}{\gamma-1} + \frac{\gamma-1}{\alpha-1}$ is equal to

The perimeter of the locus represented by arg $\left( \frac{z + i}{z-i}\right) = \frac{\pi}{4}$ is equal to