AIEEE 2005 Maths Question Paper Mock Test

If $z_1$ and $z_2$ are two non-zero complex numbers such that $|z_1+z_2|=|z_1|+|z_2|$, then $\arg z_1-\arg z_2$ is equal to:

If $\omega =\frac{z}{z-(i/3)}$ and $|\omega |=1$, then $z$ lies on:

If $a^2+b^2+c^2=-2$ and $f(x)=\left|\begin{array}{ccc}1+a^{2}x& (1+b^2)x& (1+c^2)x\\ (1+a^2)x& 1+b^{2}x& (1+c^2)x\\ (1+a^2)x& (1+b^2)x& 1+c^{2}x\end{array}\right|$, then $f(x)$ is a polynomial of degree:

The normal to the curve $x=a(\cos \theta +\theta \sin \theta )$, $y=a(\sin \theta -\theta \cos \theta )$ at any point $\theta$ is such that:

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?