The argument of the complex number $- 1 + \mathrm{i}\sqrt{3}$ is

• 45°

• 60°

• 120°

• 150°

If the roots of the equation x² + px + q = 0 differ by 1, then

• p² = 4q + 1

• p² = 4q

• p² = 4q - 1

• p² = - 4q

If $\mathrm{x} = 9^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} 9^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$9$}\right.} 9^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$27$}\right.} ... \infty$, $\mathrm{y} = 4^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} 4^{\raisebox{1ex}{$- 1$}\!\left/ \!\raisebox{-1ex}{$9$}\right.} 4^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$27$}\right.} ... \infty$ and $\mathrm{z} = \sum _{\mathrm{r} = 1}^{\infty }{\left(1 + \mathrm{i}\right)}^{- \mathrm{r}}$, then arg (x + yz) will be

• $- {\tan }^{-1}\left(\frac{2}{\sqrt{3}}\right)$

• $- {\tan }^{-1}\left(\frac{\sqrt{2}}{3}\right)$

• $\mathrm{\pi } - {\tan }^{-1}\left(\frac{\sqrt{2}}{3}\right)$

• 0

If z = x + iy is a complex numberwhere x and y are integers. Then, the area of the rectangle whose vertices are the roots of the equation $\mathrm{z}{\overline{\mathrm{z}}}^3 + \overline{\mathrm{z}}{\mathrm{z}}^3 = 350$, is

• 48

• 32

• 40

• 90

How many real roots does the quadratic equation f(x) = x ² + 3$\left|\mathrm{x}\right|$ + 2 = 0 have ?

• One

• Two

• Four

• No real root

If $\mathrm{\alpha }, \mathrm{\beta }$ are the roots of the equation x² + bx + c = 0 and a$\mathrm{\alpha } + \mathrm{h}, \mathrm{\beta } + \mathrm{h}$ are the roots of the equation x² + qx + r = 0, then h is equal to

• b + q

• b - q

• $\frac{1}{2}\left(\mathrm{b} + \mathrm{q}\right)$

• $\frac{1}{2}\left(\mathrm{b} - \mathrm{q}\right)$

Each of the roots of the equation x³ - 6x² + 6x - 5 = 0 are increased by h. So that the new transformed equation does not contain x term, then h is equal to

• 1

• 2

• $\frac{1}{2}$

• $\frac{1}{3}$

If 1 is a multiple root of order 3 for the equation x⁴ - 2x³ + 2x - 1 = 0, then the other root is

• 0

• - 1

• 1

• 2

The biquadratic equation, two of whose roots are $1 + \mathrm{i}, 1 - \sqrt{2}$, is

• x⁴ - 4x³ + 5x² - 2x - 2 = 0

• x⁴ + 4x³ - 5x² + 2x + 2 = 0

• x⁴ + 4x³ - 5x² + 2x - 2 = 0

• x⁴ + 4x³ + 5x² - 2x + 2 = 0

270.

If the equations x² + ax + b = 0 and x² + bx + a = 0(a ± b) have a common root, then a + b is equal to

• - 1

• 1

• 3

• 4