The quadratic equation whose roots are $\frac{1}{3 + \sqrt{2}} \mathrm{and} \frac{1}{3 - \sqrt{2}}$, will be

• 7x² - 6x + 1 = 0

• 6x² - 7x + 1 = 0

• x² - 6x + 7 = 0

• x² - 7x + 6 = 0

If z = $\mathrm{ilog}\left(2 - \sqrt{3}\right)$, then the value of cos(Z) will be

• i

• 2i

• 1

• 2

The value of ${\left(\sqrt{5} + 1\right)}^5 - {\left(\sqrt{5} - 1\right)}^5$ is

• 232

• 352

• 452

• 532

The value of i² + i⁴ + i⁶ + ... (2n + 1) terms is

• - 1

• 1

• - i

• i

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

180.

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

• $\frac{1}{2}$

• $\frac{1}{3}$