If the equations ax² + 2cx + b = 0 and ax² + 2bx + c = 0 $\left(\mathrm{b} \ne \mathrm{c}\right)$ have a common root, then the value of a + 4b + 4c will be

• 2

• 1

• - 1

• Non eof these

If one root of ax² + bx + c = 0 is twice the other root, then

• b² = 9ac

• 2b² = 9ac

• 2b² = ac

• b² = ac

The number of solutions of ${\mathrm{x}}^2 + 3\left|\mathrm{x}\right| + 2 = 0$ the equation is

• 0

• 1

• 2

• 4

Which of the following is correct?

• 2 + 3i > 1 + 4i

• 6 + 2i > 3 + 3i

• 5 + 8i > 5 + 7i

• None of these

${\left[\frac{- 1 + \sqrt{\left(- 3\right)}}{2}\right]}^{3\mathrm{n}} + {\left[\frac{- 1 - \sqrt{\left(- 3\right)}}{2}\right]}^{3\mathrm{n}}$ is equal to

• 0

• 1

• 2

• 3

$\mathrm{Evaluate} \sum _{\mathrm{k} = 1}^6\left(\sin \left(\frac{2\mathrm{k\pi }}{7}\right) - \mathrm{icos}\left(\frac{2\mathrm{k\pi }}{7}\right)\right)$

• 2i

• - i

• i

• - 2i

If x² - 4x + log_1/2(a) = 0 does not have two distinct real roots, then maximum value of a is

• $- \frac{1}{4}$

• $\frac{1}{16}$

• $\frac{1}{4}$

• None of these

The value of (1 + i)³ + (1 - i)⁶ is

• i

• 2(- 1 + 5i)

• 1 - 5i

• 2 + 1 - 5i

249.

If n is positive integer, then (1 + i)ⁿ + (1 - i)ⁿ is equal to

• ${\left(\sqrt{2}\right)}^{\mathrm{n} - 2}\cos \left(\frac{\mathrm{n\pi }}{4}\right)$

• ${\left(\sqrt{2}\right)}^{\mathrm{n} - 2}\sin \left(\frac{\mathrm{n\pi }}{4}\right)$

• ${\left(\sqrt{2}\right)}^{\mathrm{n} + 2}\cos \left(\frac{\mathrm{n\pi }}{4}\right)$

• ${\left(\sqrt{2}\right)}^{\mathrm{n} + 2}\sin \left(\frac{\mathrm{n\pi }}{4}\right)$

The square root of 2i is

• 1 + i

• 1 - i

• $\sqrt{2}\mathrm{i}$

• $- \sqrt{2}$