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

162.

The value of (1 + i)³ + (1 - i)⁶ is

• i

• 2(- 1 + 5i)

• 1 - 5i

• 2 + 1 - 5i

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

• $\sqrt{2}\mathrm{i}$

• $- \sqrt{2}$

The root ofthe equation 2x - log₁₀(x) = 7 is between

• 3 and 3.5

• 2 and 3

• 3.5 nad 4

• None of these

The roots of the quadratic equation 2x² + 3x + 1 = 0 are

• rational

• irrational

• imaginary

• None of these

Roots of equation x³ - 6x + 1 = 0 lie in the interval

• (2, 3)

• (3, 4)

• (3, 5)

• (4, 6)

If $\frac{{\left(3 - \mathrm{i}\right)}^2}{2 + \mathrm{i}} = \mathrm{A} + \mathrm{iB}$ where A and B are real numbers, then A and Bare equal to

• A = - 4, B = 2

• A = 2, B = - 4

• A = 2, B = 4

• None of these

If 1, w and w² are the cube roots of unity, then the value of (1 - w + w²)(1 + w - w²) is equal to

• 4

• 0

• 2

• 3

The sum of the real solutions of equation $2{\left|\mathrm{x}\right|}^2 + 51 = \left|1 + 20\mathrm{x}\right|$ is

• 5

• 24

• 0

• None of these