11.

If $\mathrm{\alpha }, \mathrm{\beta }$ be the roots of the quadratic equation x² + x + 1 = 0, then the equation whose roots are ${\mathrm{\alpha }}^{19}. {\mathrm{\beta }}^7$ f is

• x² - x + 1 = 0

• x² - x - 1 = 0

• x² + x - 1 = 0

• x² + x + 1 = 0

The roots of the quadratic equation ${\mathrm{x}}^2 - 2\sqrt{3}\mathrm{x} - 22 = 0$ are

• imaginary

• real, rational and equal

• real, irrational and unequal

• real, rational and unequal

The quadratic equation x² + 15$\left|\mathrm{x}\right|$ + 14 = 0 has

• only positive solutions

• only negative solutions

• no solution

• both positive and negative solution

If $\mathrm{z} = \frac{4}{1 - \mathrm{i}}$, then $\overline{\mathrm{z}}$ is (where $\overline{z}$ is complex conjugate of z)

• 2(1 + i)

• (1 + i)

• $\frac{2}{1 - \mathrm{i}}$

• $\frac{4}{1 + \mathrm{i}}$

If

• π

• - π

• π/2

• - π/2

Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is

• $\frac{1}{36}$

• $\frac{3}{36}$

• $\frac{11}{36}$

• $\frac{20}{36}$

The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A') + P(B') is

• 0.9

• 0.15

• 1.1

• 1.2

The value of $\frac{{\log }_3\left(5\right) \times {\log }_{25}\left(27\right) \times {\log }_{49}\left(7\right)}{{\log }_{81}\left(3\right)}$ is

• 1

• 6

• $\frac{2}{3}$

• 3

In a right-angled triangle, the sides are a, b and c with c as hypotenuse and c - b $\ne$ 1, c + b $\ne$ 1. Then the value of (log_{c + b}(a) + log_{c - b}(a))/ (2log_{c + b}(a) x log_{c - b}(a)) will be

• 2

• - 1

• $\frac{1}{2}$

• 1

Sum of n terms of the following series 1³ + 3³ + 5³ + 7³ + ... is

• n²(2n² - 1)

• n³(n - 1)

• n³ + 8n + 4

• 2n⁴ + 3n²