If the harmonic mean between the roots of (5 + $\sqrt{2}$) x² - bx + (8 + 2$\sqrt{5}$) = 0 is 4, then the value of b is

• 2

• 3

• 4 - $\sqrt{5}$

• $4 + \sqrt{5}$

The set of solutions satisfying both x² + 5x + 6 $\ge$ 0 and x² + 3x - 4 < 0 is

• (- 4, 1)

• $\left(- 4, - 3\right) \cup (- 2, 1)$

• $\left(- 4, - 3\right) \cup \left(- 2, 1\right)$

• $\left(- 4, - 3\right) \cup \left( - 2, 1\right)$

The relation between pressure p and volume V is given by pV^1/4 constant. If the percentage decrease in volume is 1/2, then the percentage increase in pressure is

• $- \frac{1}{8}$

• $\frac{1}{16}$

• $\frac{1}{8}$

• $\frac{1}{2}$

The least positive integer n for which (1 + i)ⁿ = (1 - i)ⁿ , is

• 8

• 2

• 4

• 6

If the mean and variance of a binomial variate X are 8 and 4 respectively, then P(X < 3) equals to 

• $\frac{265}{2^{15}}$

• $\frac{137}{2^{14}}$

• $\frac{137}{2^{16}}$

• $\frac{265}{2^{16}}$

If ${\mathrm{x}}_1, {\mathrm{x}}_2, ... , {\mathrm{x}}_{\mathrm{n}}$ are n observations such that $\sum _{\mathrm{i} = 1}^{\mathrm{n}}{{\mathrm{x}}_1}^2 = 400 \mathrm{and} \sum _{\mathrm{i} = 1}^{\mathrm{n}}{\mathrm{x}}_1 = 80$, then the least value of n is 

• 18

• 12

• 15

• 16

If $\left|\mathrm{x}\right|$ < 1, then the coefficient of x⁵ in the expansion of $\frac{3\mathrm{x}}{\left(\mathrm{x} - 2\right)\left(\mathrm{x} + 1\right)}$ is

• $\frac{33}{32}$

• $\frac{- 33}{32}$

• $\frac{31}{32}$

• $\frac{- 31}{32}$

If the coefficients of x⁹, x1⁰ and x¹¹ in the expansion of (1 + x)ⁿ are in arithmetic progression, then n² - 41n is equal to

• 399

• 298

• - 398

• 198

The probability that an event does not happen in one trial is 0.8. The probability that the event happens atmost once in three trials is

• 0.896

• 0.791

• 0.642

• 0.592

 $$\begin{gathered} \mathrm{If} 1, {\mathrm{z}}_1, {\mathrm{z}}_2, ..., {\mathrm{z}}_{\mathrm{n} - 1} \mathrm{are} \mathrm{the} \mathrm{nth} \mathrm{roots} \mathrm{of} \mathrm{unity}, \\ \mathrm{then} \left(1 - {\mathrm{z}}_1\right)\left(1 - {\mathrm{z}}_2\right) ... \left(1 - {\mathrm{z}}_{\mathrm{n} - 1}\right) = ? \end{gathered}$$

• 0

• n - 1

• n

• 1