Let S be the set of all persons living in Delhi. We say that x, y in S are related if they were born in Delhi on the same day. Which one of the following is correct ?

• The relation is an equivalent relation

• The relation is not reflexive but it is symmetric and transitive

• The relation is not symmetric but it is reflexive and transitive

• The relation is not transitive but it is reflexive and symmetric

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then, the number of subsets of A containing two or three elements is

• 45

• 120

• 165

• 330

The value of ${\mathrm{i}}^{2\mathrm{n}} + {\mathrm{i}}^{2\mathrm{n} + 1} + {\mathrm{i}}^{2\mathrm{n} + 2} + {\mathrm{i}}^{2\mathrm{n} + 3}$, where i = $\sqrt{ - 1}$ is

• 0

• 1

• i

• - i

If the difference between the roots of the equation x² + kx + 1 = 0 is strictly less than $\sqrt{5}, \mathrm{where} \left| \mathrm{k}\right| \ge 2$, then k can be any element of the interval

• $( - 3, - 2] \cup [2, 3)$

• ( - 3, 3)

• $\left[ - 3, - 2\right] \cup \left[2, 3\right]$

• None of the above

If the roots of the equation x² + px + q = 0 are in the same ratio as those of the equation x² + lx + m = 0, then which one of the following is correct ?

• p²m = l²q

• m²p = l²q

• m²p = q²l

• m²p² = l²q

$\mathrm{The} \mathrm{value} \mathrm{of} {\left(\frac{ - 1 + \mathrm{i}\sqrt{3}}{2}\right)}^{\mathrm{n}} + {\left(\frac{ - 1 - \mathrm{i}\sqrt{3}}{2}\right)}^{\mathrm{n}} \mathrm{where} \mathrm{n} \mathrm{is} \mathrm{not} \mathrm{a} \mathrm{multiple} \mathrm{of} 3 \mathrm{and} \mathrm{i} = \sqrt{ - 1}, \mathrm{is}$

• 1

•  - 1

• i

•  - i

Three-digit numbers are formed from the digits 1, 2 and 3 in  such a way that the digits are ot repeated. What is the sum of such three-digit numbers ?

• 1233

• 1322

• 1323

• 1332

What is the sum of the serie 0.3 + 0.33 + 0.333 +... n terms 

• $\frac{1}{3}\left[\mathrm{n} - \frac{1}{9}\left(1 - \frac{1}{{10}^{\mathrm{n}}}\right)\right]$

• $\frac{1}{3}\left[\mathrm{n} - \frac{2}{9}\left(1 - \frac{1}{{10}^{\mathrm{n}}}\right)\right]$

• $\frac{1}{3}\left[\mathrm{n} - \frac{1}{3}\left(1 - \frac{1}{{10}^{\mathrm{n}}}\right)\right]$

• $\frac{1}{3}\left[\mathrm{n} - \frac{1}{9}\left(1 + \frac{1}{{10}^{\mathrm{n}}}\right)\right]$

9.

$\mathrm{If} 1, \mathrm{\omega }, {\mathrm{\omega }}^2 \mathrm{are} \mathrm{the} \mathrm{cube} \mathrm{roots} \mathrm{of} \mathrm{unity}, \mathrm{then} (1 + \mathrm{\omega })(1 + {\mathrm{\omega }}^2)(1 + {\mathrm{\omega }}^3)(1 + \mathrm{\omega } + {\mathrm{\omega }}^2) \mathrm{is} \mathrm{equal} \mathrm{to}$

•  - 2

•  - 1

• 0

• 2

If the sum of m terms of an AP is n and the sum of n terms is m, then the sum of (m + n) terms is

• mn

• m + n

• 2(m + n)

• - (m + n)