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?
A.
The relation is an equivalence relation
B.
The relation is not reflexive but it is symmetric and transitive
C.
The relation is not symmetric but it is reflexive and transitive
D.
The relation is not transitive but it is reflexive and symmetric
If the difference between the roots of the equation \( x^{2} + kx + 1 = 0 \) is strictly less than \( \sqrt{5} \), where \( |k| \geq 2 \), then k can be any element of the interval
If the roots of the equation \( x^{2} + px + q = 0 \) are in the same ratio as those of the equation \( x^{2} + lx + m = 0 \), then which one of the following is correct?
The value of \( \left(\frac{-1+i\sqrt{3}}{2}\right)^{n} + \left(\frac{-1-i\sqrt{3}}{2}\right)^{n} \), where n is not a multiple of 3 and \( i = \sqrt{-1} \), is
A. \( \frac{1}{3}\left[n - \frac{1}{9}\left(1 - \frac{1}{10^{n}}\right)\right] \)
9.
If 1, \( \omega \), \( \omega^{2} \) are the cube roots of unity, then \( (1 + \omega)(1 + \omega^{2})(1 + \omega^{3})(1 + \omega + \omega^{2}) \) is equal to
