MCQ
The argument of every complex number is:
- ADouble valued
- BSingle valued
- CMany valued
- DTriple valued
Solutions:
z = x + iy
amplitude $=\tan^{-1}\frac{\text{y}}{\text{x}}$
⇒ amplitude $=\theta\pm2\text{k}\pi$ where $\theta\in[-\pi,\pi]\ \forall\text{k}\in\text{R}$
since $\text{k}\in\text{R}$
⇒ Amplitude of any complex number is many valued.
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If equation of line is y = 5x + 10 then find the value of x-intercept made by the line:
$\lim\limits_{\text{x} \rightarrow0}\frac{\text{x}^{\text{m}}-1}{\text{x}^{\text{n}}-1}$ is equal to:
$1$
$\frac{\text{m}}{\text{n}}$
$\frac{-\text{m}}{\text{n}}$
$\text{m}^{2}\text{n}^{2}$
The middle term in the expansion of $\Big(\frac{2\text{x}}{3}=\frac{3}{2\text{x}^{2}}\Big)^{2\text{n}}$ is:
${^\text{2n}}\text{C}_{\text{n}}$
$(-1)\ {^\text{2n}}\text{C}_{\text{n}}\ \text{x}^{-\text{n}}$
${^\text{2n}}\text{C}_{\text{n}}\ \text{x}^{-\text{n}}$
None of these.
In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 read both. Then the number of persons who read neither is,
Two dice are thrown:
P is the event that the sum of the scores on the uppermost faces is a multiple of 6.
Q is the event that the sum of the scores on the uppermost faces is at least 10.
R is the event that same scores on both dice.
Which of the following pairs is mutually exclusive?