Question
A set which does not have even single element is called a _________ set.

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The equation of the hyperbola with vertices at $(0,\pm6)$ and eccentricity $\frac{5}{3}$ is ___________ and its foci are ___________.
If the seventh terms from the beginning and the end in the expansion of $\Big(3\sqrt{2}+\frac{1}{3\sqrt{3}}\Big)^\text{n}$ are equal, then n equals _____________.
[Hint: $\text{T}_7=\text{T}_{\text{n}-7+2}\Rightarrow\ ^\text{n}\text{C}_6\Big(2^\frac{1}{3}\Big)^{\text{n}-6}\bigg(\frac{1}{3^\frac{1}{3}}\bigg)^6$ $=\ ^\text{n}\text{C}_{\text{n}-6}\Big(2^\frac{1}{3}\Big)^6\bigg(\frac{1}{3^\frac{1}{3}}\bigg)^{\text{n}-6}$
$\Rightarrow\Big(2^\frac{1}{3}\Big)^{\text{n}-12}=\bigg(\frac{1}{3^{\frac{1}{3}}}\bigg)^{\text{n}-12}\Rightarrow$ only problem when $\text{n}-12=0\Rightarrow\text{n}=12]$
A _________ collection of objects is called a set.
Data is divided into two types - (i) ____________ (ii) ____________.
Fill in the blanks.
$\arg(\text{z})+\arg\bar{\text{z}}(\bar{\text{z}}\neq0)\text{ is}$ _________.
$\lim _{x \rightarrow a} \frac{x^n-a^n}{x-a}=$ _________.
If $\tan\text{A}=\frac{1-\cos\text{B}}{\sin\text{B}},$ then $\tan2\text{A}=$ _______.
Fill in the Blank.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
[Hint: Number of ways of arranging 6 consonants of which two are alike is $\frac{6!}{2!}$ and number of ways of arranging vowels 
$=\ ^7\text{P}_6\times\frac{1}{3!}\times\frac{1}{2!}.$ ]
If x > -5 then 4x .....-20.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
[Hint: Number of ways of arranging 6 consonants of which two are alike is $\frac{6!}{2!}$ and number of ways of arranging vowels $=\ ^7\text{P}_6\times\frac{1}{3!}\times\frac{1}{2!}.$ ]