Greatest Integer Function

Q. Simplify: $3^{-2}\times {81}^{\frac{3}{4}}÷{729}^{-\frac{1}{3}}$

Q. Find the cardinal number for a set $A=\left\{\right(x:x=5n,n\in W,n<4\}$ . [2 Marks]

Q. Mr. Numbers, a mathematician, has been challenged by a rival mathematician to find the sum of a series that is infinite. If the series progresses as given, calculate its sum.

1. $\frac{1}{2}$
2. $1$
3. $\frac{2}{3}$
4. $\frac{3}{2}$

Q. Find the whole number such that four times the number subtracted from three times the square of the number makes 15.

Q. Solve the following equations.
$\frac{3^x+3-x}{3^x-3-x}=2.$

Q. State whether the following statements are true or false.
If $a>b,$ then $a+c>b+c$
Where a, b, c and d are real numbers and c $\ne 0$.

1. True
2. False