CMAT Logarithms, Surds and Indices Questions

If $$5^{a} = 9^{b} = 2045$$, then the value of $$\frac{ab}{a + b}$$ = _____.

Arrange the following numbers in increasing order :
A. $$\sqrt{59} - \sqrt{51}$$
B. $$\sqrt{37} - \sqrt{29}$$
C. $$\sqrt{87} - \sqrt{79}$$
D. $$\sqrt{79} - \sqrt{71}$$
Choose the correct answer from the options given below:

Given below are two statements:
Statement I: $$(243)^{0.16} \times (9)^{0.1} = 0.3$$
Statement II: If $$3.105 \times 10^{P} = 0.00239 + 0.000715$$, then $$P = -3$$
In the light of the above statements choose the most appropriate answer from the options given below:

If x = $$\sqrt[6]{5}$$  and y = $$\sqrt[5]{4}$$, Which of the following is true?

If a and b are positive real numbers and $$a * b$$ denotes $$\sqrt{a \times b}$$, what is the value of 8 * (4 * 16)?

Find the value of $$\sqrt{\frac{2 + \sqrt3}{2 - \sqrt3}}$$

Correct to three places of decimal.